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Alnaas, Waled. "Nonlinear finite element analysis of quasi-brittle materials." Thesis, Cardiff University, 2016. http://orca.cf.ac.uk/93465/.
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The development of robust solution schemes for the nonlinear finite element analysis of quasi-brittle materials has been a challenging undertaking, due mainly to the stability and convergence difficulties associated with strain-softening materials. The work described in this thesis addresses this issue by proposing a new method for improving the robustness and convergence characteristics of a finite element damage model. In this method, a smooth unloading-reloading function is employed to compute an approximate tangent matrix in an incremental iterative Newton type solution procedure. The new method is named ‘the smooth unloading-reloading’ (SUR) method. A range of examples, based on a set of idealised quasi-brittle specimens, are used to assess the performance of the SUR method. The results from these example analyses show that the proposed approach is numerically robust, effective and results in considerable savings relative to solutions obtained with a reference secant model. Three acceleration approaches are also proposed in this thesis to further improve the convergence properties of the new SUR method. The first acceleration approach, named ‘the predictive-SUR method’, predicts a converged value of a damage evolution variable using an extrapolation in semi-log space. The second proposed method is designated ‘the fixing approach’, in which a damage evolution parameter is updated from the last converged step in Stage-1 iterations and then fixed in Stage-2 iterations. The third acceleration technique employs ‘a slack tolerance’ at key stages in a computation. The improvement of the convergence properties of the SUR method, when the proposed acceleration approaches are introduced, is illustrated using a series of example computations based on the analysis of a range of plain and reinforced concrete structural elements. In addition, a new element with an embedded strong discontinuity is proposed for simulating cracks in quasi-brittle structures. The new formulation is applied to quadrilateral elements and exploited to simulate mode-I, mode-II and mixed mode fracture. The interface element approach and the smeared crack approach are used as reference methods. The results from a series of examples show that the new proposed embedded strong discontinuity approach is both effective and accurate.
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Mühlich, Uwe. "Generalised continuum approach for modelling quasi-brittle failure." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-137217.
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A proper description of quasi-brittle failure within the frame of continuum Mechanics can only be achieved by models based on so-called generalised continua. This thesis focuses on a strain gradient generalised continuum and provides a specific methodology to derive corresponding models which account for the essential features of quasi-brittle failure. This methodology is discussed by means of four peer-reviewed journal articles. Furthermore, an extensive overview of the state of the art in the field of generalised continua is given at the beginning of the thesis. This overview discusses phenomenological extensions of standard Continuum Mechanics towards generalised continua together with corresponding homogenisation strategies for materials with periodic or random microstructureEine geeignete, kontinuumsmechanische Beschreibung quasi-spröden Versagens ist nur unter Verwendung verallgemeinerter Kontinuumstheorien möglich. In dieser Habilitationsschrift stehen sogenannte Gradientenkontinua im Vordergrund. Für diese wird eine Methodik vorgeschlagen, welche die Herleitung von Modellen erlaubt, die in der Lage sind, quasi-sprödes Versagen adäquat abzubilden. Diese Methodik wird anhand von vier Publikationen dargestellt und diskutiert. Ein umfangreicher Überblick über den Stand der Forschung auf dem Gebiet der veralgemeinerten Kontinuumstheorien wird am Anfang der Habilitationschrift gegeben. Dabei werden neben phänomenologischen Ansätzen zur Ableitung verallgemeinerter Kontinuumstheorien auch die entsprechenden Homogenisierungskonzepte dargestellt. Letztere werden für Materialien mit periodischer Mikrostruktur und für Materialien mit zufälliger Mikrostruktur diskutiert
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Narayan, Sooraj. "A gradient-damage theory for quasi brittle fracture." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/122236.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2019Cataloged from PDF version of thesis.
Includes bibliographical references (pages 73-77).
Phase-field modeling of brittle fracture of linear elastic solids has been the subject of several studies in the past 25 years. An attractive feature of this approach to model fracture is its seamless ability to simulate the complicated fracture processes of nucleation, propagation, branching and merging of cracks in arbitrary geometries. While most existing models have focussed on fracture of "ideal brittle" materials, we consider fracture of "quasi-brittle" materials. The material is considered to be quasi-brittle in the sense that it does not lose its entire load-carrying capacity at the onset of damage. Instead there is a gradual degradation of the strength of the material, which is the result of microscale decohesion/damage micromechanisms. In this thesis we discuss the formulation of our gradient-damage theory for quasi-brittle fracture using the virtual-power method. The macro- and microforce balances, obtained from the virtual power approach, together with a standard free-energy imbalance law under isothermal conditions, when supplemented with a set of thermodynamically-consistent constitutive equations will provide the governing equations for our theory. We have specialized our general theory to formulate a simple continuum model for fracture of concrete - a quasi-brittle material of vast importance. We have numerically implemented our theory in a finite element program, and simulated numerical examples which show the ability of the simulation capability to reproduce the macroscopic characteristics of the failure of concrete in several technically relevant geometries reported in the literature..
by Sooraj Narayan.
S.M.
S.M. Massachusetts Institute of Technology, Department of Mechanical Engineering
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Xenos, Dimitrios. "Nonlocal modelling of fracture in heterogeneous quasi-brittle materials." Thesis, University of Glasgow, 2015. http://theses.gla.ac.uk/6515/.
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Integral-type nonlocal models provide a mesh-independent description of fracture in quasi-brittle materials. According to these constitutive models, the stress at a point is evaluated by a weighted average of the variable describing the state of the material in the vicinity of this point. The weights of the material points depend on a model parameter, called interaction radius, that controls the size of the final failure zones. The objective of the present thesis is to develop nonlocal models, that can provide a realistic description of failure in quasi-brittle materials. In particular, it is aimed to identify a realistic approach to take into account boundaries. Furthermore, a strategy to calibrate the nonlocal radius is developed. It is also required to demonstrate that the nonlocal models can describe fracture in reinforced concrete structures mesh-independently. The performance of different nonlocal models in analysing boundaries is investigated. Nonlocal damage models with different averaging schemes as well as nonlocal and overnonlocal damage-plasticity models are applied to analyse failure in beams subjected to three-point bending. The original formulation of nonlocal averaging and the overnonlocal damage-plasticity model lead to excessive energy dissipation close to boundaries compared to meso-scale analysis results. The spurious energy dissipation is reduced in the analyses with the modified averaging schemes. A new calibration strategy to determine the interaction radius is proposed based on the final experimental fracture patterns. The main assumption is that the majority of energy is dissipated in a localised rough crack and is validated based on meso-scale analyses results. The potential of the calibration strategy was shown by applying it to calibrate a nonlocal damage model based on the experimental fracture surface and load-displacement curve of a beam subjected to three-point bending. Furthermore, a nonlocal extension of the damage-plasticity model CDPM2 is applied in the analyses of a reinforced concrete beam and a column. These experiments were selected because both localised and distributed cracking are experimentally observed and the material points are subjected to various stress states. It was illustrated that nonlocal models describe failure in reinforced concrete mesh-independently.
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Brooks, Zenzile (Zenzile Z. ). "Fracture process zone : microstructure and nanomechanics in quasi-brittle materials." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82831.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Civil and Environmental Engineering, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 343-355).
Cracks begin (and end) at a crack tip; the "Fracture Process Zone" (FPZ) is a region of damage around the crack tip. The context of this research is the FPZ in quasi-brittle materials, which is characterized by cracking at various scales. This study focuses on crack propagation and FPZ development at a fundamental material scale: the scale of the grain. With regard to the FPZ, the study seeks to understand how the FPZ develops and manifests in quasi-brittle material, what the physical and mechanical structure of the FPZ is, and how pre-existing material microstructure influences the developed FPZ. The attainment of several research objectives marks the course of the investigation: the development of a multi-disciplinary technique to assess both intact and FPZ regions of quasi-brittle material, the assessment of the fundamental properties (microstructure, small-scale mechanical properties) of intact and FPZ quasi-brittle material, and a conceptual model of FPZ development in quasi-brittle material. In pursuit of these objectives, the study uses nanoindentation to probe the nanomechanical properties of the FPZ for two marbles of varying grain size, and microscopy to probe the structure of the FPZ at the grain scale. The marbles are from Carrara, Italy (typical grain size 300 m), and Danby, Vermont (typical grain size 520 m). Grids of nanoindentations and microscopy were placed within the FPZ regions of Danby and Carrara marble specimens. Both marbles exhibited lower nanomechanical properties near the crack tip and/or near the area of future wing-crack formation, i.e. the FPZ. However, the Danby marble exhibited this trend over a larger distance, and thus nanomechanically supports the increase of the FPZ with grain size. The microscopy investigations suggested increased microcracking near FPZ regions, and increased microcrack density with decreased grain size. Ultimately the study provides four contributions to the study of fracture of quasi-brittle materials: an algorithm for the automatic assessment of microcracking from ESEM micrographs, new nanomechanical information on the two marble types, validation of the use of nanomechanics as a tool for identifying damage in quasi-brittle materials, and a quantitative assessment of the role of grain size in the damage of quasi-brittle materials.
by Zenzile Brooks.
Ph.D.
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Berthier, Estelle. "Quasi-brittle failure of heterogeneous materials : damage statistics and localization." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066588/document.
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Nous proposons une nouvelle approche inspirée des modèles d'endommagement non-locaux pour décrire la ruine des matériaux quasi-fragiles désordonnés. Les hétérogénéités matériaux sont introduites à une échelle continue mésoscopique via des variations spatiales de la résistance à l'endommagement alors que le mécanisme de redistribution des contraintes est décrit à travers une fonction d'interaction que l'on peut faire varier. L'évolution spatio-temporelle de l'endommagement est déterminée à partir du principe de conservation d'énergie et caractérisée via une étude statistique des précurseurs à la rupture. Cette approche nous permet de prédire la valeur des seuils de localisation et de rupture en fonction de la nature des redistributions. A l'approche de la rupture, nous mettons également en évidence une augmentation en loi de puissance du taux d'énergie dissipée ainsi qu'une longueur de corrélation, supportant l'interprétation de la rupture quasi-fragile comme un phénomène critique. En effet, nous démontrons que notre model d'endommagement s'apparente à la loi d'évolution d'une interface élastique évoluant dans un milieu désordonné. Cette analogie nous permet d'identifier les paramètres d'ordre et de contrôle de cette transition critique et d'expliquer les invariances d'échelle des fluctuations dans la limite champ moyen. Enfin, nous appliquons ces concepts théoriques à travers l'étude expérimentale de la compression d'un empilement bidimensionnel de cylindres élastiques. Notre approche permet de décrire de façon quantitative la réponse mécanique non-linéaire du matériau, et en particulier la statistique des précurseurs ainsi que la localisation des déformationsWe propose a novel approach inspired from non-local damage continuum mechanics to describe damage evolution and quasi-brittle failure of disordered solids. Heterogeneities are introduced at a mesoscopic continuous scale through spatial variations of the material resistance to damage. The central role played by the load redistribution during damage growth is analyzed by varying the interaction function used in the non-local model formulation. The spatio-temporal evolution of the damage field is obtained from energy conservation arguments, so that the formulation is thermodynamically consistent. We analytically determine the onsets of localization and failure that appear controlled by the redistribution function. Damage spreading is characterized through a complete statistical analysis of the spatio-temporal organization of the precursors to failure. The power law increase of the rate of energy dissipated by damage and an extracted correlation length close to failure supports the interpretation of quasi-brittle failure as a critical phenomena. Indeed, we establish a connection between our damage model and the evolution law of an elastic interface driven in a disordered medium. It allows to identify the order and control parameters of the critical transition, and capture the scale-free statistical properties of the precursors within the mean field limit. Finally, we experimentally investigate the coaction of localized dissipative events and elastic redistributions in disordered media via compression experiments of two-dimensional arrays of hollow soft cylinders. Our experimental observations show a quantitative agreement with the predictions derived following our approach
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Kourepinis, Dimitrios. "Higher-order discontinuous modelling of fracturing in quasi-brittle materials." Thesis, Connect to e-thesis, 2008. http://theses.gla.ac.uk/370/.
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Thesis (Ph.D.) - University of Glasgow, 2008.Ph.D. thesis submitted to the Department of Civil Engineering, Faculty of Engineering, University of Glasgow, 2008. Includes bibliographical references. Print version also available.
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Kabeel, Abdallah Mahmoud Bayoumi. "Nominal strength and size effect of quasi-brittle structures with holes." Doctoral thesis, Universitat de Girona, 2015. http://hdl.handle.net/10803/289985.
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The main contribution of this work is to introduce analytical models able to create simple design charts that would allow designers to quickly determine the strength of quasi-brittle structures containing circular holes. Cohesive Zone Models are an excellent tool to model quasi-brittle structures with holes in which a large failure process zone is confined in a plane. Also, the CZM is able to predict the effect of the structure size on its strength. Moreover, it is one of the few models (or the only model) that takes into account the material cohesive law explicitly. Therefore, most of the presented models in this work are based on the cohesive zone model.La principal contribució d'aquest treball és la dʼintroduïr un model analític capaç de generar diagrames de disseny que permeten obtenir la resistència nominal dʼestructures quasi-fràgils que continguin forats. Els models de zona cohesiva permeten predir la resistencia dʼestructures amb forats formades de materials quasi-fràgils amb una gran zona de procés de fallada confinada en un pla. Aquests models també són capaços de predir lʼefecte de la mida de lʼestructura en la resistència nominal. A mès els models de zona cohesiva són un dels pocs (o els únics) que consideren dʼuna manera explítica la llei cohesiva en la seva formulació. Per aquestes raons, la majoria de resultats presentats es basen en els models de zona cohesiva.
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Klerck, Paul Alexander. "The finite element modelling of discrete fracture in quasi-brittle materials." Thesis, Swansea University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.539299.
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An effective methodology for discrete fracture in quasi-brittle material is presented within an explicit finite discrete element framework. Simple pragmatic models are envisaged that reflect the data deficiency of the quasi-brittle material and recover the observed physical response within engineering accuracy. Phenomenological strain-softening constitutive models are adopted for the modelling of micromechanical processes in an average sense. An extensional basis for fracture is assumed in both tensile and compressive stress fields, with only the mechanism with which inelastic strain is realised differing between the two stress states. To overcome the mesh dependence introduced by local softening constitutive relationships, the socalled localisation limiters are adopted in the form of the tensile crack band, nonlocal and viscous smeared crack models. Effective localisation lengthscales introduced by these regularisation methods ensure mesh objective failure localisation a priori to discrete crack insertion. A nonlocal map of failure indicators initiates fracture, with discrete cracks inserted into the finite element continuum by the splitting of the discretisation. An isotropic, non-associative Mohr-Coulomb model is derived in principal stress space as a first order approximation to the quasi-brittle response in compression. A model for discrete fracture in tensile and compressive stress fields is proposed, defined by a composite yield surface consisting of the fully anisotropic rotating crack band model coupled with the isotropic, non-associative Mohr-Coulomb model. The novel inclusion of an explicit coupling between the extensional inelastic dilation strain accrued during compressive failure and tensile strength degradation in the dilation directions permits the realisation of discrete fracturing in purely compressive stress fields. The so-called continuum-discrete transition introduces additional degrees of freedom into quasi-brittle systems and permits large deformation to be realised through the process of cataclastic flow. This advancement is considered significant and necessary in the recovery of the observed quasi-brittle response. The effectiveness of the proposed constitutive fracture models is verified by application to a number of physical quasi-brittle fracture systems, including borehole breakout, fracturing around excavations, strip punch tests, dynamic spalling and anchor pullout tests, amongst others.
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Wang, Xiaofeng. "Computational technology for damage and failure analysis of quasi-brittle materials." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/computational-technology-for-damage-and-failure-analysis-of-quasibrittle-materials(a7c91eb6-5058-4e73-95de-b2f3efd645d2).html.
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The thesis presents the development and validation of novel computational technology for modelling and analysis of damage and failure in quasi-brittle materials. The technology is demonstrated mostly on concrete, which is the most widely used quasi-brittle material exhibiting non-linear behaviour. Original algorithms and procedures for generating two-dimensional (2D) and three-dimensional (3D) heterogeneous material samples are developed, in which the mesoscale features of concrete, such as shape, size, volume fraction and spatial distribution of inclusions and pores/voids are randomised. Firstly, zero-thickness cohesive interface elements with softening traction-separation relations are pre-inserted within solid element meshes to simulate complex crack initiation and propagation. Monte Carlo simulations (MCS) of 2D and 3D uniaxial tension tests are carried out to investigate the effects of key mesoscale features on the fracture patterns and load-carrying capacities. Size effect in 2D concrete is then investigated by finite element analyses of meso-structural models of specimens with increasing sizes. Secondly, a 3D meso-structural damage-plasticity model for damage and failure analysis of concrete is developed and applied in tension and compression. A new scheme for identifying interfacial transition zones (ITZs) in concrete is presented, whereby ITZs are modelled by very thin layers of solid finite elements with damage-plasticity constitutive relations. Finally, a new coupled method named non-matching scaled boundary finite element-finite element coupled method is proposed to simulate crack propagation problems based on the linear elastic fracture mechanics. It combines the advantage of the scaled boundary finite element method in modelling crack propagation and also preserves the flexibility of the finite element method in re-meshing. The efficiency and effectiveness of the developed computational technology is demonstrated by simulations of crack initiation and propagation problems.
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Mercatoris, Benoît. "Multi-scale modelling of shell failure for periodic quasi-brittle materials." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210194.
