Academic literature on the topic 'Representative Volume Element (RVE)'
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Journal articles on the topic "Representative Volume Element (RVE)"
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Shahzamanian, M. M., and W. J. Basirun. "Modeling of Cementitious Representative Volume Element with Additives." Journal of Multiscale Modelling 08, no. 02 (2017): 1750003. http://dx.doi.org/10.1142/s1756973717500032.
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CEMHYD3D has been employed to simulate the representative volume element (RVE) of cementitious systems (Type I cement) containing fly ash (Class F) through a voxel-based finite element analysis (FEA) approach. Three-dimensional microstructures composed of voxels are generated for a heterogeneous cementitious material consisting of various constituent phases. The primary focus is to simulate a cementitious RVE containing fly ash and to present the homogenized macromechanical properties obtained from its analysis. Simple kinematic uniform boundary conditions as well as periodic boundary conditions were imposed on the RVE to obtain the principal and shear moduli. Our current work considers the effect of fly ash percentage on the elastic properties based on the mass and volume replacements. RVEs with lengths of 50, 100 and 200[Formula: see text][Formula: see text] at different degrees of hydration are generated, and the elastic properties are modeled and simulated. In general, the elastic properties of a cementitious RVE with fly ash replacement for cement based on mass and volume differ from each other. Moreover, the finite element (FE) mesh density effect is studied. Results indicate that mechanical properties decrease with increasing mesh density.
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Ostoja-Starzewski, M. "Microstructural Randomness Versus Representative Volume Element in Thermomechanics." Journal of Applied Mechanics 69, no. 1 (2001): 25–35. http://dx.doi.org/10.1115/1.1410366.
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Continuum thermomechanics hinges on the concept of a representative volume element (RVE), which is well defined in two situations only: (i) unit cell in a periodic microstructure, and (ii) statistically representative volume containing a very large (mathematically infinite) set of microscale elements (e.g., grains). Response of finite domains of material, however, displays statistical scatter and is dependent on the scale and boundary conditions. In order to accomplish stochastic homogenization of material response, scale-dependent hierarchies of bounds are extended to dissipative/irreversible phenomena within the framework of thermomechanics with internal variables. In particular, the free-energy function and the dissipation function become stochastic functionals whose scatter tends to decrease to zero as the material volume is increased. These functionals are linked to their duals via Legendre transforms either in the spaces of ensemble average velocities or ensemble-average dissipative forces. In the limit of infinite volumes (RVE limit (ii) above) all the functionals become deterministic, and classical Legendre transforms of deterministic thermomechanics hold. As an application, stochastic continuum damage mechanics of elastic-brittle solids is developed.
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Kudrjavčeva, Ljudmila T., and Milan V. Mićunović. "ON DIFFUSE INSTABILITY OF ORTHOTROPIC VISCOPLASTIC PLATES." Journal of the Serbian Society for Computational Mechanics 15, no. 2 (2021): 101–10. http://dx.doi.org/10.24874/jsscm.2021.15.02.10.
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Elastic strain is covered by the effective medium homogenization method inside a representative volume element (RVE). It has an incremental quasi rate-independent (QRI) form obtained by the endochronic concept of thermodynamic time. The rate dependence takes place by means of stress rate dependent value of the initial yield stress. Free meso rotations and constrained micro rotations within a representative volume element (RVE) are assumed. A comparison between QRI and J2 diffuse instability equations is presented for orthotropic materials. A new QRI nonlinear evolution equation for orthotropic materials is derived by tensor function representation with Spencer-Boehler structural tensors.
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Nasser, Houssein, A. Deraemaeker, and Salim Belouettar. "Electric Field Distribution in Macro Fiber Composite Using Interdigitated Electrodes." Advanced Materials Research 47-50 (June 2008): 1173–76. http://dx.doi.org/10.4028/www.scientific.net/amr.47-50.1173.
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In this paper, an attempt has been made to understand the electric field distribution in the Representative Volume Element (RVE) of the Macro Fiber Composite (MFC) using interdigitated electrodes IDEs. Since the magnitude of the electric field within the Representative Volume Element (RVE) using the IDEs is not uniform, an electrostatic study of the electric field behavior is carried out. An approximate RVE model with conventional electrodes, which is useful for the analytical solution, has been proposed instead of the RVE model with IDEs. Finally, the results obtained by the proposed analytical solution are compared to those obtained numericaly using the RVE model with IDEs.
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TANG, C., M. A. SHEIKH, and D. R. HAYHURST. "FINITE ELEMENT MODELING OF TRANSVERSE DEFORMATION IN REPRESENTATIVE VOLUME ELEMENTS OF CERAMIC MATRIX COMPOSITES (CMCs)." Journal of Multiscale Modelling 02, no. 01n02 (2010): 107–26. http://dx.doi.org/10.1142/s1756973710000308.