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In a context of restoration of historical masonry structures, it is crucial to properly estimate the residual strength and the potential structural failure modes in order to assess the safety of buildings. Due to its mesostructure and the quasi-brittle nature of its constituents, masonry presents preferential damage orientations, strongly localised failure modes and damage-induced anisotropy, which are complex to incorporate in structural computations. Furthermore, masonry structures are generally subjected to complex loading processes including both in-plane and out-of-plane loads which considerably influence the potential failure mechanisms. As a consequence, both the membrane and the flexural behaviours of masonry walls have to be taken into account for a proper estimation of the structural stability.
Macrosopic models used in structural computations are based on phenomenological laws including a set of parameters which characterises the average behaviour of the material. These parameters need to be identified through experimental tests, which can become costly due to the complexity of the behaviour particularly when cracks appear. The existing macroscopic models are consequently restricted to particular assumptions. Other models based on a detailed mesoscopic description are used to estimate the strength of masonry and its behaviour with failure. This is motivated by the fact that the behaviour of each constituent is a priori easier to identify than the global structural response. These mesoscopic models can however rapidly become unaffordable in terms of computational cost for the case of large-scale three-dimensional structures.
In order to keep the accuracy of the mesoscopic modelling with a more affordable computational effort for large-scale structures, a multi-scale framework using computational homogenisation is developed to extract the macroscopic constitutive material response from computations performed on a sample of the mesostructure, thereby allowing to bridge the gap between macroscopic and mesoscopic representations. Coarse graining methodologies for the failure of quasi-brittle heterogeneous materials have started to emerge for in-plane problems but remain largely unexplored for shell descriptions. The purpose of this study is to propose a new periodic homogenisation-based multi-scale approach for quasi-brittle thin shell failure.
For the numerical treatment of damage localisation at the structural scale, an embedded strong discontinuity approach is used to represent the collective behaviour of fine-scale cracks using average cohesive zones including mixed cracking modes and presenting evolving orientation related to fine-scale damage evolutions.
A first originality of this research work is the definition and analysis of a criterion based on the homogenisation of a fine-scale modelling to detect localisation in a shell description and determine its evolving orientation. Secondly, an enhanced continuous-discontinuous scale transition incorporating strong embedded discontinuities driven by the damaging mesostructure is proposed for the case of in-plane loaded structures. Finally, this continuous-discontinuous homogenisation scheme is extended to a shell description in order to model the localised behaviour of out-of-plane loaded structures. These multi-scale approaches for failure are applied on typical masonry wall tests and verified against three-dimensional full fine-scale computations in which all the bricks and the joints are discretised.
Doctorat en Sciences de l'ingénieur
info:eu-repo/semantics/nonPublished
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Santandrea, Mattia <1988>. "Bond behavior between fiber reinforced composites and quasi-brittle material interfaces." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amsdottorato.unibo.it/8645/1/Santandrea_Mattia_Tesi.pdf.
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The present dissertation presents an investigation of the bond behavior of newly developed fiber reinforced composite systems applied to quasi-brittle material interfaces. Direct shear tests were performed on steel reinforced polymer (SRP) and steel reinforced grout (SRG) composite strips applied to both concrete and masonry substrates. Different types of cementitious matrices and different densities of steel fiber sheets were employed. Tests were performed investigating several parameters, i.e. bonded width, bonded length, loading rate, and face to which the composite strip was applied. Failure modes and load responses were presented and discussed. It was observed that the fracture energy GF of SRP-concrete joints is independent of the composite density but varies as the composite is bonded to different faces of the concrete prism. The width effect was considered in the evaluation of the load-carrying capacity of SRP-concrete joints, while the loading rate influenced the peak load of both SRP and SRG specimens. The behavior of SRP-concrete joints was also investigated through a numerical analysis, using lattice discrete particle model (LDPM), obtaining an excellent match with the experimental results. Some concrete prisms were reinforced and tested using a geopolymer matrix that showed interesting results. Some masonry specimens were subjected to artificially weathering cycles to investigate the durability performances of SRG strips with respect to salt attack. Furthermore, monotonic compressive tests were performed on concrete columns confined with both SRP and SRG composites. Several parameters were investigated, i.e. the density of steel fiber sheets, the concrete corner condition, the overlapping length, the number of confinement layers, the scale effect, and the shape effect. Failure modes and load responses were presented and discussed. Finally, several applications of basalt-fiber reinforced cementitious matrix (B-FRCM) composites bonded to masonry substrates were showed, including full scale tests on existing masonry arches.
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Gbetchi, Kokouvi. "Multi-scale modeling of thermo-mechanical dynamic damage in quasi-brittle materials." Electronic Thesis or Diss., Université de Lorraine, 2020. http://www.theses.fr/2020LORR0049.
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Sous l’effet des impacts mécaniques, les structures constituées de matériaux fragiles peuvent être exposés à la rupture dynamique. La modélisation appropriée des mécanismes de rupture à différentes échelles d’observation et la prédiction de l’endommagement thermomécanique dans ces matériaux sont essentielles pour la conception de structures fiables. Des observations expérimentales sur la rupture dynamique des matériaux fragiles montrent des effets de refroidissement et d’échauffement importants à proximité d’une pointe de fissure. La modélisation du couplage thermomécanique lors de la rupture fragile a été entreprise, en général, sans tenir compte des aspects microstructuraux. L’objectif de cette thèse est de développer une procédure pour obtenir des lois d’endommagement thermomécaniques dans lesquelles l’évolution de l’endommagement est déduite à partir de la propagation des microfissures et des effets thermiques associés à l’échelle petite du matériau. Nous utilisons la méthode d’homogénéisation asymptotique pour obtenir la réponse macroscopique thermomécanique et d’endommagement du solide. Pour la propagation des microfissures, en mode I ou II, un critère de type Griffith est adopté. Des sources de chaleur sont considérés aux pointes des microfissures en mouvement, en lien avec l’énergie dissipée pendant la propagation. Nous considérons aussi des sources de chaleur représentant la dissipation par frottement sur les lèvres des microfissures qui se propagent en mode de cisaillement. Grâce à une analyse énergétique combinée avec la méthode d’homogénéisation nous obtenons des lois d’endommagement macroscopiques. Dans le système thermoélastique et d’endommagement ainsi obtenu, on identifie de forts couplages entre les champs mécaniques et thermiques. Le calcul des coefficients effectifs nous a permis d’étudier la réponse locale prédite par les nouveaux modèles. Cette réponse montre des effets de vitesse de déformation, de taille de la microstructure, de dégradation des propriétés thermoélastiques et des évolutions thermiques spécifiques engendrées par la microfissuration et le frottement à l’échelle petite du matériau. Dans l’équation macroscopique de la température, on retrouve des termes sources de chaleur distribuées en lien avec les dissipations d’endommagement et de frottement. L’implémentation de modèles d’endommagement dans un logiciel d’éléments finis nous a permis d’effectuer des simulations numériques à l’échelle des structures. Nous avons reproduit numériquement certains tests expérimentaux publiés dans la littérature concernant la rupture rapide d’échantillons de PMMA sous sollicitation d’impact. Les résultats des simulations obtenus sont en bon accord avec les observations expérimentalesUnder impact mechanical loadings, structural components made of brittle materials may be exposed to dynamic failure. The appropriate modeling of the failure mechanisms at different scales of observation and the prediction of the corresponding thermomechanical damage evolution in such materials is essential for structural reliability predictions. Experimental observations on dynamic failure in brittle materials report important cooling and heating effects in the vicinity of the crack tip. Theoretical modeling of the thermo-mechanical coupling during fracture have been generally undertaken without accounting for microstructural aspects. The objective of the present thesis is to develop a procedure to obtain macroscopic thermo-mechanical damage laws in which the damage evolution is deduced from the propagation of microcracks and the associated small-scale thermal effects in the material. We use the asymptotic homogenization method to obtain the macroscopic thermo-mechanical and damage response of the solid. A Griffith type criterion is assumed for microcracks propagating in modes I or II. Heat sources at the tips of microcracks are considered as a consequence of the energy dissipated during propagation. Frictional heating effects are also considered on the lips of microcracks evolving in the shear mode. An energy approach is developed in combination with the homogenization procedure to obtain macroscopic damage laws. The resulting thermoelastic and damage system involves strong couplings between mechanical and thermal fields. Computation of the effective coefficients allowed us to study the local response predicted by the new models. The macroscopic response exhibits strain-rate sensitivity, microstructural size effects, degradation of thermoelastic properties and specific thermal evolutions due to microcracking and frictional effects at the small scale. Distributed heat sources are present in the macroscopic temperature equation linked to damage and frictional dissipations. The implementation of the proposed damage models in a FEM software allowed us to perform numerical simulations at the structural level. We reproduced numerically experimental tests reported in the literature concerning the rapid failure of PMMA samples impact. The results obtained in the simulations are in good agreement with the experimental observations
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Tamayo, Mas Elena. "Continuous-discontinuous modelling for quasi-brittle failure: propagating cracks in a regularised bulk." Doctoral thesis, Universitat Politècnica de Catalunya, 2013. http://hdl.handle.net/10803/134803.
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A new strategy to describe failure of quasi-brittle materials -concrete, for example- is presented. Traditionally, numerical simulation of quasi-brittle failure has been tackled from two different points of view: damage mechanics and fracture mechanics. The former, which belongs to the family of continuous models, describes fracture as a process of strain localisation and damage growth. The latter, which falls in the family of discontinuous models, explicitly introduces displacement discontinuities. Recently, some new approaches that merge these two classical theories have been devised. Although these combined approaches allow a better characterisation of the whole failure process, there are still some issues that need to be addressed, specially regarding the model switching -from the continuous to the continuous-discontinuous strategy.
The goal of this thesis is to present a new contribution in this direction. Our main concern is to properly account for the three main difficulties that emerge when dealing with combined strategies: (1) the pathological mesh-dependence exhibited by local softening models needs to be corrected; (2) the crack-path location has to be determined and (3) the switching from the continuous to the continuous-discontinuous strategy should be done in such a way that the two approaches are energetically equivalent.
First, we extend the applicability to a two- and three-dimensional setting of an alternative approach to regularise strain-softening -where non-locality is introduced at the level of displacements rather than some internal variable. To this end, we propose new combined boundary conditions for the regularisation equation (for the smoothed displacement field). As illustrated with different two- and three-dimensional examples, these boundary conditions allow to obtain physical realistic results for the first stages of the failure process.
Second, we present a new combined formulation that allows the propagation of cracks through a regularised bulk. To define the crack-path, instead of the classical mechanical criteria, we propose to use a geometrical criterion. More specifically, given a regularised damage field D(x), the discontinuity propagates following the direction dictated by the medial axis of the isoline (or isosurface in 3D) D(x) = D*. That is, a geometric tool widely used for image analysis, computer vision applications or mesh generation purposes is used here to locate cracks. We illustrate the capabilities of this new approach by carrying out different two- and three-dimensional numerical tests.
Last, we propose a new criterion to estimate the energy not yet dissipated by the bulk when switching models, so it can be transferred to the cohesive crack. This ensures that the continuous and the continuous-discontinuous strategies are energetically equivalent. Compared to other existing techniques, we present a strategy that accounts for the different unloading branches of damage models thus better estimating the energy that has to be transferred. We illustrate the performance of this technique with one- and two-dimensional examples.En aquesta tesi, presentem una nova estratègia per tal de descriure el procés de fallida de materials quasi-fràgils, com ara el formigó. Típicament la simulació numèrica d'aquest procés s'ha dut a terme mitjançant models de dany o models de fractura. Els primers |models continus| descriuen la fractura com un procés de localització de deformacions on el dany creix i es propaga. Els models de fractura, en canvi, són models discontinus que introdueixen de manera explícita discontinuïtats en el camp de desplaçaments. Recentment s'han proposat estratègies que combinen aquestes dues teories clàssiques. Tot i que aquestes formulacions alternatives permeten simular millor el procés de fallida, encara queden alguns aspectes per aclarir, especialment pel que fa al canvi de models |de l’estratègia contínua a la discontínua. En aquesta tesi es presenta una nova estratègia contínua-discontínua. El nostre principal objectiu és proposar nous mètodes per tal de resoldre tres de les dificultats que presenten aquests models combinats: (1) solucionar la dependència patològica de la malla d'elements finits que presenten els models locals amb reblaniment; (2) determinar la trajectòria de la fissura i (3) assegurar-se que el canvi de models del continu al discontinu| es fa de manera que les dues estratègies siguin energèticament equivalents. En primer lloc, ampliem l’ús |per tal de poder simular problemes dos i tres dimensionals d'una estratègia alternativa que regularitza el reblaniment de les lleis de tensió-deformació. Aquí la no-localitat s'introdueix a nivell del camp de desplaçaments i no a través d'una variable interna com succeeix en les formulacions estàndards. Per aquest motiu, proposem noves condicions de contorn combinades per l’equació de regularització (pel camp de desplaçaments suavitzat). Tal com s'observa en diferents exemples dos i tres dimensionals, aquestes condicions permeten simular de manera físicament realista les primeres etapes del procés de fallida. En segon lloc, presentem una nova formulació combinada on les fissures es propaguen a través del medi regularitzat. Per tal de definir la trajectòria d'aquestes fissures, utilitzem un criteri geomètric, a diferència dels criteris mecànics clàssics. En particular, sigui D(x) un camp regularitzat de dany, les discontinuats es propaguen seguint la direcció marcada per l'eix mitjà de la isolínia (o isosuperfície mitjana en 3D) D(x) = D_. _Es a dir, utilitzem aquí aquesta eina geomètrica, molt emprada en d'altres aplicacions com ara l’anàlisi d'imatges, la visió artificial o la generació de malles| per tal de propagar les fissures. En aquest cas, donem també exemples dos i tres dimensionals. Finalment, proposem un nou criteri per tal d'estimar l'energia que l'estructura encara no ha dissipat en el moment en que canviem de model, per tal que pugui ser transferida a la fissura cohesiva. D'aquesta manera, s'assegura que l’estratègia contínua i la contínua-discontínua siguin energèticament equivalents. En comparació amb d'altres tècniques, aquesta estratègia té en compte les diferents branques de descàrrega dels models de dany i permet estimar de manera més precisa l'energia que cal transmetre. Per tal de mostrar aquest balanç energètic es duen a terme diferents exemples en una i dues dimensions.
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Gironacci, Elia. "Numerical modelling of crack propagation in quasi-brittle heterogeneous materials : a stochastic approach." Thesis, University of Warwick, 2018. http://wrap.warwick.ac.uk/110786/.
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Deformation and damage processes in brittle and quasi-brittle materials, such as rock and concrete, are strongly influenced by their heterogeneous nature, related to their formation processes. The presence of heterogeneities leads in fact to noticeable variation in material properties values: it is of extreme importance that a numerical model which aims to realistically, reliably reproduce with low computational effort deformation and damage processes is able to include the effect of laminations, micro-cracks, voids and other types of heterogeneities; this is even more important when a numerical models has to reproduce the propagation of fractures. This thesis presents the development of a numerical framework for the simulation of crack propagation in shale rocks and concrete which also looks at the optimisation problem in the sense of computational efficiency (defined as optimal computational time needed to obtain realistic and accurate results). The numerical framework for crack propagation developed in this thesis is a variational phase-field model based on a finite elements smeared approach, able to automatically and realistically capture crack initiation processes for a variety of loading conditions; this numerical framework is based on the relation between potential energy associated to body deformation and the energy released during fracture formation. Heterogeneity is considered in the model by means of a stochastic approach based on the assumption that some mechanical properties of heterogeneous brittle materials (such as fracture energy) follow a non-Gaussian Weibull distribution. To guarantee adequate convergence of the results, Monte Carlo Simulation (MCS) method has been used in combination with the developed stochastic methodology. A non-linear dimensionality reduction technique has been developed and incorporated in the algorithm to reduce the computational effort required for the generation of sample realisations. The methodology has been validated using experimental results from both laboratory tests on shale rocks and literature on fracture in concrete. Results show that the developed algorithm is capable of realistically reproducing the mechanical behaviour of the chosen case studies, showing an applicability to problems where cracks propagate in mode-I, mode-II and mixed-mode I and II, guaranteeing a fast generation of sampling realisations of realistic stochastic fields and convergence of results after a maximum of 130 MCS analyses. This methodology can be applied to materials with random spatially-distributed variations of mechanical properties and to those showing laminar natural formations.
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Chen, Hongniao, and 陈红鸟. "Incremental displacement collocation method for the determination of fracture properties of quasi-brittle materials." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B49799447.
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This thesis presents experimental and numerical investigations on the fracture properties of quasi-brittle materials, including mortar, concrete and graphite. Fracture toughness in terms of the critical stress intensity factor K_IC and fracture energy G_F of the materials were determined through three-point bending tests on centre-notched beams. Furthermore, full-field displacement of the beams subjected to bend was obtained using Electronic Speckle Pattern Interferometry (ESPI) technique.
In order to verify the accuracy of the displacement data measured using the ESPI technique and to obtain reliable deformation information, the displacement and strain errors induced by the rigid-body motions of the specimen were quantified. This study found that the displacement errors were negligible whereas the strain errors were notable and must be eliminated. The influence of different rigid-body motions was analyzed. It was found that the out-of-plane movement of the specimen was critical and affected considerably the accuracy of strain data. Thus the experimental setup was improved accordingly to eliminate the influence of critical rigid-body motions.
Quasi-brittle materials have a finite stress region near the crack tip, known as the fracture process zone (FPZ). The materials exhibit nonlinear fracture behaviour in the FPZ. The cohesive crack model (CCM) is widely used to characterize the nonlinear fracture behaviour of quasi-brittle materials. According to the CCM, all the nonlinear behaviours in the FPZ can be represented by a cohesive crack, and the crack propagation is controlled by the relationship between the cohesive stress and crack opening, namely, the tension softening curve (TSC). Thus an accurate estimation of the TSC is essential.
In order to determine the TSC of quasi-brittle materials, an incremental displacement collocation method (IDCM) was originally developed in this study. In the IDCM, the deformation data measured by the ESPI sensor was analyzed to obtain the crack opening displacement (COD) of the notched specimens. The experimental COD profiles together with the CCM were then integrated into a finite element model to simulate the nonlinear fracture response of the specimen. By minimizing the difference between the computed and measured displacements at selected collocation points, the cohesive stress corresponding to certain crack opening was determined. The entire TSC was constructed in a step-by-step manner following the loading steps.
The IDCM was first applied to estimate the TSC of mortar. By using the estimated TSC, the displacements of the specimen under certain loading levels were computed. By comparing the computed displacements with the experimental data, the reliability of the IDCM and the accuracy of the estimated TSC were verified.
The application of the IDCM was further extended to the determination of the TSCs of concrete and graphite. The parameters used to define the shape of the TSC of the materials were determined using regression analysis. The applicability of those parameters was verified by comparing the TSCs estimated in the present study with those derived by other researchers. Recommendations were put forward to choose appropriate tensile properties of quasi-brittle materials in the numerical simulations. Furthermore, by using the ESPI technique, fracture phenomena of quasi-brittle materials were observed and reported. Such records can greatly enhance the understanding of crack initiation, growth and arrest in quasi-brittle materials, and lead to improvements to the existing fracture models.published_or_final_version
Civil Engineering
Doctoral
Doctor of Philosophy
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Trivellato, Edoardo. "Softening damage contributions to the failure zone around deep tunnels in quasi-brittle rocks." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC1170.
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L'Agence nationale pour la gestion des déchets radioactifs (Andra) gère un laboratoire souterrain de recherche au Centre de la Meuse/Haute-Marne (CMHM), pour étudier la faisabilité d’un stockage géologique profonde dans l’argilite du Callovo-Oxfordien. Les galeries suivent les deux contraintes horizontales principales majeure et mineure. Tandis que certaines galeries possèdent un état de contraintes presque isotrope dans leur section, les autres montrent une anisotropie plus importante.Ces travaux étudient les phénomènes de rupture et fracturation à court terme, induits par l’excavation autour des ouvrages. L’endommagement fragile est considéré comme mécanisme fondamental de rupture. En effet, on retrouve dans la littérature scientifique une estimation de cette zone à partir d'un post-traitement du champ des contraintes en élasticité ou basée sur un calcul élasto-plastique. Si la première méthode ne considère pas la redistribution des contraintes due aux phénomènes dissipatifs, les approches élasto-plastiques semblent parfois insuffisantes pour expliquer la géométrie de cette zone dans certains cas des excavations en roches quasi-fragiles (Pouya et al 2016). Deux phénomènes sont étudiés, avec des simulations numériques aux Eléments Finis 2d : le développement d’une rupture diffusé, autour de la section des galeries, et l’apparition des fractures le long de l’excavation. Alors qu’une modélisation en déformations planes simule le premier cas, le deuxième est étudié en axisymétrie.Pour la première approche, deux décharges isotropes, en élasto-plasticité ou élasto-endommagement radoucissant, démontrent une instabilité globale liée au premier modèle, alors que des ruptures localisées se produisent avec le deuxième. Ceci, enrichi pour considérer les anisotropies d’élasticité, de résistance et d’endommagement du matériau, permet une bonne estimation de la zone de rupture à court terme, avec des valeurs des convergences conformes aux données, pour une galerie testée comme cas d’étude. Ensuite, la transition de la rupture du matériau de fragile à ductile, avec le confinement, est aussi prise en compte, avec les différentes conditions aux limites d’une deuxième galerie. Les zones endommagées à court terme estiment correctement la forme et l'extension de la rupture et les valeurs des convergences instantanées sont comparables aux mesures (Trivellato et al 2018).Le deuxième axe de recherche concerne la prédiction de la longueur des fractures, simplifiées comme des discontinuités finies et parallèles, ainsi que leur espacement. Numériquement, ces sont assimilées aux éléments joints (Goodman 1976). Le modèle de la fracture cohésive (Pouya et Bemani 2015) a été choisi pour ces éléments. Avec une seule discontinuité, on observe une initiation instable de la fracture, possiblement suivi par une évolution stable, d’une longueur réduite. Plusieurs séquences des joints ont été employés pour calculer la périodicité des fractures. Ces travaux ont permis aussi l’étude de différentes méthodes numériques qui simulent l’avancement d’un front d’excavation. Selon un choix précis des paramètres, on calcule des longueurs de fracturation comparables aux mesures, ainsi que la possibilité d’obtenir l’activation d’une seule fracture parmi plusieurs (Trivellato et al 2018).Ces travaux constituent une nouvelle approche de prédiction des effets du creusement sur l’argilite du Callovo-Oxfordien. Ils étudient une rupture à court terme due au comportement fragile sous faible confinement. Le mécanisme de dissipation en endommagement est intégré par les effets à la fois de l’anisotropie intrinsèque du matériau et de sa transition fragile-ductile. Les résultats obtenus par les deux axes de recherche favorisent l’utilisation de ce modèle comme complément aux études des excavations. En perspective, on peut envisager d’intégrer ces modèles avec les effets de la plasticité/fluage du matériau ainsi qu’avec la poro-élastique en comptant les effets hydrauliquesThe French National Radioactive Waste Management Agency (Andra) manages an Underground Research Laboratory (URL) at the Meuse / Haute-Marne Center to study the feasibility of a deep geological repository in the Callovo-Oxfordian claystone (COx). The galleries follow the major and minor principal stress directions. Some galleries show a quasi-isotropic stress state in their cross-section, while others show a greater anisotropy.These works study the short-term failure and fracturing phenomena induced by the underground structures’ excavation. Brittle softening damage is considered as a fundamental failure mechanism. The major part of scientific literature reports an estimation of this area from an elastic post-treatment or based on elastic-plastic analyses. If the first method does not consider the stresses’ redistribution due to dissipative phenomena, elastic-plastic approaches sometimes seem insufficient to explain the geometry of these zones in some cases of deep excavations in quasi-brittle rocks (Pouya et al 2016). Two phenomena are studied, through numerical simulations by 2d Finite Elements: the development of a diffused failures, around the galleries’ cross-section, and the fractures occurrence at their perimeter, along the excavation. While a plane strain analysis is suitable for the first problem, the second one is studied in axial symmetry.For the first part of the research, two isotropic unloading processes, in softening elastic-plasticity or elastic-damage, reproduce a global instability related to the first modelling, whereas localized failure occurs with the second one. The latter model, upgraded to consider intrinsic anisotropies in terms of elasticity, resistance and damage dissipative law, allows a consistent estimation of the short-term failure zone, with values of convergences in accordance to the data, for a gallery considered as a case study. Then, the transition of material’s failure from a brittle to ductile behaviour, with the confinement, is also simulated, according to different boundary conditions of a second gallery. The short-term damaged zones well reproduce the shape and extension of failure systems and the values of the instantaneous convergences are comparable to in-situ measurements (Trivellato et al 2018).The second research axis concerns the elongation and mutual spacing of fractures, simplified as a system of finite and parallel discontinuities. Numerically, they are assimilated to joint elements (Goodman 1976). The cohesive fracture model, based on damage, (Pouya and Bemani 2015) was chosen for these elements. In presence of a single potential fracture, an unstable initiation is observed, possibly followed by a stable evolution, of reduced length. Then, models with a sequences of several joints were used to analyse the fracture periodicity. This work also allowed the study of different numerical techniques simulating the advancement of an excavation front. According to a precise choice of parameters, fractures’ lengths are comparable to the geological and geophysical surveys. Similarly, the activation of one potential fracture among different discontinuities was calculated, showing a periodic occurrence (Trivellato et al 2018).This dissertation constitutes a new approach to reproduce the immediate effects of deep excavations in the Callovo-Oxfordian claystone. They study a short-term failure due to the material’s brittleness, under low confinement. Damage is adopted as the only dissipation mechanism and is integrated by the effects of material’s intrinsic anisotropy as well as its brittle-ductile post-peak transition. Results obtained by every research axis appear favourable to employ these models as complements to excavation studies. In perspective, the integration of plasticity / creep effects, as well as a poro-elastic framework accounting for hydraulic effects, may be considered
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Mühlich, Uwe [Verfasser], Meinhard [Gutachter] Kuna, Samuel [Gutachter] Forest, and Reinhold [Gutachter] Kienzler. "Generalised continuum approach for modelling quasi-brittle failure / Uwe Mühlich ; Gutachter: Meinhard Kuna, Samuel Forest, Reinhold Kienzler." Freiberg : Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2014. http://d-nb.info/1220837547/34.
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Carrara, Pietro [Verfasser], and H. [Akademischer Betreuer] Budelmann. "Interface behavior of fiber reinforced polymer composites externally glued to quasi-brittle substrates / Pietro Carrara ; Betreuer: H. Budelmann." Braunschweig : Technische Universität Braunschweig, 2014. http://d-nb.info/1175820091/34.
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Luther, Torsten Verfasser], and Carsten [Akademischer Betreuer] [Könke. "Adaptation of atomistic and continuum methods for multiscale simulation of quasi-brittle intergranular damage / Torsten Luther ; Betreuer: Carsten Könke." Weimar : Institut für Strukturmechanik, 2010. http://d-nb.info/1115806416/34.
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Sicsic, Paul. "Modeling and simulation of the nucleation and propagation of damage in quasi-brittle materials: Contribution of the variational approach." Palaiseau, Ecole polytechnique, 2013. http://pastel.archives-ouvertes.fr/docs/00/90/33/60/PDF/13_these_sicsic.pdf.
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Cette thèse explore l'utilisation de modèles d'endommagement pour prédire la nucléation et la propagation de la rupture de manière cohérente. Les résultats sont basés sur la donnée d'une énergie, qui définit le matériau, et d'une loi d'évolution construite sur un principe de stabilité, de conservation d'énergie et d'irreversibilité. Dans un premier temps, on étudie l'initiation de fissures dans une structure contenant un coin. Le chargement limite se réduit à trois composantes : un facteur d'échelle, une composante géométrique fonction de l'angle, et une composante propre au modèle. Ces modèles donnent naissance à des fissures dont le profil est caractéristique et dont la largeur est de l'ordre de la longeur interne du modèle. Cette dernière étant petite devant les dimensions de la structure, dans le cadre d'une séparation d'échelles et en utilisant un principe de minimum local, on montre que le modèle d'endommagement considéré converge vers la loi de propagation de Griffith. Ce résultat fondamental étend ceux existants, basés sur la minimisation globale, mais avec une base physique plus forte. Une étude approfondie donne une meilleure compréhension de la phase d'initiation dans le cas d'un choc thermique et on établit la propriété globale qu'est l'éemergence d'une solution periodique. Ces résultats s'appuient sur le cadre variationnel, les propriétées seraient probablement perdues pour un modèle d'endommagement développé dans un autre cadre. Dans un dernier temps, les résultats numériques basés sur un algorithme de minimisation alternée capturent une initiation contrôlée par la contrainte critique, ainsi que la propagation des fissures controlée par la densité d'énergie de fissuration. Des effets d'échelle en deux et trois dimensions sont mis en évidence. Les simulations sont alors confrontées à des résultats expérimentauxThis thesis explores the use of damage models to predict the onset and propagation of cracks in a coherent manner. The results are based on the definition of a bulk energy density and a stability principle. Firstly, we study the nucleation of cracks in a notched domain. The limit loading can be decomposed as the product of three stress intensity factors: a scale effect, a geometry induced factor, function of the angle of the notch, and one due to the damage model. The cracks that appear have a characteristic profile whose width is of the order of the internal length. When the latter is small in front of the dimensions of the structure, by separating scales, and using a local minimum principle, we prove that the length of these damage bands follow Griffith's law. This fundamental results extends those based on global minimization but with a sounder physical base. A thorough investigation of the thermal shock problem leads to a better understanding of the nucleation of cracks. Especially the global property of crack periodicity is exhibited. These results are based on the variational approach and the properties would probably be lost for models developed in an other framework. Finally, numerical results based on an alternate minimization algorithm are established. The nucleation phase is controlled by the critical stress whereas the propagation is governed by the toughness. Size effects in two and three dimensions are captured. These numerical simulations are then confronted to experimental results
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Baietti, Giulia <1991>. "Mode-I fracture parameters of quasi-brittle materials: direct evaluation using DIC and relationship with Mode-II interfacial parameters." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amsdottorato.unibo.it/9788/1/baietti_giulia_tesi.pdf.
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The objective of this thesis is the investigation of the Mode-I fracture mechanics parameters of quasi-brittle materials to shed light onto the influence of the width and size of the specimen on the fracture response of notched beams. To further the knowledge on the fracture process, 3D digital image correlation (DIC) was employed. A new method is proposed to determine experimentally the critical value of the crack opening, which is then used to determine the size of the fracture process zone (FPZ). In addition, the Mode-I fracture mechanics parameters are compared with the Mode-II interfacial properties of composites materials that feature as matrices the quasi-brittle materials studied in Mode-I conditions. To investigate the Mode II fracture parameters, single-lap direct shear tests are performed. Notched concrete beams with six cross-sections has been tested using a three-point bending (TPB) test set-up (Mode-I fracture mechanics). Two depths and three widths of the beam are considered. In addition to concrete beams, alkali-activated mortar beams (AAMs) that differ by the type and size of the aggregates have been tested using the same TPB set-up. Two dimensions of AAMs are considered. The load-deflection response obtained from DIC is compared with the load-deflection response obtained from the readings of two linear variable displacement transformers (LVDT). Load responses, peak loads, strain profiles along the ligament from DIC, fracture energy and failure modes of TPB tests are discussed. The Mode-II problem is investigated by testing steel reinforced grout (SRG) composites bonded to masonry and concrete elements under single-lap direct shear tests. Two types of anchorage systems are proposed for SRG reinforced masonry and concrete element to study their effectiveness. An indirect method is proposed to find the interfacial properties, compare them with the Mode-I fracture properties of the matrix and to model the effect of the anchorage.
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Ribeiro, Nogueira Breno. "Non-local damage mechanics with evolving interactions for modeling quasi-brittle materials : anisotropic damage and gradient-enhanced Eikonal approach." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPAST072.
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La prévision de la nucléation et de la propagation des fissures est essentielle pour décrire la réponse des structures dans des conditions de chargement complexes. On observe l'apparition de microfissures diffuses avant la formation d'une macrofissure. Dans le cas de matériaux quasi-fragiles, on observe un comportement adoucissant lié à une perte progressive de rigidité. D'un point de vue thermodynamique, ce comportement peut être décrit de manière continue par une variable d'état d'endommagement. Cependant, les modèles d'endommagement locaux conduisent inévitablement à un problème aux valeurs limites mal posé. Dans un contexte d'éléments finis, les résultats numériques dépendent donc du maillage. Les modèles d'endommagement non locaux permettent d'obtenir des résultats indépendants du maillage en introduisant des interactions de voisinage par le biais d'une longueur interne. Les approches non locales classiques considèrent des interactions isotropes et constantes, ce qui ne permet pas de reproduire correctement l'ensemble du processus de dégradation. Des approches prenant en compte des interactions évolutives existent et peuvent mieux décrire le comportement de la fissuration.Cette thèse vise à fournir des aspects théoriques et numériques pour le développement de modèles d'endommagement à gradient implicite avec interactions évolutives. Tout d'abord, les modèles non-locaux sont étudiés et comparés en analysant les effets de bord et la diffusion de l'endommagement dans un essai d'écaillage unidimensionnel en dynamique explicite.L'approche non-locale Eikonale est étudiée, où les interactions évolutives sont considérées par le biais d'une métrique riemannienne dépendante de l'endommagement. La version avec gradient de ce modèle (ENLG) est ensuite dérivée d'un cadre micromorphe basé sur la géométrie différentielle, conduisant à une expression de dissipation respectant au second principe de la thermodynamique. Une formulation variationnelle simplifiée est développée pour évaluer les capacités du modèle dans des simulations numériques quasi-statiques bidimensionnelles avec endommagement isotrope. Enfin, la régularisation ENLG est couplée à un modèle d'endommagement anisotrope prenant en compte un tenseur d'endommagement de second ordre. L'anisotropie induite est naturellement prise en compte dans le comportement et dans les interactions évolutives. Des simulations en deux et trois dimensions sont étudiées et comparées aux résultats expérimentaux existants dans la littérature, tout en soulignant les aspects numériques associés. Une analyse détaillée décrit les avantages de la prise en compte de l'endommagement anisotrope et des interactions anisotropes dépendantes de l'endommagementPredicting the cracking nucleation and propagation is essential to describe structural response under complex loading conditions. Diffuse micro-cracks are observed to appear before coalescing into a macro-crack. In the case of quasi-brittle materials, strain-softening behavior is observed and is related to a progressive loss of stiffness. From a thermodynamics viewpoint, this can be described in a continuum way by a damage state variable.However, local continuum damage mechanics models inevitably lead to an ill-posed rate equilibrium problem. In a finite element context, numerical results are, therefore, mesh-dependent. Non-local damage models can recover mesh-independent results by introducing neighborhood interactions through an internal length. Classic non-local approaches consider isotropic and constant interactions, which cannot reproduce the entire degradation process appropriately. Evolving interaction approaches exist and may better describe the cracking behavior. This thesis aims to provide theoretical and numerical aspects for developing evolving interactions gradient-enhanced damage models. Firstly, non-local models are studied and compared by analyzing boundary effects and damage diffusion in a one-dimensional explicit dynamics spalling test.The Eikonal non-local approach is given attention, where evolving interactions are considered through a damage-dependent Riemannian metric. The gradient-enhanced version of this model (ENLG) is then derived from a differential geometry-based micromorphic framework, leading to a dissipation expression fulfilling thermodynamics second principle. A simplified variational formulation is developed to evaluate the model's capabilities in two-dimensional isotropic damage quasi-static numerical simulations. Finally, the ENLG regularization is coupled to an anisotropic damage model considering a second-order damage tensor. Damage-induced anisotropy is naturally considered in the behavior and the evolving interactions. Simulations in two and three-dimensional contexts are studied and compared to existing experimental results from the literature while highlighting the numerical aspects involved. A detailed analysis describes the advantages of considering anisotropic damage and damage-dependent anisotropic interactions
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Albuerne, Alejandra. "Seismic collapse of vaulted structures : unreinforced quasi-brittle materials and the case study of the Basilica of Maxentius in Rome." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:380ad3b8-c973-4184-8f67-9d6c785760c9.
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Seismic loading is one of the biggest threats to the stability of masonry architecture is many parts of the world. Buildings that have stood for centuries under their self-weight, could suffer collapse in an unprecedented seismic event. The current research aims at furthering our understanding of how masonry vaulted buildings behave in earthquakes. Our ability to anticipate damages or collapse of existing structures will depend on this understanding. Based on the study of ancient Roman buildings, this work focuses on types of masonry that exhibit cohesive behaviour due to the presence of strong mortar or to the interlocking between the components of the material matrix. Roman concrete is one of those materials. The idea behind this work is to be able to base the experimental and theoretical work on real buildings, and vice-versa, to be able to relate any experimental and theoretical findings to real buildings. Hence the work has evolved around the case study of the Basilica of Maxentius in Rome. The Basilica of Maxentius is a valuable case study for the study of the seismic behaviour of vaulted structures: not only does it feature the largest barrel and cross vaults known to have been built by the Romans, but it also underwent partial collapse, believed to have been triggered by an earthquake at some unknown point in the middle ages. A detailed survey of the Basilica of Maxentius has been carried out to obtain a geometrical model of its current state; to study the deformations as a source of information for exploring the mechanical history of the structure; and to obtain a geometrical model of the original geometry of the building. The main techniques used in the survey were total station surveying and 3D photogrammetry. The foundations of the south nave of the Basilica, built over the remains of earlier ruins, were also surveyed to assess their quality and to look for potential signs of seismic damage. No clear signs of structural damage were observed on the foundations themselves, but some of the earlier remains featured clear signs of damage under the effect of lateral loads. Shaking table tests on continuous circular arches and cross vaults constructed in lime mortar, a quasi-brittle material like Roman concrete but with weaker strength, have yielded interesting results that demonstrate that the dynamic behaviour of these structures is different to that of structures made of discrete blocks. Arches collapse by forming a four-link mechanism, but the hinge position is different to that observed in block arches: hinges are placed symmetrically about the mid-span axis. Only 2 cracks formed in all arches, leading to collapse by four-link mechanisms with hinges at the 2 cracks and at the 2 supports. Hinges were observed to remain fixed at these positions during rocking. When inwards sliding of supports is possible, the first crack typically forms by mobilising a slider-crank mechanism, the final crack forming a four-link mechanism in the reversed half-cycle. It was also observed that pre-existing cracks in the arch had a very significant effect: these cracks become hinges and only 1 more crack is needed to form a four-link mechanism. The common crack at mid-span frequently found in real arches caused by spreading of the supports leads to mechanisms that require higher accelerations than a pre-existing crack offset from midspan. It is arguable that many real masonry structures will feature a degree of cohesiveness, and thus this observation opens a path for further investigations into the need to consider pre-existing cracks. The formation of cracks has been analysed using limit and quasi-static linear elastic approaches. These analyses have been unsuccessful in predicting the formation of the first crack in undamaged arches (hyperstatic arches with hinges at the supports). Conventional limit analysis cannot be used because of the quasi-brittle nature of the material, while the elastic analysis fails to capture the behaviour observed in tests. The formation of the fourth hinge in pre-cracked arches has been analysed by application of equilibrium equations alone to the three-pin statically determinate arch. Good correlation has been obtained between experimental results and this analysis. Finally, discrete element modelling code LMGC90 has been validated for analysis of dynamic behaviour of block arches, by comparison with experimental results.
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Errico, Carmine. "Determination of the influence of SRG anchors on the bond behavior of SRG/FRCM strips bonded to a quasi-brittle substrate." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019.
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The use of FRCM composites (Fiber Reinforced Cementitious Matrix) is becoming more and more widespread. The inorganic matrix guarantees many advantages, especially when dealing with masonry substrates, including a good compatibility from both a physical and a chemical point of view and the lower sensitivity to debonding phenomena at the interface.
Compared to FRP composites, which presents many data in the literature, FRCM composites must be studied in detail and research in this field has only begun in recent years. This work deals with an important problem: the realization of an anchorage system to improve the strength of composites and allow their use even in the absence of adequate development length.
In this study, the effectiveness of the anchorage system and the interaction with an externally bonded FRCM were studied on masonry columns. The columns were tested until failure condition in the Laboratory of Structural and Geotechnical Engineering (DICAM – LISG) of the University of Bologna, via del Lazzaretto 15/5, Bologna.
Test results demonstrate that the introduction of additional anchorages improves the effectiveness of the FRCM composites in terms of resistance and loading capacity.
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Shi, Yue. "Micro-mechanics-based models of monotonic and cyclic behaviors of quasi-brittle rock-like materials having an elasto-viscoplastic matrix with microcracks." Electronic Thesis or Diss., Université de Lille (2022-....), 2023. https://pepite-depot.univ-lille.fr/ToutIDP/EDENGSYS/2023/2023ULILN057.pdf.
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L'objectif principal de cette thèse est de modéliser le comportement mécanique macroscopique des géomatériaux dans des conditions de chargement instantané et dépendant du temps. Dans ce contexte, le matériau étudié est modélisé du point de vue de la microstructure en utilisant des schémas de localisation et d'homogénéisation bien adaptés. À l'échelle microscopique, on suppose que les microfissures ont une morphologie en forme de penny et qu'elles sont intégrées de manière aléatoire dans une matrice solide isotrope. Dans le cadre de la thermodynamique, deux variables internes, la déformation inélastique et les dommages induits par les microfissures, sont toutes deux classées en fonction de la microfissuration instantanée et de la microfissuration sous-critique. L'endommagement instantané est régi par une force thermodynamique conjuguée, tandis que l'endommagement dépendant du temps évolue vers l'équilibre de la microstructure. En outre, l'accent est mis sur la modélisation de la matrice solide en tant que composante de cohésion-friction. Cela nécessite l'introduction d'une nouvelle variable interne, la déformation plastique de la matrice, qui se traduit par une transition fragile-ductile plus claire dans le régime de pré-crête, en particulier sous des pressions de confinement relativement élevées. Ensuite, la matrice plastique compressible est décrite séparément par une règle d'écoulement associée et une règle d'écoulement non associée, en comparaison avec un grand nombre de résultats d'essais. Il s'avère que le modèle non associé peut bien reproduire la transition compaction-dilatation avec des nombres cycliques. Enfin, le modèle unifié est développé pour étudier le comportement à long terme en termes de viscoplasticité de la matrice. Les mécanismes de déformation sont analysés en ce qui concerne le couplage entre la viscoplasticité de la matrice et la propagation sous-critique des microfissuresThe primary objective of this thesis is to model the macroscopic mechanical behavior of geomaterials under both instantaneous and time-dependent loading conditions. In this context, the studied material is modeled from the view of microstructure using well-suited localization and homogenization schemes. At the microscopic scale, it is assumed that microcracks have a penny-shaped morphology and are randomly embedded in an isotropic solid matrix. In framework of thermodynamics, two internal variables, inelastic strain and microcrack-induced damage, are both classified in consideration of instantaneous microcracking and sub-critical microcracking. The instantaneous damage is driven by a conjugated thermodynamics force, while the time-dependent damage evolves towards microstructure equilibrium. Further, the emphasis is put on modeling the solid matrix as a cohesive-friction component. This needs to introduce a new internal variable, plastic strain of matrix, resulting in a clearer brittle-ductile transition in the pre-peak regime, especially under relative high confining pressures. Next, the plastic compressible matrix is separately described by an associated and a non-associated flow rule in comparison with a large amount of test results. It is found that the non-associated model can well reproduce the compaction-dilatation transition with cyclic numbers. Finally, the unified model is developed to investigate the long-term behavior in terms of matrix viscoplasticity. The deformation mechanisms are analyzed regarding the coupling between matrix viscoplasticity and sub-critical propagation of microcracks
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DI, BATTISTA EMANUELA. "Interpretation of fracture mechanisms in ductile and brittle materials by the Acoustic Emission Technique." Doctoral thesis, Politecnico di Torino, 2015. http://hdl.handle.net/11583/2607555.
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Nowadays, the measure of the damage phenomena inside a structure is a complex problem that requires the use of innovative Structural Health Monitoring (SHM) and non-destructive investigation methodologies. The non-destructive method based on the Acoustic Emission (AE) technique has proved highly effective, especially to predict fracture behavior that take place inside a material subjected to mechanical loading.
Objective of the research is to use the Acoustic Emission monitoring to evaluate the fracture propagation process during tensile tests, three-point bending (TPB) tests and compression tests. The most representative AE parameters have been measured by sensors in order to obtain detailed information on the wave propagation velocity, signals localization as well as on the dominant fracture mode. As a matter of fact, the waves frequency and the Rise Angle are used to discriminate the prevailing cracking mode from pure opening or sliding. Moreover, the cumulated number of AE events and their amplitude are used to compute the signal energy. For the three-point bending tests on concrete beams, the energy dissipated to create the fracture surfaces and the energy emitted and detected by the AE sensors have been compared on the basis of their cumulative value at the end of the test and their rate during the process loading, in order to investigate on their correlation.
A numerical simulation of the mechanical response of the TPB tests has been also performed on the basis of the cohesive crack model. This approach has permitted to obtain a step-by-step evaluation of the crack propagation and a more detailed analysis of the mechanical energy dissipation rate during the loading test.
In addition, a dedicated in-situ monitoring at the San Pietro - PratoNuovo gypsum quarry located in Murisengo (AL) - Italy, is started and it is still in progress, developing the application aspects of the AE technique, which has been widely studied from a theoretical and experimental point of view by some Authors in the safeguard of civil and historical buildings.
Preliminary laboratory compression tests on gypsum specimens with different slenderness (λ=0.5, λ=1, λ=2) were conducted to assess the validity and efficiency of the system in view to a permanent installation for in-situ monitoring.
Currently the quarry is subjected to a multiparameter monitoring, by the AE technique and the detection of the environmental neutron field fluctuations, in order to assess the structural stability and, at the same time, to evaluate the seismic risk of the surrounding area.
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Phan, Ngoc Anh. "Simulation of time-dependent crack propagation in a quasi-brittle material under relative humidity variations based on cohesive zone approach : application to wood." Thesis, Bordeaux, 2016. http://www.theses.fr/2016BORD0008/document.
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Cette thèse est consacrée à la simulation du comportement à la rupture de bois sous des chargements à long terme et sous des conditions d'Humidité Relatives (HR) de l'air variables. Il est connu que le bois est un matériau fortement hygroscopique, ses propriétés mécaniques et de rupture sont en effet très dépendantes de sa teneur en eau. En outre, la stabilité d'une fissure existante dans un élément structural peut être fortement influencée parles variations, en particulier brusques, d'humidité relative qui peut conduire à la rupture inattendue de l'élément.L'approche thermodynamique proposée intègre l'effet de mécanosorption dans l'expression analytique de la déformation, en découplant les déformations mécaniques et celles dues au comportement mécanosorptif du matériau. En outre, la rupture quasi-fragile du matériau boisest traduite par un modèle de zone cohésive dont les paramètres de cohésion sont fonctions de la teneur en eau afin de simuler l’effet de l'humidité sur les propriétés de rupture. Sur cette base, une formulation incrémentale permet l'intégration de l'effet des variations soudaines d’humidité relative (autrement dit, le choc hydrique) sur la zone d’élaboration(zone cohésive) en introduisant un champ de contraintes supplémentaires le long de cette zone. Fonction de la variation de HR, ce champ de contraintes supplémentaires dépend de l'état de contrainte et de l'ouverture de la fissure le long de la zone cohésive, mais également de l'humidité en pointe de fissure (matériau non endommagé). Dans l'analyse par éléments finis, un opérateur tangent algorithmique est utilisé pour résoudre le problème non linéaire en combinant le modèle de mécanosorption et le modèle de zone cohésive et en intégrant l'effet du choc hydrique.La simulation du comportement d'une éprouvette entaillée soumise à un chargement constant et à des variations cycliques de HR montre un fort couplage entre le comportement mécanosorptif et l'effet du choc hydrique HR sur la zone d’élaboration. Ce couplage entraîne une augmentation de la propagation des fissures et conduit à une fissuration plus précoce par rapport à celle obtenue à partir du modèle de mécanosorption seul ou à partir du modèle de zone cohésive en intégrant l'effet des variations soudaines de HR. En outre, le couplage entre le modèle mécanosorptif et le modèle de zone cohésive en intégrant l'effet du chochydrique montre l'intérêt d'une telle approche numérique pour décrire le comportement complexe des éléments de charpente en bois soumis à des conditions climatiques variables,comportement qui ne peut être prédit par une simple superposition des deux modélisationsThis thesis is dedicated to the simulation of the fracture behavior of wood under long-termloading and variable relative humidity conditions. Indeed, wood is well-known to be a highlyhygroscopic material in so far as its mechanical and fracture properties are very dependenton moisture. Moreover, the stability of an existent crack in a structural element can bestrongly affected by the sudden variations of relative humidity (RH) and can lead tounexpected failure of the element.The thermodynamic approach proposed in this thesis includes the mechano-sorptive effect inthe analytical expression of the deformation, by operating a decoupling of the strain in amechanical part and a mechano-sorptive part in material. Moreover, the quasi-brittle fractureof wood is here simulated from a cohesive zone model whose cohesive parameters arefunctions of the moisture in order to mimic the moisture-dependent character of the fractureproperties. On this basis, an increment formulation allows the integration of the effect ofsudden RH variations on the fracture process zone (cohesive zone) by introducing anadditional stress field along this zone. As a function of the RH variation, this additional stressfield depends on not only the stress state and the crack opening along the cohesive zone butalso the material moisture ahead of the zone (undamaged material). In the finite elementanalysis, an algorithmic tangent operator is used to solve the non-linear problem combiningmechano-sorptive model and cohesive zone model including the effect of sudden RHvariations.The simulation of a notched structural element submitted to a constant load and cyclic RHvariations exhibits a strong coupling between the mechano-sorptive behavior and the effectof the RH variations on the fracture process zone (FPZ). This coupling results in an increaseof the crack propagation kinetic and leads to a precocious failure compared to those obtainedfrom the mechano-sorptive model or from the effect of sudden RH variations on the FPZ.Moreover, the coupling between the mechano-sorptive model and the effect of sudden RHvariations on the FPZ which cannot be predicted by a simple superposition of both effects,showing the interest of such a numerical approach in order to describe the complex behaviorof wood structural elements submitted to variable climatic conditions
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Lefort, Vincent. "Un modèle lattice pour simuler la propagation de fissures sous l’effet d’une injection de fluide dans un milieu hétérogène quasi-fragile." Thesis, Pau, 2016. http://www.theses.fr/2016PAUU3011/document.
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Cette thèse vise à développer un modèle numérique de type lattice permettant de simuler la propagation de fissures sous l’effet d’une injection de fluide dans un milieu hétérogène quasi-fragile. Si la finalité de l'étude concerne l'étude de matrices rocheuses naturelles, dans les différentes parties du manuscrit détaillée ci-après et dans un souci de validation, le modèle a été régulièrement confronté à des résultats expérimentaux obtenus sur des matériaux cimentaires similaires à des roches naturelles en termes de comportements mécaniques et de transport mais présentant des hétérogénéités mieux contrôlées. La première partie du document est dédiée à l'étude du processus de fissuration caractéristique des matériaux quasi-fragiles présentant une zone d'élaboration. Un outil d'analyse statistique basé sur les fonctions de Ripley et permettant d'extraire une longueur caractéristique à partir d'un nuage de points -- lieux d'un endommagement mécanique -- et présenté. Il est ensuite utilisé dans le cadre d'essais numériques et expérimentaux de rupture par flexion 3 points sur des éprouvettes de bétons. Les résultats montrent que le modèle numérique de type lattice est capable de rendre compte à la fois du processus global de fissuration mais également du processus local de fissuration. Par ailleurs, cet outil permet également de montrer l'influence du mode de sollicitation sur le développement de l'endommagement au sein d'une structure. La deuxième partie du document présente une loi de comportement élasto-plastique endommageable représentative du comportement de joints. L'originalité du modèle réside dans le couplage entre l'endommagement sous sollicitation normale et la plasticité sous sollicitation tangentielle. Cette nouvelle loi permet de reproduire correctement des résultats d'essais de cisaillement indirects effectués sur des joints de plâtre séparant des épontes en mortier alors qu'un modèle de Mohr-Coulomb classique ne le permet pas. La troisième partie est dédiée à l'introduction d'un couplage hydromécanique complet dans le modèle lattice utilisé précédemment. Le couplage hydromécanique est introduit au travers du comportement poromécanique du milieu basé sur une description mécanique-hydraulique duale et intrinsèque du modèle lattice. La contrainte totale fait le lien entre la contrainte mécanique du lattice mécanique et la pression de pore du lattice hydraulique au travers du coefficient du Biot du milieu alors que la perméabilité locale pilotant le gradient de pression hydraulique est indexée sur les ouvertures locales de fissures estimées au travers du lattice mécanique. Les résultats obtenus par ce modèle hydro-mécanique dual ont été confrontés à des solutions analytiques données dans la littérature pour des fissures de type "bi-wings", et il est montré que les deux approches sont cohérentes pour une fissure parfaitement rectiligne. Après les différentes étapes de validation du modèle présentées dans les parties précédentes, la quatrième et dernière partie est dédiée à la simulation numérique du couplage hydromécanique sous-jacent à la propagation libre d'une fissure propageant sous l'effet d'une injection de fluide et de son interaction avec un joint rocheux naturel. Les trajets de fissuration, non maillés a priori, et les profils de pression au sein de la matrice poreuse sont obtenus et comparés en fonction de l'inclinaison du joint rocheux. Par ailleurs, le traitement statistique concernant les lieux d'endommagement développé en première partie est repris ici afin de caractériser l'évolution des longueurs de corrélation entre point s'endommageant au cours de la propagation de la fissure et de son interaction avec le joint. Il est montré que le modèle hydromécanique lattice permet de représenter différent mécanismes de ré-initiation de fissure à partir d'un joint suivant son inclinaisonThis research study aims at developing a lattice-type numerical model allowing the simulation of crack propagation under fluid injection in a quasi-brittle heterogeneous medium. This numerical tool will be used to get a better understanding of initiation and propagation conditions of cracks in rock materials presenting natural joints where the coupling between mechanical damage and fluid transfer properties are at stake. If the final goal of the study does concern natural rocks, the model has been validated by different comparisons with experimental results obtained on cementitious materials mimicking natural rocks in term of mechanical and transport behaviours but presenting heterogeneities which are better controlled. The first part of the manuscript presents a general state of the art. The second part of the manuscript is dedicated to the study of crack propagation in quasi-brittle materials where a significant fracture process zone is evolving upon failure. Only the solid phase is studied here and a statistical tool based on Ripley’s functions is adapted in order to extract a characteristic length representative of the correlations appearing between a set of point undergoing mechanical damage. This tool is then used in the context of numerical and experimental fracture tests on 3 point bending concrete beams. The results show that the lattice-type numerical model is able to capture the global fracture process – in term of force vs. crack opening mouth displacement – but also the local fracture process – in term of dissipated energy and correlation length evolution between damage points. Moreover, this statistical tool shows how the solicitation mode may influence the development of damage within a structure. The third part presents a new elasto-plastic damage constitutive law for joint modelling. The originality of the model lies in the coupling between mechanical damage under normal strain and plasticity under tangential strain. This new constitutive law is able to reproduce indirect shear experimental tests performed on mortar specimens presenting a plaster joint where a classical Mohr-Coulomb criterion fails. The fourth part is dedicated to the representation of the full hydro-mechanical coupling within the lattice-type numerical model. The hydro-mechanical coupling is introduced through a poromechanical framework based on the intrinsic and dual hydro-mechanical description of the lattice model, which is based on a "hydraulic" Voronoï tessellation and a "mechanical" Delaunay triangulation. The total stress links the mechanical stress and the pore pressure through the Biot coefficient of the medium whereas the local permeability, which drives the hydraulic pressure gradient, depends on the local crack openings. The numerical results are compared with analytical solutions from the literature for "bi-wings" shape cracks and it is shown that both approaches present similar results for a perfect straight crack. Once the lattice-model has been successfully validated within the former parts of the manuscript, its fifth and last part is dedicated to the numerical simulation of the fully hydro-mechanical coupling problem of a free crack propagation due to fluid injection and its interaction with a natural joint in an heterogeneous rock medium. Different crack paths, which are not pre-meshed a priori, and different pressure profiles are obtained and compared for different joint inclinations. Finally, our statistical tool, which has been primarily developed for the analysis of the failure behaviour of the solid phase, is used to characterise the evolution of correlation lengths between points undergoing damage upon the crack propagation and its interaction with a natural joint. It is shown that the hydro-mechanical lattice model is able to represent different mechanism of crack stop and restart from a joint depending on its inclination
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Rodrigues, Eduardo Alexandre [UNESP]. "Um modelo constitutivo de dano composto para simular o comportamento de materiais quase-frágeis." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/97142.
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No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o comportamento de materiais que apresentam diferentes respostas quando solicitados à tração ou à compreensão. obtem-se uma representação constitutiva através da composição de modelos simples e específicos para tratar cada tipo de solicitação. Este modelo combinado é capaz inclusive de lidar com carregamentos alternados (tração e compreensão), envolvendo fechamento e reabertura de fissuras existentes. Para modelar o comportamento em compreensão emprega-se o modelo constitutivo que tem como critério de degradação o segundo invariante do tensor de tensão desviador (critério de Von Mises ou J2). Para simular o aparecimento de fissuras de tração, usa-se o modelo de dano com critério de degradação baseado na energia de deformação da parte positiva do tensor efetivas. A integração dos modelos é feita com base em tensões efetivas associadas a duas escalas distintas (escala grosseira e refinada). O modelo é apto para representar a formação de descontinuidades no campo de deslocamento (descontinuidades fortes) em materiais quase-frágeis. Nesse caso, a região de localização de deformação (zona de processo da fatura) pode ser descrita pelo modelo de dano combinado, com lei de abrandamento de tensões (softening) exponencial, que estabelece dissipação compatível com a energia de fratura. A região contínua pode ser descrita pelo modelo de dano J2, com parâmetros ajustados com base no comportamento não linear à compreensão. Valida-se o modelo proposto mediante testes básicos, focando a capacidade do modelo em representar os principais aspectos do comportamento de materiais quase-frágeis. A aplicabilidade do modelo é demonstrada através do estudo da capacidade de rotação plástica de vigas de concreto armado, confrontando-se os resultados numéricos com os experimentais
A combined constitutive model based on the Continuum Damage Mechanics (CDM) is presented to represent the nonlinear behavior of quasi-brittle materials, which present different response when subjected to tension or compreession. The constitutive model is a composition of two simple and specific models designed to treat each type of behavior. The combined model is able to deal with alternating load (tension-compression), involving formation, closure and reopening cracks. To model the compressive behavior, a degradation criterion based on the second invariant of the deviatoric part of the effective stress tensor (Von Miser or J2 criterion) is used. To simulate cracking, a damage model with degradation criterion based on the strain energy associated to the positive part the effective stress tensor is adopted. The combination of the models is made on the basis of the effective stresses associated to two distinct scales (coarse and fine scales) The model is able to represented the formation of discontinuities in the displacement field (strong discontinuities) for quasi-brittle materials. The region of strain localization (fracture process zone) is described by a softening law which establishes dissipation energy compatible with the fracture energy. The continuous region is described by the J2 damage model, with parameters ajusted to describle the compressive nonlinear behavior in compression. Some basic tests are performed to asses the ability of the model to represent the main aspects of the behavior of quasi-brittle materials. The applicability of the model is demonstrated by the study of the plastic rotation capacity of reinforced concrete beams, comparing the numerical responses with the experimental ones
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Dib, Dayana. "Analyse théorique et numérique de l'endommagement par micro-fissuration descomposites à matrice quasi-fragile." Thesis, Paris Est, 2015. http://www.theses.fr/2015PEST1099.
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Le problème initial traité dans cette thèse relève du cadre général de la modélisation des tunnels profonds. Pour cela, on a adopté l'approche basée sur la mécanique linéaire de la rupture. L'étude s'est appuyée sur le critère mixte de Leguillon. Suite à cette étude, on a pu tirer que ce n'est pas le critère mixte qui est insuffisant mais plutôt la façon d'aborder le problème. D'où le passage à la prise en compte de l'hétérogénéité du matériau constitutif et la possibilité d'amorçage d'une fissure sous une contrainte de compression. Une première approche a été entreprise par l'étude d'une bicouche périodique sous contrainte de compression verticale. La couche de grande raideur s'est apparue le siège d'une traction transversale. Effectivement la possibilité d'amorçage d'une fissure est tout à fait probable grâce toujours à la vérification des critères d'énergie et de contrainte. Une deuxième approche consistait à observer au plus près la microstructure du matériau ; on a considéré le problème d'une inclusion elliptique dans une matrice infinie. Par la méthode des variables complexes et la technique de la transformation conforme, on a analysé le champ de contrainte autour de l'inclusion et on a mis en évidence la présence d'une traction qui dépend fortement des paramètres choisis. Par la méthode des éléments finis étendus, on a calculé la variation de l'énergie potentielle mise en jeu par la création d'une fissure. Par une démarche semblable à l'approche précédente, à savoir la vérification des critères d'énergie et de contrainte, on a conclu à la possibilité d'amorçage d'une fissure. Mots clefs : mécanique linéaire de la rupture, critère mixte de Leguillon, énergie potentielle, taux de restitution d'énergie, méthode des éléments finis étendus, bicouche périodique, méthode des variables complexesThe initial problem treated in this thesis falls within the general framework of modeling deep tunnels. For this reason, the approach based on linear fracture mechanics was adopted. The study was based on the mixed criterion of Leguillon. Following This study, the mixed criterion was not insufficient but the way to approach the problem was. Where the transition to the consideration of the heterogeneity of the material component and the possibility of initing a crack under a compressive stress. A first approach was undertaken the study of periodic bilayer under the stress of vertical compression. The layer of the highest stiffness has appeared the seat of a transverse traction. Indeed the possibility to initiate a crack is quite likely always through the verification of the energy and the stress criteria. A second approach was to observe more closer the microstructure of the material; we have considered the problem of elliptic inclusion in an infinite matrix. By the method of complex variables and the technique of conformal mapping, we analyzed the stress field around the inclusion and were revealed the presence of a traction which depends strongly of the selected parameters. By the extended finite element method, we calculated the variation of the potential energy involved by creating a fracture. In a similar approach to the previous one, namely verification of the energy and the stress criteria, we concluded the possibility of initiating a crack. Keywords: linear fracture mechanics, mixed criterion of Leguillon, potential energy, energy release rate, extended finite element method, periodic bilayer, method of complex variables
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Cayro, Evandro Esteban Pandia. "Efeito de escala no crescimento de trincas por fadiga em materiais quase-frágeis." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/143745.
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No trabalho estuda-se o crescimento de trincas em carga monotônica e cíclica nos casos de materiais quase-frágeis, introduzindo uma lei de dano cíclico. Revisam-se conceitos sobre modelos coesivos, leis de carga-descarga, leis de evolução de dano e efeito de escala. É seguido o modelo coesivo irreversível proposto por Wang e Siegmund (2006). Em particular se dá ênfase aos efeitos de escala não estatísticos. O modelo de zona coesiva irreversível apresenta uma formulação de dano e considera carregamento em fadiga. Quando o tamanho estrutural é reduzido (ou as trinca se extendem), a fratura por fadiga não mais ocorre por propagação de trinca, mas sim por uma decoesão uniforme. O objetivo desde trabalho é implementar este modelo e verificar sua potencialidade na captura de efeitos de escala, comparando com experimentos e dados disponíveis na literatura.At present work is intended to study crack growth in cyclic and monotonic loading in the case of quasi-brittle materials, introducing a damage mechanism, is reviewed concepts of cohesive models, loading-unloading laws, damage evolution laws and effect of scale. The irreversible cohesive zone model proposed by Wang e Siegmund (2006) is followed. In particular emphasizes in the not statistical size effects. The irreversible cohesive zone model, presents a damage formulation and considers fatigue loading. It is demonstrated in this study that, when the structure size is reduced (or extend cracks), the fatigue fracture no longer occurs by crack propagation, then occurs by uniform decohesion . The objetive of this work is implementing this model and verify its capability to capture the scale effect compared with experiments and data available in literature.
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Bui, Huu Phuoc. "Approche multi-échelle de la rupture des structures en béton : Influence des agrégats sur la longueur interne du matériau." Thesis, Grenoble, 2013. http://www.theses.fr/2013GRENI070/document.
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Pour l'analyse de durabilité et la conception économique (moins de matériel) de structures en matériaux ressemblant à du béton, la modélisation de la rupture est essentielle. Dans le cadre de la mécanique des milieux continus, une longueur interne est introduite dans les modèles non locaux pour remédier au problème lié à la sensibilité du maillage qui est une pathologie des modèles d'endommagement classiques , lorsqu'il s'agit de matériaux adoucissantes. Toutefois, l'évaluation de la longueur interne de hétérogénéités du matériau est toujours une question difficile, ce qui rend un problème obscur en utilisant des modèles non locaux. Nos travaux portent sur le développement d'un outil numérique basée sur la méthode des éléments en treillis (LEM) qui est un modèle discret pour la simulation et la prévision de la rupture des structures en béton. En utilisant le modèle de réseau à l'échelle mésoscopique, il n'est pas nécessaire d'introduire une longueur interne dans la loi de comportement, comme cela se fait dans les modèles non locaux, et nous pouvons affranchir ce paramètre en introduisant explicitement la mesotructure matérielle via une description géométrique. Basé sur l'outil numérique développé, nous avons étudié, en effectuant des tests numériques de traction uniaxiale, l'influence géométrique de la mesotructure du matériau ainsi que l'influence des conditions aux limites et de tailles d'échantillons (qui se traduisent par le gradient de sollicitation et le champ de rotation de matériel différents) sur le taille de la FPZ (fracture process zone) et sur la longueur caractéristique du matériau quasi-fragile homogénéisé. Ces études fournissent des recommandations/avertissements lors de l'extraction d'une longueur interne nécessaire pour les modèles nonlocaux à partir de la microstructure du matériau. Par ailleurs, les études contribuent un aperçu direct de l'origine mésoscopic de la taille FPZ et la longueur de la caractéristique du matériau, et par conséquent sur l'origine et la nature du comportement non linéaire du matériau. Ensuite, nous avons implanté le modèle du treillis dans la bibliothèque de SOFA développé par l'INRIA pour réaliser le couplage avec la méthode des éléments finis (MEF) afin de faire face avec des structures à grande échelle. Nous avons proposé un algorithme de couplage entre une approche macroscopique représentée par MEF et une approche mésoscopique infligés par LEM au sein d'une manière adaptative. Le modèle de couplage est d'abord utilisée pour valider l'approche multi-échelle proposée sur des simulations heuristiques. Et à long terme, il fournit un outil prometteur pour des simulations de grandes structures en matériaux quasi-fragiles de la vie réelleFor durability analysis and economic design (less material) of structures made of concrete-like materials, modeling of cracking process and failure is essential. In the framework of continuum mechanics, an internal length is introduced in nonlocal models to remedy the problem related to mesh sensitivity which is a pathology of classical damage models, when dealing with softening materials. However, the assessment of the internal length from heterogeneities of the material is still a difficult question, which makes an obscure issue in using nonlocal models. Our work concerns developing of a numerical tool based on the Lattice Element Method (LEM) which is a discrete model for simulating and predicting fracture in concrete(-like) material. Using the lattice model at the mesoscopic scale, there is no need to introduce any internal length in the constitutive law, as done in nonlocal models, and we can enfranchise this parameter by explicitly introducing the material mesotructure via geometric description. Based on the developed numerical tool, we studied, by performing numerical uniaxial tensile tests, the geometric influence of the material mesotructure as well as the influence of the boundary conditions and specimen sizes (that result in different stress gradient and material rotation field) on the size of the FPZ (Fracture Process Zone) and on the characteristic length of the homogenized quasi-brittle material. These studies provide recommendations/warnings when extracting an internal length required for nonlocal damage models from the material microstructure. Moreover, the studies contribute a direct insight into the mesoscale origin of the FPZ size and the material characteristic length, and consequently into the origin and nature of the nonlinear behavior of the material. Then, we implemented the lattice model into SOFA library developed by INRIA for realizing the coupling with the Finite Element Method (FEM) in order to deal with large-scale structures. We proposed a strong coupling algorithm between a macroscopic approach represented by FEM and a mesoscopic approach dealt by LEM within an adaptive manner. The coupling model is first used to validate the multiscale approach proposed on heuristic simulations. And in the long term, it provides a promising tool for simulations of large-scale structures made of quasi-brittle materials of real life
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Rojas, Solano Laura Beatriz. "Endommagement non-local, interactions et effets d’échelle." Thesis, Pau, 2012. http://www.theses.fr/2012PAUU3032/document.
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Cette thèse porte sur la description du processus de fissuration du béton soumis à des sollicitations mécaniques. L'objectif principal est d'améliorer la description macroscopique à l'aide d'un modèle continu. Un modèle décrivant de façon cohérente le comportement à la rupture du béton devrait au moins représenter : (i) la transition continu/discret et l'effet d'écran induit par une macrofissure, (ii) la discontinuité du déplacement, (iii) l'interaction entre le processus de fissuration et un bord libre (iv) il doit aussi être capable de reproduire la réponse mécanique obtenue expérimentalement. Dans un premier temps, nous avons fait une analyse comparative entre le modèle d'endommagement non-local classique et différents modèles continus améliorés proposés dans la littérature. Des outils de comparaison ont été proposés pour cette analyse : (i) du point de vue numérique, deux exemples considérant la rupture dynamique d'une barre (barre en traction et test d'écaillage) et (ii) du point de vue expérimental, une base de données issue d'une série d'essais sur des poutres homothétiques entaillées et non-entaillées en flexion trois points. Nous avons conclu que seule une combinaison entre différentes formulations peut rendre compte de tous les mécanismes mis en jeu lors du processus de fissuration. Elle inclue à la fois la façon dont l'information non-locale est transmise, la croissance de défauts et la description des effets de bord. Nous avons mis en évidence que son implémentation 2D ou 3D reste complexe et donc la comparaison avec des données expérimentales s'avère impossible. Dans un deuxième temps, nous avons choisi de changer l'échelle d'analyse pour connaitre en détail les mécanismes ayant lieu au sein de la mésostructure du béton (pâte, granulat, interface) à l'aide d'un modèle mésoscopique basé sur des éléments lattice. Cette analyse a permis de conclure que la prise en compte des interactions entre les composants de la mésostructure du béton fournit des résultats numériques plus proches de la réalité que ceux obtenus avec le modèle non-local macroscopique classique. Le mésomodèle est capable de représenter aussi bien la charge maximale (effet d'échelle) que la phase adoucissante pour toutes les tailles de poutre et pour toutes les géométries d'entaille. Nous avons transposé la prise en compte des interactions de l'échelle mésoscopique à l'échelle macroscopique au travers de la fonction poids d'un nouveau modèle non-local. Elle est estimée en décrivant le matériau comme étant un ensemble d'inclusions qui interagissent entre elles lors du chargement. Ces inclusions sont dilatées élastiquement et successivement afin de caractériser le transfert d'information au sein du matériau et de reconstruire la fonction poids du modèle proposé. Ce nouveau modèle est capable de décrire la transition continu/discret et l'effet d'écran, la discontinuité du déplacement et de retrouver un effet de bord cohérent avec les résultats de la micromécanique. Son implémentation en 2D est présentée et les premiers résultats de calculs illustrent la démarche. Finalement, nous revenons sur la modélisation mésoscopique du comportement du béton. Sa richesse en information peut conduire à une compréhension plus fine du processus de fissuration et de la création puis l'évolution de la zone d'élaborationThis work focuses on the description of the process of cracking of concrete subjected to mechanical stresses. The main objective is to improve the understanding of the mechanisms involved using a continuous macroscopic model. A model describing consistently the fracture behavior of concrete should at least represent: (i) the continuous / discrete transition and the shielding effect induced by a macrocrack, (ii) the discontinuity of displacement, (iii) the interaction between the cracking process and a free boundary, (iv) it must also be able to reproduce the mechanical response obtained experimentally. At first, we made a comparative analysis of the classical non-local damage model and others improved continuous models proposed in the literature. Comparison tools have been proposed for this analysis: (i) from a numerical point of view, two examples considering the dynamic rupture of a bar (tensile test and spalling test) and (ii) from an experimental point of view, a database obtained from three-point bending test on notched and unnotched geometrically similar beams made from the same concrete formulation. We found that only a combination of this formulations may account for the different mechanisms involved in the process of cracking. It includes the transmission of the non-local information, the growing of voids and the description of boundary effects. We shown that its implementation in 2D or 3D remains complex and thus comparison with experimental results are impossible. In a second step, we decided to change the scale of analysis to precise the mechanisms which are taking place within the mesostructure of concrete using a mesomodel based on lattice elements. This analysis shown that since the mesomodel intrinsically took into account the interactions evolution within the structure, it is able to provide relevant results when classical macroscopic non-local models failed. It is able to represent both the maximum load (size effect) and the softening regime whatever the beam size or the pre-notch geometry. In addition, we proposed a new non-local framework where the interactions were upscale from the mesoscale to the macroscale through a new weight function. This function is estimated by describing the material as a set of inclusions that interact upon loading. These inclusions are successively elastically dilated to characterize the transfer of information within the material and rebuild the non-local weight function. This new model is able to describe the continuous / discrete transition, the shielding effect and the discontinuity of displacement. The model has been implemented in 2D in a finite element code and first results shown its capabilities to reproduce experimental results in term of maximum loads. In a third step, the richness of the mesoscopic approach has been used to describe precisely the local process of failure in term of fracture process zone evolution
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Gao, Xiaofeng. "Modèle pour la prévision de la résistance nominale des matériaux quasi-fragiles : application à la modélisation de l'endommagement et de la rupture des enrobés bitumineux sous sollicitations de fatigue par la méthode des éléments discrets." Thesis, Strasbourg, 2017. http://www.theses.fr/2017STRAD007/document.
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L’estimation de la durée de vie et de la rupture de structures composées par des matériaux quasi-fragiles nécessite le développement de nouveaux modèles théoriques et numériques. Dans ce travail, la modélisation de l’apparition des fissures et leur propagation en chargement monotone est d'abord étudiée. Un modèle d'effet de taille pour les structures fissurées et sa forme généralisée pour les structures présentant des défauts plus complexes qu’une fissure sont développés. Les prédictions du modèle de rupture sont comparées à des résultats expérimentaux de la littérature pour divers spécimens composés de différents matériaux et de différentes tailles. Des échantillons présentant des défauts initiaux en forme de V et en forme de trou illustrent les capacités de la formulation. Ensuite, l’endommagement et la fissuration induite par des chargements cycliques en fatigue sont discutés. Un modèle local en éléments discrets est développé, qui permet de coupler les deux mécanismes (endommagement et fissuration). Les prédictions numériques sont comparées aux résultats théoriques et expérimentaux. À la fin, les applications associées au comportement du béton bitumineux renforcé par des grilles en fibres de verres sont analysées en détailThe prediction of the fatigue life and the rupture of structures made of quasi-brittle materials requires the development of new theoretical and numerical models. In this work, the modelling of the crack initiation and propagation under monotonic loading is firstly investigated. A size effect model for cracked structures and its generalized form for structures with defects more complex than a crack are developed. The predictions of the proposed model are compared with experimental results from the literature for various specimens of different materials and sizes. Samples with initial V-shaped and hole-shaped defects exemplify the formulation's capabilities. Then, the damage and cracking induced by cyclic fatigue loads is discussed. A local model using discrete elements is developed, that allows the coupling of two mechanisms (damage and fatigue cracking). The numerical results are compared to those of experimental bending fatigue tests. Finally, applications associated with the behavior of fiber glass reinforced asphalt concrete are analyzed in detail
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De, Vittorio Giancarlo. "Crack measurements in structural concrete with D.I.C. system and validation of a tensile constitutive law." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2011. http://amslaurea.unibo.it/2048/.
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Compared with other mature engineering disciplines, fracture mechanics of concrete is still a developing field and very important for structures like bridges subject to dynamic loading. An historical point of view of what done in the field is provided and then the project is presented. The project presents an application of the Digital Image Correlation (DIC) technique for the detection of cracks at the surface of concrete prisms (500mmx100mmx100mm) subject to flexural loading conditions (Four Point Bending test). The technique provide displacement measurements of the region of interest and from this displacement field information about crack mouth opening (CMOD) are obtained and related to the applied load. The evolution of the fracture process is shown through graphs and graphical maps of the displacement at some step of the loading process. The study shows that it is possible with the DIC system to detect the appearance and evolution of cracks, even before the cracks become visually detectable.
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Vassaux, Maxime. "Comportement mécanique des matériaux quasi-fragiles sous sollicitations cycliques : de l’expérimentation numérique au calcul de structures." Thesis, Cachan, Ecole normale supérieure, 2015. http://www.theses.fr/2015DENS0010/document.
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Les modèles de comportement mécanique, dits macroscopiques, sont développés à la fois pour leur légèreté, permettant le calcul d’éléments structuraux pouvant atteindre d’importantes dimensions, et pour leur finesse de représentation des phénomènes mécaniques observés par le matériau à des échelles plus fines. Le développement de tels modèles est ici effectué dans le cadre de la sollicitation sismique, donc des chargements cycliques alternés, appliquée à des ouvrages en matériaux quasi-fragiles, et plus précisément en béton. À ce jour, les modèles macroscopiques, effectivement applicables au calcul de structures, et représentatifs du comportement cyclique du béton sont encore rares. En conséquence de la complexité du problème de fissuration à homogénéiser, les modèles macroscopiques existants affichent une robustesse limitée ou ne permettent pas de reproduire l’ensemble des phénomènes mécaniques observés par le matériau. Une des barrières à la résolution de ces deux problématiques est le manque de données expérimentales relatives aux phénomènes à modéliser. En effet, en cause de la difficulté technique de les réaliser, peu de résultats d’essais cycliques alternés sur du béton sont disponibles dans la littérature.
Une démarche d’expérimentation numérique a donc été élaborée sur la base d’un modèle fin du matériau, dit microscopique, capable de fournir les résultats nécessaires à la formulation et à l’identification d’un modèle macroscopique. Dans le modèle microscopique le matériau est considéré comme une structure à part entière, il a été développé afin de ne nécessiter qu’une quantité réduite de résultats d’essais, maîtrisés, pour être mis en oeuvre. Le modèle microscopique, un modèle particulaire lattice, a été développé sur la base d’un modèle lattice existant, enrichi pour être en mesure de simuler le comportement des matériaux quasi-fragiles sous chargements multi-axiaux et cycliques. Le modèle microscopique a alors été validé en tant qu’outil d’expérimentation numérique, et exploité afin d’établir les équations constitutives du modèle macroscopique fondées sur les théories de l’endommagement et de la plasticité. La régularité de la relation de comportement proposée, intégrant un effet unilatéral progressif, a notamment été garantie par l’utilisation d’un modèle d’élasticité non-linéaire. Le modèle macroscopique a finalement été calibré, entièrement, à l’aide du modèle microscopique, et mis à l’oeuvre dans la simulation de la réponse d’un voile en béton armé soumis à un chargement de cisaillement cyclique alterné. Cette simulation a permis de mettre en avant la robustesse numérique du modèle développé, ainsi que la contribution significative du comportement uni-axial cyclique alterné du béton à l’amortissement de telles structuresMacroscopic mechanical behavior models are developed for their light computational costs, allowing the simulation of large structural elements, and the precise description of mechanical phenomena observed by the material at lower scales. Such constitutive models are here developed in the seismic solicitation framework, therefore implying cyclic alternate loadings at the material scale, and applied to civil engineering buildings, often made of concrete, or more generally of quasi-brittle materials. To date, macroscopic models applicable to structural computations, while representing the cyclic mechanical behavior are rare. In consequence of the intricacy of the fracture processes to homogenize, macroscopic constitutive models either do not present sufficient robustness or miss on important phenomena. One of the limitations to the resolution of this issue is the lack of experimental data. Indeed, because of the complexity of the experiments to set up, few results on alternate cyclic tests on concrete are available in the literature.A virtual testing approach has therefore been established on a microscopic model of the material, able to provide results needed to the formulation and the calibration of a macroscopic model. In the microscopic model, the material is considered as structure itself, it is developed so as to only necessitate a reduced amount of results from controlled experimental tests, in order to be used. The microscopic model, a lattice discrete element model, has been developed on the basis of an existing lattice model and extended to the simulation of multi-axial and cyclic loadings. The microscopic model has then been validated as a virtual testing tool and used to establish equations of the macroscopic model, on the basis of damage and plasticity theories. The consistency of the proposed constitutive relation, embedding progressive unilateral effect, has been achieved using non-linear elasticity. The macroscopic model has finally been calibrated, entirely with the microscopic model, and employed to simulate the response of a reinforced concrete wall under alternate shear loading. This simulation has served to showcase the numerical robustness of the proposed model, as well as the significant contribution of the uni-axial alternate behavior of concrete to the structural damping of such structures
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Rodrigues, Eduardo Alexandre. "Um modelo constitutivo de dano composto para simular o comportamento de materiais quase-frágeis /." Bauru : [s.n.], 2011. http://hdl.handle.net/11449/97142.
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Resumo: No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o comportamento de materiais que apresentam diferentes respostas quando solicitados à tração ou à compreensão. obtem-se uma representação constitutiva através da composição de modelos simples e específicos para tratar cada tipo de solicitação. Este modelo combinado é capaz inclusive de lidar com carregamentos alternados (tração e compreensão), envolvendo fechamento e reabertura de fissuras existentes. Para modelar o comportamento em compreensão emprega-se o modelo constitutivo que tem como critério de degradação o segundo invariante do tensor de tensão desviador (critério de Von Mises ou J2). Para simular o aparecimento de fissuras de tração, usa-se o modelo de dano com critério de degradação baseado na energia de deformação da parte positiva do tensor efetivas. A integração dos modelos é feita com base em tensões efetivas associadas a duas escalas distintas (escala grosseira e refinada). O modelo é apto para representar a formação de descontinuidades no campo de deslocamento (descontinuidades fortes) em materiais quase-frágeis. Nesse caso, a região de localização de deformação (zona de processo da fatura) pode ser descrita pelo modelo de dano combinado, com lei de abrandamento de tensões (softening) exponencial, que estabelece dissipação compatível com a energia de fratura. A região contínua pode ser descrita pelo modelo de dano J2, com parâmetros ajustados com base no comportamento não linear à compreensão. Valida-se o modelo proposto mediante testes básicos, focando a capacidade do modelo em representar os principais aspectos do comportamento de materiais quase-frágeis. A aplicabilidade do modelo é demonstrada através do estudo da capacidade de rotação plástica de vigas de concreto armado, confrontando-se os resultados numéricos com os experimentaisAbstract: A combined constitutive model based on the Continuum Damage Mechanics (CDM) is presented to represent the nonlinear behavior of quasi-brittle materials, which present different response when subjected to tension or compreession. The constitutive model is a composition of two simple and specific models designed to treat each type of behavior. The combined model is able to deal with alternating load (tension-compression), involving formation, closure and reopening cracks. To model the compressive behavior, a degradation criterion based on the second invariant of the deviatoric part of the effective stress tensor (Von Miser or J2 criterion) is used. To simulate cracking, a damage model with degradation criterion based on the strain energy associated to the positive part the effective stress tensor is adopted. The combination of the models is made on the basis of the effective stresses associated to two distinct scales (coarse and fine scales) The model is able to represented the formation of discontinuities in the displacement field (strong discontinuities) for quasi-brittle materials. The region of strain localization (fracture process zone) is described by a softening law which establishes dissipation energy compatible with the fracture energy. The continuous region is described by the J2 damage model, with parameters ajusted to describle the compressive nonlinear behavior in compression. Some basic tests are performed to asses the ability of the model to represent the main aspects of the behavior of quasi-brittle materials. The applicability of the model is demonstrated by the study of the plastic rotation capacity of reinforced concrete beams, comparing the numerical responses with the experimental ones
Orientador: Osvaldo Luís Manzoli
Coorientador: André Luís Gamino
Banca: Leonardo José do Nascimento Guimarães
Banca: Edson Antonio Capello Sousa
Mestre
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Silva, Cristiane Zuffo da. "Uso de descontinuidades fortes na simulação de problemas de fratura." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/134890.
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A formação e propagação de fissuras é um fenômeno observado em diversos materiais utilizados na engenharia, como concreto, metais, cerâmicas e rochas. Tendo em vista a grande influência que fissuras têm no comportamento global da estrutura o objetivo deste trabalho consiste na implementação de um modelo de fissura com descontinuidades fortes incorporadas a fim de analisar o processo de fratura em materiais quase-frágeis. A descontinuidade no campo de deslocamentos (descontinuidade forte) é representada através da introdução de graus de liberdade adicionais no interior do elemento finito, sendo esta abordagem denominada enriquecimento elementar (E-FEM). Nestes modelos a fissura pode se propagar em qualquer direção dentro do elemento finito, evitando a necessidade de redefinição da malha em cada etapa, além de fornecer resultados relativamente independentes da malha de elementos finitos utilizada. Por serem internos a cada elemento finito, os graus de liberdade adicionais podem ser eliminados da solução global por condensação estática. Desta forma as descontinuidades são definidas em nível de elemento e o modelo pode ser facilmente implementado em códigos computacionais existentes. O modelo implementado foi proposto por Dvorkin, Cuitiño e Gioia (1990), o qual pertence à classe de modelos com formulação assimétrica estaticamente e cinematicamente consistente (SKON). Esta formulação é caracterizada por garantir o movimento de corpo rígido entre as partes do elemento além de assegurar a continuidade de tensões na linha de fissura, resultando numa matriz de rigidez assimétrica. Diferentes relações constitutivas podem ser utilizadas para descrever o comportamento das regiões com e sem fissura. Portanto, para a região não fissurada, utilizouse um modelo constitutivo elástico linear e para a região fissurada foi analisada a performance de dois modelos constitutivos distintos: linear e exponencial. A capacidade de representar o comportamento de elementos estruturais fissurados foi ilustrada através de exemplos de tração e flexão comparados com outros modelos de fissura existentes e com resultados experimentais. Em relação aos modelos constitutivos para a linha da fissura, o modelo linear não se mostrou adequado por superestimar as tensões de pico além de apresentar um ramo de amolecimento mais frágil. Já o modelo exponencial mostrou-se bastante eficiente representando de forma correta o comportamento de materiais quase-frágeis.The formation and propagation of cracks is a phenomenon observed in many materials used in engineering, such as concrete, metals, ceramics and rocks. In view of the influence of cracks in the global behavior of the structure, the aim of this work is the implementation of an embedded strong discontinuity model in order to analyze the fracture process in quasi-brittle materials. The discontinuity in the displacement field (strong discontinuity) is represented by the introduction of additional degrees of freedom within the finite element. This approach is called elemental enrichment (E-FEM). The embedded models allow the propagation of crack in any direction within the finite element, avoiding the need of remeshing and providing objective results (mesh independent). The additional degrees of freedom are introduced into the finite element, then these degrees can be eliminated from the global solution by static condensation and the model can be easily implemented in existent computational codes. The model used here was proposed by Dvorkin, Cuitiño and Gioia (1990), which belongs to the statically and kinematically optimal non-symmetric (SKON) formulation. In this formulation, the kinematics that allows for relative rigid body motion and the enforcement of the traction continuity are introduced at element level, resulting a non-symmetric formulation. Different constitutive relations can be used to describe the behavior of the zones with and without cracks. For the zone without cracks it was used a linear elastic model and for the cracked zone it was analyzed the behavior of two different constitutive models: linear and exponential. The ability of the model to represent the behavior of cracked structural elements was illustrated by bending and tensile tests and the results were compared with numerical and experimental data. Regarding the constitutive models for the fracture zone, it was concluded that the linear model was not suitable because it overestimated the maximum stress and promoted a britller softening. In contrast, the exponential model proved to be very efficient to represent the behavior of quasi-brittle materials.
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Klon, Jiří. "Modelování lomového procesu v kvazikřehkých materiálech." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2016. http://www.nusl.cz/ntk/nusl-240265.
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This work is focused on the evaluation of the selected fracture parameters of quasi-brittle material, especially concrete, and an assessment of their dependence on the size and shape of the fracture process zone developing at the tip of the macroscopic crack during fracture. For this purpose, experimentally obtained loading diagrams published in the scientific literature have been utilized. These diagrams have been processed into a form enabling creation and calibration of numerical models of these tests in the ATENA FEM program. The results obtained from simulations of the three-point bending tests on beams of four sizes, with three notches lengths, using the created numerical models were used for determination of fracture parameters of concrete. Results of the work consist of the determined values of the specific energy dissipated for creation of new surfaces of the effective crack and an estimation of the specific energy dissipated in the volume of the fracture process zone, which exhibits specific parameters for each beam size and notch length.
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Wrzesniak, Aleksandra. "Modélisation double-échelle de la rupture des roches : influence du frottement sur les micro-fissures." Thesis, Grenoble, 2012. http://www.theses.fr/2012GRENI104/document.
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Propagation des fissures microscopiques, est représentée par des variables d’endommagement. L’évolution de la variable d’endommagement est généralement formulée sur la base d’observations expérimentales. De nombreux modèles phénoménologiques d’endommagement ont été proposés dans la littérature. L’objet de cette thèse est de développer une nouvelle procédure pour obtenir des lois d’évolution macroscopique d’endommagement,dans lesquelles l’évolution de l’endommagement est entièrement déduite de l’analyse de la microstructure. Nous utilisons une homogénéisation basée sur des développements asymptotiques pour décrire le comportement global à partir de la description explicite d’un volume élémentaire microfissuré.Nous considérons d’une part un critère quasi-fragile (indépendant du temps) puis un critère sous-critique(dépendant du temps) pour décrire la propagation des microfissures. De plus, le frottement entre les lèvres des microfissures est pris en compte. Une analyse énergétique est proposée, conduisant à une loi d’évolution d’endommagement qui intègre une dégradation de la rigidité, un adoucissement du comportement du matériau, des effets de taille et d’unilatéralité, mettant en avant un comportement différent à la rupture en contact avec et sans frottement. L’information sur les micro-fissures est contenue dans les coefficients homogénéisés et dans la loi d’évolution de l’endommagement. Les coefficients homogénéisés décrivent la réponse globale en présence de micro-fissures (éventuellement statiques), tels qu’ils sont calculées avec la(quasi-) solution microscopique statique. La loi d’endommagement contient l’information sur l’évolution des micro-fissures, résultant de l’équilibre énergétique dans le temps pendant la propagation microscopique.La loi homogénéisée est formulée en incrément de contrainte. Les coefficients homogénéisés sont calculées numériquement pour des longueurs de fissures et des orientations différentes. Cela permet la construction complète des lois macroscopiques. Une première analyse concerne le comportement local macroscopique, pour des trajets de chargement complexes, afin de comprendre le comportement prédit par le modèle à deux échelles et l’influence des paramètres micro structuraux, comme par exemple le coefficient de frottement. Ensuite, la mise en œuvre en éléments finis des équations macroscopiques est effectuée et des simulations pour différents essais de compression sont réalisées. Les résultats des simulations numériques sont comparés avec les résultats expérimentaux obtenus en utilisant un nouvel appareil triaxial récemment mis au point au Laboratoire 3SR à Grenoble (France)In continuum damage models, the degradation of the elastic moduli, as the results of microscopic crackgrowth, is represented through damage variables. The evolution of damage variable is generally postulatedbased on the results of the experimental observations. Many such phenomenological damage modelshave been proposed in the literature. The purpose of this contribution is to develop a new procedurein order to obtain macroscopic damage evolution laws, in which the damage evolution is completelydeduced from micro-structural analysis. We use homogenization based on two-scale asymptotic developmentsto describe the overall behaviour starting from explicit description of elementary volumes withmicro-cracks. We consider quasi-brittle (time independent) and sub-critical (time dependent) criteria formicro-cracks propagation. Additionally, frictional contact is assumed on the crack faces. An appropriatemicro-mechanical energy analysis is proposed, leading to a damage evolution law that incorporates stiffnessdegradation, material softening, size effect, and unilaterality, different fracture behaviour in contactwithout and with friction. The information about micro-cracks is contained in the homogenized coefficientsand in the damage evolution law. The homogenized coefficients describe the overall response inthe presence of (possibly static) micro-cracks, as they are computed with the (quasi-) static microscopicsolution. The damage law contains the information about the evolution of micro-cracks, as a result ofthe energy balance in time during the microscopic propagation. The homogenized law is obtained in therate form. Effective coefficients are numerically computed for different crack lengths and orientations.This allows for the complete construction of the macroscopic laws. A first analysis concerns the localmacroscopic behaviour, for complex loading paths, in order to understand the behaviour predicted bythe two-scale model and the influence of micro structural parameters, like for example friction coefficient.Next, the FEM implementation of the macroscopic equations is performed and simulations for variouscompression tests are conducted. The results of the numerical simulations are compared with the experimentalresults obtained using a new true-triaxial apparatus recently developed at the Laboratory 3SRin Grenoble (France)
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Dourado, Nuno Miguel. "R-Curve behaviour and size effect of a quasibrittle material : wood." Thesis, Bordeaux 1, 2008. http://www.theses.fr/2008BOR13734/document.
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Ce travail concerne des expériences mécaniques, des analyses numériques et des modélisations analytiques de la rupture cohésives (Mode I), vis-à-vis de l’étude du comportement mis en évidence par la courbe de Résistance (Courbe-R) et l’effet d’échelle de structures entaillées en bois massif. Des expériences de fissuration sont combinées à des analyses numériques pour déterminer les propriétés de rupture au moyen d’une procédure appelée Théorie de la Mécanique de la Rupture Linéaire Élastique équivalente (TMRLE), basée sur la complaisance de la structure. La courbe-R, obtenue à partir des expériences, selon une méthode de correction du poids propre, montre l’existence d’un domaine endommagé (Zone de Processus de Rupture) de taille non négligeable se développant en fond de fissure. Dans des conditions de fissuration stationnaire, ce domaine atteint une taille critique, et l’énergie nécessaire pour faire propager la fissure avec ce domaine endommagé (par unité de surface de rupture), reste constante. Le taux de libération de l’énergie de fissuration ainsi attendu, joue un rôle important en Mécanique de la Rupture, car il est possible simuler le comportement quasi-fragile du matériau en combinaison avec les autres propriétés de cohésion. La loi d’effet d’échelle de Bažant, utilisée pour prévoir l’influence de la taille sur la contrainte nominale, est estimée à partir de la réunion de deux comportements asymptotiques réalisés sur de petites tailles (Analyse limite ou RdM) et des grandes tailles. Une procédure analytique est présentée pour évaluer le comportement asymptotique additionnel exhibé par la contrainte nominale dans le régime intermédiaire, de façon plus exacte. Une validation numérique est présentée, et l’information expérimentale vient confirmer ce comportement asymptotiqueThis work concerns the mechanical testing, numerical analysis and modelling of cohesive fracture (Mode I) on the purpose to study the Resistance-curve behaviour and the size effect in wooden notched structures. The mechanical testing is combined with the numerical analysis to evaluate fracture properties by means of an equivalent LEFM approach based on the structure compliance. The Resistance-curve being revealed from the experiments, by means of a self-weight compensation method, correction puts into evidence that a non-negligible damaged domain (Fracture Process Zone) is under development in the crack front during the loading process. This being the case, among other fracture parameters issued from the Resistance-curve, the critical (asymptotic) energy release rate is determined, turning possible to use it in combination with other cohesive crack properties in the crack modelling (in Mode I). Thus, for a given geometry it is possible to monitor the critical dimension being revealed by the Fracture Process Zone (FPZ) during the crack propagation. The well known Bažant’s size effect law provides the scaling of the nominal strength through the asymptotic matching performed both on the small (Strength Theory) and on the large (LEFM) structure sizes. An analytical procedure is proposed to determine an additional asymptotic regime in the intermediate size range through a more accurate manner. Numerical validations of the proposed procedure are made and experimental data is presented revealing the scaling of the nominal strength through an envelop of values
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Pröchtel, Patrick. "Anisotrope Schädigungsmodellierung von Beton mit Adaptiver Bruchenergetischer Regularisierung." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1224751435667-29771.
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Der Gegenstand der vorliegenden Arbeit ist die Simulation von Betonstrukturen beliebiger Geometrie unter überwiegender Zugbelastung. Die Modellierung erfolgt auf Makroebene als Kontinuum und zur Lösung des mechanischen Feldproblems wird die Finite-Elemente-Methode verwendet. Ein neues Materialmodell für Beton und eine Erweiterung der Bruchenergetischen Regularisierung werden vorgestellt. Die Arbeit ist in zwei Teile gegliedert. Im ersten Teil wird ein lokales, anisotropes Schädigungsmodell abgeleitet, wobei als Schädigungsvariable ein symmetrischer Tensor zweiter Stufe gewählt wird. Die Verwendung einer Normalenregel im Raum der dissipativen Kräfte zur Bestimmung der Schädigungsevolution und die Definition der Schädigungsgrenzflächen im Raum der dissipativen Kräfte gewährleisten die Gültigkeit der Hauptsätze der Thermodynamik und des Prinzips der maximalen Dissipationsrate. Vorteilhaft ist die Symmetrie der Materialtangente, die sich aus diesem Vorgehen ergibt. Eine Formulierung mit drei entkoppelten Schädigungsgrenzflächen wird vorgeschlagen. Eine wichtige Forderung bei der Ableitung des Materialmodells war die Verwendung einer möglichst geringen Anzahl von Materialparametern, welche darüber hinaus aus wenigen Standardversuchen bestimmbar sein sollten. Das Schädigungsmodell enthält als Materialparameter den Elastizitätsmodul, die Querdehnzahl, die Zugfestigkeit und die auf eine Einheitsfläche bezogene Bruchenergie. Im zweiten Teil der Arbeit stehen Lokalisierung und Regularisierung im Fokus der Betrachtungen. Aufgrund der lokalen Formulierung des Materialmodells tritt bei Finite-Elemente Simulationen eine Netzabhängigkeit der Simulationsergebnisse auf. Um dieser Problematik zu begegnen und netzunabhängige Simulationen zu erreichen, werden Regularisierungstechniken angewendet. In dieser Arbeit wird die Bruchenergetische Regularisierung eingesetzt, die durch die Einführung einer äquivalenten Breite in ein lokal formuliertes Stoffgesetz gekennzeichnet ist. Die spezielle Wahl eines Wertes für die äquivalente Breite beruht auf der Forderung, dass in der Simulation die korrekte Bruchenergie je Einheitsfläche für den Bruchprozess verbraucht wird, d.h. die Energiedissipation der Realität entspricht. In vorliegender Arbeit wird die neue These aufgestellt, dass die Energiedissipation nur für den Fall korrekt abgebildet wird, wenn die im Stoffgesetz enthaltene äquivalente Breite in jedem Belastungsinkrement der Breite des Bereiches entspricht, in dem in der Simulation Energie dissipiert wird. In einer Simulation wird in den Bereichen Energie dissipiert, in denen die Schädigung im aktuellen Belastungsinkrement zunimmt. In vorliegender Arbeit werden die energiedissipierenden Bereiche daher als Pfad der Schädigungsrate bezeichnet. Um Erkenntnisse über die Entwicklung des Pfades der Schädigungsrate über den Belastungsverlauf zu erhalten, wurden umfangreiche Untersuchungen anhand von Simulationen eines beidseitig gekerbten Betonprobekörpers unter kombinierter Zug-Schubbeanspruchung durchgeführt, wobei die gewählten Werte für die äquivalente Breite variiert wurden. Es wurde stets eine Diskretisierung mit linearen Verschiebungselementen verwendet, wobei die Bereiche mit zu erwartender Schädigung feiner und regelmäßig mit Elementen quadratischer Geometrie diskretisiert wurden. Die Ergebnisse der Untersuchungen zeigen, dass die Breite des Pfades der Schädigungsrate abhängig ist von der Schädigung am betrachteten Materialpunkt, dem von Schädigungsrichtung und Elementkante eingeschlossenen Winkel, der Elementgröße und den Materialparametern. Um die geforderte Übereinstimmung von äquivalenter Breite und der Breite des Pfades der Schädigungsrate zu erreichen, werden neue Ansätze für die äquivalente Breite vorgeschlagen, die die erwähnten Einflüsse berücksichtigen. Simulationen unter Verwendung der neuen Ansätze für die äquivalente Breite führen zu einer guten Übereinstimmung von äquivalenter Breite und der Breite des Pfades der Schädigungsrate in der Simulation. Die Ergebnisse der Simulationen, wie z.B. Last-Verformungsbeziehung und Rissverläufe, sind netzunabhängig und stimmen gut mit den experimentellen Beobachtungen überein. Basierend auf den gewonnenen Erkenntnissen wird eine Erweiterung der Bruchenergetischen Regularisierung vorgeschlagen: die Adaptive Bruchenergetische Regularisierung. Im abschließenden Kapitel der Arbeit werden mit der vorgeschlagenen Theorie, dem neuen Schädigungsmodell und der Adaptiven Bruchenergetischen Regularisierung, noch zwei in der Literatur gut dokumentierte Versuche simuliert. Die Simulationsergebnisse entsprechen den experimentellen BeobachtungenThis doctoral thesis deals with the simulation of predominantly tensile loaded plain concrete structures. Concrete is modeled on the macro level and the Finite Element Method is applied to solve the resulting mechanical field problem. A new material model for concrete based on continuum damage mechanics and an extended regularization technique based on the fracture energy approach are presented. The thesis is subdivided into two parts. In the first part, a local, anisotropic damage model for concrete is derived. This model uses a symmetric second-order tensor as the damage variable, which enables the simulation of orthotropic degradation. The validity of the first and the second law of thermodynamics as well as the validity of the principle of maximum dissipation rate are required. Using a normal rule in the space of the dissipative forces, which are the thermodynamically conjugated variables to the damage variables, and the definition of the loading functions in the space of the dissipative forces guarantee their validity. The suggested formulation contains three decoupled loading functions. A further requirement in the derivation of the model was the minimization of the number of material parameters, which should be determined by a small number of standard experiments. The material parameters of the new damage model are the Young’s modulus, the Poisson’s ratio, the tensile strength and the fracture energy per unit area. The second part of the work focuses on localization and regularization. If a Finite Element simulation is performed using a local material model for concrete, the results of the Finite Element simulation are mesh-dependent. To attain mesh-independent simulations, a regularization technique must be applied. The fracture energy approach, which is characterized by introducing a characteristic length in a locally formulated material model, is used as regularization technique in this work. The choice of a value for the characteristic length is founded by the requirement, that the fracture energy per unit area, which is consumed for the fracture process in the simulation, must be the same as in experiment, i.e. the energy dissipation must be correct. In this dissertation, the new idea is suggested that the correct energy dissipation can be only attained if the characteristic length in the material model coincides in every loading increment with the width of the energy-dissipating zone in the simulation. The energy-dissipating zone in a simulation is formed by the integration points with increasing damage and obtains the name: damage rate path. Detailed investigations based on simulations of a double-edge notched specimen under mixed-mode loading are performed with varying characteristic lengths in order to obtain information concerning the evolution of the damage rate path during a simulation. All simulations were performed using displacement-based elements with four nodes. The range with expected damage was always finer and regularly discretized. The results of the simulations show that the width of the damage rate path depends on the damage at the specific material point, on the angle between damage direction and element edges, on the element size and on the material parameters. Based on these observations, new approaches for the characteristic length are suggested in order to attain the coincidence of the characteristic length with the width of the damage rate path. Simulations by using the new approaches yield a sufficient coincidence of the characteristic length with the width of the damage rate path. The simulations are mesh-independent and the results of the simulation, like load-displacement curves or crack paths, correspond to the experimental results. Based on all new information concerning the regularization technique, an extension of the fracture energy approach is suggested: the adaptive fracture energy approach. The validity and applicability of the suggested theory, the new anisotropic damage model and the adaptive fracture energy approach, are verified in the final chapter of the work with simulations of two additional experiments, which are well documented in the literature. The results of the simulations correspond to the observations in the experiments
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Amorim, David Leonardo Nascimento de Figueiredo. "On the lumped damage mechanics for nonlinear structural analyses: new developments and applications." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-06042016-112414/.
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The accurate description of the nonlinear structural behaviour is an important issue in engineering science. Usually, classic nonlinear theories, such as fracture and damage mechanics, applied to finite element programmes are used to fulfil that purpose. Classic fracture mechanics describes the structural deterioration process by a few discrete cracks. This theory presents good precision for structures with simple geometries, few cracks and homogeneous materials. Classic damage mechanics measures the deterioration process by an internal variable called damage. This theory has been successful in the description of several deterioration mechanisms in continuum media. Despite their accuracy, classic fracture and damage mechanics present some drawbacks. Firstly, regarding civil engineering problems, both theories are not suitable for some practical applications. Secondly, fracture mechanics demands the consideration of initial cracks to begin the analysis. Lastly, classic damage models may present an issue known as localisation, what essentially leads to ill-posed problems and mesh-dependent numerical algorithms. Alternatively, a recent theory, called lumped damage mechanics, was proposed in order to achieve good accuracy in actual engineering problems. Such theory applies key concepts from fracture and damage mechanics in plastic hinges. In the light of the foregoing, the main goal of this thesis is the extension of the lumped damage mechanics framework to analyse different engineering problems. So far, lumped damage mechanics was characterised as a simplified methodology to analyse reinforced concrete frames under seismic and monotonic loadings; even with a few contributions on the analysis of local buckling in metallic structures. Therefore, this work extends the lumped damage mechanics framework to analyse reinforced concrete arches, unreinforced concrete structures, high cycle fatigue and continuum problems. The application examples show the accuracy of the proposed methodologies.A descrição acurada do comportamento não linear de estruturas é um problema importante na engenharia. Usualmente, teorias não lineares clássicas, tais como as mecânicas da fratura e do dano, aplicadas a programas de elementos finitos são utilizadas a fim de cumprir aquele propósito. A mecânica da fratura clássica descreve o processo de deterioração estrutural por meio de um pequeno número de fissuras discretas. Esta teoria apresenta boa precisão para estruturas com geometrias simples, poucas fissuras e materiais homogêneos. A mecânica do dano clássica tem sido exitosa na descrição de diversos mecanismos de deterioração em meios contínuos. Apesar de precisas, as abordagens clássicas em fratura e dano apresentam alguns entraves. Primeiramente, tratando-se de problemas da engenharia civil, ambas teorias não são adequadas para aplicações práticas. Em segundo lugar, os modelos clássicos de fratura demandam a consideração de fissuras iniciais para iniciar a análise. Por fim, os modelos clássicos de dano podem apresentar um problema conhecido como localização, o que essencialmente implica em problemas mal colocados e algoritmos com dependência de malha. Alternativamente, uma teoria recente, chamada teoria do dano concentrado, foi proposta a fim de obter boa precisão em problemas reais de engenharia. Tal teoria aplica conceitos-chave das mecânicas da fratura e do dano em rótulas plásticas. À luz do exposto, o principal objetivo desta tese é a extensão da teoria do dano concentrado para analisar diferente problemas da engenharia. Até então, a teoria do dano concentrado era caracterizada como uma metodologia simplificada para analisar pórticos de concreto armado sob solicitações monotônicas ou sísmicas; mesmo com algumas poucas contribuições na análise de instabilidade local em estruturas metálicas. Desta forma, este trabalho estende a teoria do dano concentrado a fim de analisar arcos de concreto armado, estruturas de concreto simples, fadiga de alto ciclo e problemas contínuos. Os exemplos de aplicação mostram a acurácia das metodologias propostas.
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Bordovský, Gabriel. "Simulace lomové zkoušky ve stavebnictví." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2017. http://www.nusl.cz/ntk/nusl-363858.
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In this thesis, a program for fracture test in civil engineering has been optimized. The simulation is used for a validation of the fracture characteristics for blocks of construct material used for historic buildings reconstructure. This thesis illustrates the possibilities of an effective usage of the processor’s potential without the loss of the output quality. The individual parts of the simulation are analyzed and this thesis proposes for the critical sections some possible optimizations such as vectorization or parallel processing. The techniques used in this thesis may be used on similar computing problems and help shorten the required runtime. The prototype of the simulation was able to process the simulation in 7.7 hours. Optimized version is capable to process the same simulation in 2.1 hours on one core or 21 minutes on eight cores. The parallel optimized version is 21 times faster than the prototype.
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Atiezo, Megbeme Komla. "Modélisation multi-échelle de l'endommagement dynamique des matériaux fragiles sous chargements complexes." Electronic Thesis or Diss., Université de Lorraine, 2019. http://www.theses.fr/2019LORR0212.
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Dans cette thèse, la modélisation de l’endommagement et de la rupture dynamique des matériaux quasi-fragiles est proposée en utilisant une approche double-échelle basée sur la méthode d’homogénéisation asymptotique. Des lois d’endommagement dynamique sont établies et des simulations numériques du comportement associé sont effectuées dans les cas de sollicitations correspondants aux trois modes classiques de la Mécanique de la Rupture. Le premier modèle d’endommagement dynamique est proposé pour le chargement en mode de cisaillement antiplan (mode III). La loi d’endommagement est déduite à partir d’un critère énergétique de type Griffith décrivant la propagation des microfissures, en utilisant la méthode de changement d’échelle basée sur des développements asymptotiques. Une étude locale de la réponse macroscopique prédite par ce nouveau modèle est faite pour mettre en évidence l’influence des paramètres, comme la taille de la microstructure et la vitesse de chargement, sur l’évolution de l’endommagement. Les résultats des simulations macroscopiques de rupture dynamique et les instabilités de branchement associées sont présentés et comparés à ceux des observations expérimentales. Le modèle est implémenté dans un code Éléments finis/Différences finies en utilisant le logiciel de calcul Matlab. Des simulations numériques de rupture rapide en mode d’ouverture (mode I) en utilisant une loi d’endommagement dynamique sont ensuite présentées. Le modèle utilisé pour ces simulations, est déduit à partir d’un critère microscopique de type Griffith en mode I en utilisant la méthode d’homogénéisation asymptotique. La loi d’endommagement obtenue est sensible à la vitesse de chargement qui influence le mode de rupture macroscopique. Des simulations numériques sont effectuées afin d’identifier les prédictions du modèle et les résultats obtenus sont comparés aux résultats expérimentaux. Différents tests, comme ceux de traction directe et de l’échantillon en forme de L pour les bétons, les essais d’impact sur des échantillons CCS en PMMA et le test d’impact de Kalthoff pour des roches calcaires sont reproduits numériquement. Ces simulations montrent que la vitesse de chargement détermine essentiellement la trajectoire de rupture macroscopique et la formation des branches associées, en accord avec les résultats expérimentaux. La loi a été implémentée dans le code d’éléments finis Abaqus/Explicit via une sub-routine VUMAT. Un troisième modèle d’endommagement est obtenu pour le mode de cisaillement plan (Mode II) par une démarche de modélisation double-échelle similaire à celle utilisée dans les deux premiers modèles, en tenant compte du contact unilatéral avec frottement sur les lèvres des microfissures. Une étude locale concernant l’effet du chargement de compression et du coefficient du frottement sur les fissures est faite. L’influence des paramètres comme la taille de la microstructure et la vitesse de déformation sur l’évolution de l’endommagement sont étudiés. Ces études sont complétées par des simulations des essais de rupture/frottement sur des échantillons en PMMA en utilisant le logiciel Abaqus/ExplicitIn this thesis, the modeling of dynamic damage and failure of quasi-materials is addressed using a two-scale approach based on the asymptotic homogenization method. Dynamic damage laws are obtained and numerical simulations of the associated behavior are performed for loadings corresponding to the classical three modes of Fracture Mechanics. The first dynamic model of damage is proposed for the anti-plane shear loading case (Mode III). The damage evolution law is deduced from the Griffith’s energy criterion governing the dynamic propagation of microcracks, by using the homogenization method based on asymptotic expansions. A study of the local macroscopic response predicted by the new model is conducted to highlight the influence of parameters, like the size of the microstructure and the loading rate, on the evolution of damage. Results of macroscopic simulations of dynamic failure and the associated branching instabilities are presented and compared with those reported by experimental observations. The model is implemented in a Finite-Elements/Finite-Differences code using the Matlab software environment. Numerical simulations of rapid failure in opening mode (Mode I) are using a dynamic damage law are presented subsequently. The model is deduced from a microscopic Griffith type criterion describing the dynamic mode I propagation of microcracks, using the asymptotic homogenization approach. The resulting damage law is sensitive to the rate of loading that determines the macroscopic failure mode. Numerical simulations are performed in order to identify the model predictions and the obtained numerical results are compared with the experimental ones. Different tests, like the compact tension and L-shape specimen tests for concrete, the compact compression test for the PMMA brittle polymer and the Kalthoff impact test for limestone rocks, are considered in the numerical simulations. These simulations show that the loading rate essentially determines the macroscopic crack trajectory and the associated branching patterns, in agreement with the experimental results. The law has been implemented in a finite element code Abaqus/Explicit via a VUMAT subroutine. A third model of damage is obtained for the in-plane shear mode (Mode II) through a similar double-scale approach by considering unilateral contact with friction conditions on the microcracks lips. A local study concerning the effects of normal compression and of the friction coefficient is carried out. The influence of the size of the microstructure and the rate of loading on damage evolution is analyzed at the local level. These studies are completed by structural failure simulations of PMMA specimens using the Abaqus/Explicit finite element software
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Gu, Hanfeng. "Multigrid methods for 3D composite material simulation and crack propagation modelling based on a phase field method." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEI090/document.
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Avec le développement des techniques d’imagerie telles que la tomographie par rayons X au cours des dernières années, il est maintenant possible de prendre en compte la microstructure réelle dans les simulations des matériaux composites. Cependant, la complexité des composites tels que des fibres inclinées et brisées, les vides, exige un grand nombre des données à l’échelle microscopique pour décrire ces détails et amène ainsi des problèmes difficiles en termes de temps de calcul et de mémoire lors de l’utilisation de méthodes de simulation traditionnelles comme la méthode Eléments Finis. Ces problèmes deviennent encore plus sérieux dans la simulation de l’endommagement, comme la propagation des fissures. Par conséquent, il est nécessaire d’étudier des méthodes numériques plus efficaces pour ce genre de problèmes à grande échelle. La méthode Multigrille (MG) est une méthode qui peut être efficace parce que son coût de calcul est proportionnel au nombre d’inconnues. Dans cette thèse, un solveur de MG efficace pour ces problèmes est développé. La méthode MG est appliquée pour résoudre le problème d’élasticité statique basé sur l’équation de Lamé et aussi le problème de la propagation de fissures basé sur une méthode de champ de phase. La précision des solutions MG est validée par une solution analytique classique d’Eshelby. Ensuite, le solveur MG est développé pour étudier le processus d’homogénéisation des composites et ses solutions sont comparées avec des solutions existantes de la littérature. Après cela, le programme de calcul MG est appliqué pour simuler l’effet de bord libre dans les matériaux composites stratifiés. Une structure stratifiée réelle donnée par tomographie X est d’abord simulé. Enfin, le solveur MG est encore développé, combinant une méthode de champ de phase, pour simuler la rupture quasi-fragile. La méthode MG présente l’efficacité à la fois en temps de calcul et en mémoire pour résoudre les problèmes ci-dessusWith the development of imaging techniques like X-Ray tomography in recent years, it is now possible to take into account the microscopic details in composite material simulations. However, the composites' complex nature such as inclined and broken fibers, voids, requires rich data to describe these details and thus brings challenging problems in terms of computational time and memory when using traditional simulation methods like the Finite Element Method. These problems become even more severe in simulating failure processes like crack propagation. Hence, it is necessary to investigate more efficient numerical methods for this kind of large scale problems. The MultiGrid (MG) method is such an efficient method, as its computational cost is proportional to the number of unknowns. In this thesis, an efficient MG solver is developed for these problems. The MG method is applied to solve the static elasticity problem based on the Lame's equation and the crack propagation problem based on a phase field method. The accuracy of the MG solutions is validated with Eshelby's classic analytic solution. Then the MG solver is developed to investigate the composite homogenization process and its solutions are compared with existing solutions in the literature. After that, the MG solver is applied to simulate the free-edge effect in laminated composites. A real laminated structure using X-Ray tomography is first simulated. At last, the MG solver is further developed, combined with a phase field method, to simulate the brittle crack propagation. The MG method demonstrates its efficiency both in time and memory dimensions for solving the above problems
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Racca, Simone. "Some models of crack growth in brittle materials." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4809.
Full textAbstract:
This work is devoted to the study of models of fractures growth in brittle elastic materials; it collects the results obtained during my Ph.D., that are contained in [77, 76, 78]. We consider quasi-static rate-independent models, as well as rate-dependent ones and the case in which the first ones are limits of the second ones when certain physical parameters vanish. The term quasistatic means that, at each instant, the system is assumed to be in equilibrium with respect to its time-dependent data; this setting is typical of systems whose internal time scale is much smaller than that of the loadings. By rate-independent system we mean that, if the time-dependent data are rescaled by a strictly monotone increasing function, then the system reacts by rescaling the solutions in the same manner.
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Saloustros, Savvas. "Tracking localized cracks in the computational analysis of masonry structures." Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/461714.
Full textAbstract:
Numerical methods aid significantly the engineering efforts towards the conservation of existing masonry structures and the design of new ones. Among them, macro-mechanical finite element methods based on the smeared crack approach are commonly preferred as an affordable choice for the analysis of large masonry structures. Nevertheless, they usu-ally result in a non-realistic representation of damage as smeared over large areas of the structure, which hampers the correct interpretation of the damage pattern. Additionally, a more critical pathology of this approach is the mesh-dependency, which influences nota-bly the safety and stability predictions.
To overcome these limitations, this thesis proposes a novel computational tool based on the {enrichment} of the classical smeared crack approach with a local tracking algorithm. The objective of this localized damage model is the realistic and efficient non-linear anal-ysis of masonry structures with an enhanced representation of cracking.
The non-linear behaviour of masonry is simulated through the adoption of a continuum damage mechanics model with two damage indices, allowing the differentiation between the tensile and compressive mechanical responses of masonry. In this context, a novel explicit formulation for the evolution of irreversible strains is proposed and implemented. Two new expressions are derived for the regularization of the tensile and compressive softening responses according to the crack-band approach, ensuring the mesh-size objec-tivity of the damage model.
The simulation of the structural behaviour of masonry structures under versatile loading and boundary conditions necessitates some developments in the context of local tracking algorithms. To this end, this thesis presents the enhancement of local tracking algorithms with novel procedures that make possible the simulation of multiple, arbitrary and inter-secting cracking under monotonic and cyclic loading. Additionally, the effect of different crack propagation criteria is investigated and the selection among more than one potential failure planes is tackled.
The proposed localized damage model is validated through the simulation of a series of structural examples. These vary from small-scale tests on concrete specimens with few dominant cracks, to medium and large-scale masonry structures with multiple tensile, shear and flexural cracking. The analyses are compared with analytical, experimental and numerical results obtained with alternative methods available in the literature. Overall, the localized damage model developed in this thesis largely improves the mesh-independency of the classical smeared crack approach and reproduces crack patterns and collapse mech-anisms in an efficient and realistic way.Los métodos numéricos son decisivos en la ingeniería para la conservación de estructuras de mampostería existentes y el diseño de estructuras nuevas. Entre ellos, los métodos macro-mecánicos de elementos finitos, basados en el concepto de fisuras distribuidas, son habitualmente los preferidos como opción asequible para el análisis de grandes estructuras de mampostería. Sin embargo, suelen resultar en a una representación poco realista del daño, distribuido en grandes áreas de la estructura, lo que impide la correcta interpretación del patrón de daño. Además, esta metodología presenta una patología más crítica, la dependencia de la malla, que influye notablemente en las predicciones de seguridad y estabilidad. Para superar estas limitaciones, esta tesis propone una nueva herramienta numérica basada en el enriquecimiento del clásico enfoque de fisuras distribuidas con un algoritmo de trazado local. El objetivo de este modelo de daño localizado es el análisis no-lineal de las estructuras de mampostería de manera realista y eficiente con una representación mejora-da de fisuras. El comportamiento no lineal de la mampostería se simula a través de la adopción de un modelo de mecánica de daño continuo con dos índices de daño, permitiendo la diferenciación entre las respuestas mecánicas de tensión y compresión de la mampostería. En este contexto, se propone e implementa una nueva formulación explícita para la evolución de deformaciones irreversibles. Se derivan dos nuevas expresiones para la regularización del ablandamiento de tracción y compresión según el ancho de banda de la fisura, garantizan-do la objetividad del modelo de daño al respecto del tamaño de la malla. La simulación del comportamiento estructural de las estructuras de mampostería en condiciones de carga y contorno generales precisa de algunos desarrollos en el contexto de los algoritmos locales de trazado. Con este objetivo, se presenta la mejora de los algoritmos locales de trazado con nuevos procedimientos que posibilitan la simulación de fisuración múltiple, arbitraria e secante bajo cargas monótonas y cíclicas. Además, se investiga el efecto de diferentes criterios de propagación de fisuras y se aborda la selección entre más de un plano de falla posible. El modelo de daño localizado propuesto se valida mediante la simulación de una serie de ejemplos estructurales. Éstos van desde pruebas a pequeña escala en probetas de hormigón, con pocas fisuras dominantes, hasta estructuras de mampostería de mediana y gran escala con fisuración múltiple de tracción, de cortante y de flexión. Los análisis se comparan con los resultados analíticos, experimentales y numéricos obtenidos con métodos alternativos disponibles en la literatura. El modelo de daño localizado mejora en gran medida la independencia de la malla del clásico método de fisuras distribuidas y reproduce patrones de daño y mecanismos de colapso de una manera eficiente y realista
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Viszlay, Viliam. "Ohýbaná tělesa: Numerická podpora v software ANSYS." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2016. http://www.nusl.cz/ntk/nusl-240183.
Full textAbstract:
The aim of the thesis is the investigation of fracture-mechanics parameters on specimens made of quasi-brittle materials. The principles of two-parameter fracture mechanics are used. Couple of numerical simulations were done and their outputs are used for two main analysed specimen geometries. For simulations the finite element method software ANSYS is used. In the first part, the thesis focuses on bended specimens. The influence of different geometric parameters on fracture mechanics behaviour of cracked specimen is investigated. For model calibration the outputs of other authors are used. In the second part the specimens for modified compact-tension test (CT test) are analysed. Similar to the first part, the influence of geometric parameters of the specimen (in this case, the specimen size) on fracture mechanics parameters were investigated. The modified CT test was derived from CT test which is commonly used for metal materials testing as the suitable geometry for cement-based composite materials testing. The outputs of both parts are calibration polynomials, which are expressions obtained for different specimen geometries, giving the value of fracture mechanics parameter as the function of specimen geometry. As the example, calibration curves are used to obtain fracture toughness of tested material using the outputs from recent experiment.