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The paper reports the use of the finite element method to model longitudinal and transverse deformation of representative volume elements (RVE) of ceramic matrix composites subjected to uniaxial loading parallel to fibers. Cohesive elements have been used to model two forms of damage: fracture initiation and propagation both within the matrix, and along the fiber–matrix interface. From the knowledge of the constituent materials behavior, the FE technique has been used to predict the stress–strain behavior and the variation of Poisson's ratio of the RVE due to these two damage forms; but the model does not cater for fiber failure. The RVE predictions have been benchmarked against experimental results for Nicalon-CAS material and good agreement has been obtained. Comparison of the predicted behavior of the single Nicalon-CAS RVE with experimental data for unidirectional tows indicates that the stress–strain curve is predominantly controlled by the Weibull distribution of fiber failure stress, while the degradation of Poisson's ratio is determined by the Weibull distribution of interfacial strength. The same approach has been used for a HITCO C/C material for which transverse deformation behavior is unknown. The results for the HITCO C/C material, as for the Nicalon-CAS, show that the fiber behavior determines the ultimate failure of the RVE, and that interface debonding is the controlling mechanism for the variation of the Poisson ratio with axial strain.
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Zhang, Nan, and Cheng Hong Duan. "Property Prediction of Composites with Different Fiber Volume Fractions by Representative Volume Element Method." Applied Mechanics and Materials 275-277 (January 2013): 1605–9. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.1605.
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In this paper, a representative volume element (RVE) model of composites with different fiber volume fraction is established by ANSYS finite element software. The stiffness matrix of the RVE model can be calculated by studying its stress field, and then the elastic properties of composites could be obtained. By comparing with the results from NASA empirical equation, the reliability of the method can be proved. This is a new way to predict the elastic properties of composites.
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Liu, Cheng Jun, Yi Xia Zhang, and Chun Hui Yang. "Representative Volume Element-Based Modelling of Closed-Cell Aluminum Foams ." Applied Mechanics and Materials 846 (July 2016): 530–34. http://dx.doi.org/10.4028/www.scientific.net/amm.846.530.
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This paper presents a representative volume element (RVE)-based modelling method to capture the mechanical behaviour of aluminum foams under compressive loadings. Octadecahedron is selected as a geometric basis shape to form closed cells of the aluminum foams in the microstructured RVE model to simulate the mechanical behaviour under compressive loadings. The stress-strain relationship obtained from the numerical modelling is compared to that from experimental study and agreements between these results demonstrate the validity of the proposed RVE model. Through observing the deformation evolution of cells during a compressive loading process, the failure modes of aluminum foams are identified and analysed using the proposed RVE model. Further the influence of strain rate on the mechanical behaviour of aluminum foams under compressive loadings is numerically studied via a parametric study.
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Ballard, Michael K., and John D. Whitcomb. "Effective use of cohesive zone-based models for the prediction of progressive damage at the fiber/matrix scale." Journal of Composite Materials 51, no. 5 (2016): 649–69. http://dx.doi.org/10.1177/0021998316651127.
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The onset and growth of damage in fiber/matrix composites under transverse loads were modelled using cohesive elements and representative volume elements of randomly arranged fibers. Switching between iterative schemes, using an appropriate tolerance and load increment size, and using an extrapolated solution as an initial guess for load increments led to over an order of magnitude reduction in the solution time. The effect of several model parameters on the failure properties for the next larger scale was studied. The crack path did exhibit a dependence on the mesh, but the RVE strength and amount of dissipated energy in the representative volume element did not vary more than 4% for any of the mesh refinements considered. Periodic boundary conditions minimally interfered with the localization of damage when the localized band of damage did not extend across the entire RVE or when the damage naturally localized parallel to a boundary or diagonal of the representative volume element. A local method for quantifying the energy dissipated within the representative volume element was proposed, which provides an improved accuracy and flexibility. An approach to precisely define the dominant crack was given, which allowed the energy dissipate diffusely and along the dominant crack to be separated. It was shown that the predicted critical strain energy release rate for the representative volume element was sensitive to the representative volume element unless the diffusely dissipated energy was accounted for separately. The proposed technique for calculating failure properties within a multiscale framework has the potential to be applied to other damage models.
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Du, X., and M. Ostoja-Starzewski. "On the size of representative volume element for Darcy law in random media." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 462, no. 2074 (2006): 2949–63. http://dx.doi.org/10.1098/rspa.2006.1704.
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Most studies of effective properties of random heterogeneous materials are based on the assumption of the existence of a representative volume element (RVE), without quantitatively specifying its size L relative to that of the micro-heterogeneity d . In this paper, we study the finite-size scaling trend to RVE of the Darcy law for Stokesian flow in random porous media, without invoking any periodic structure assumptions, but only assuming the microstructure's statistics to be spatially homogeneous and ergodic. By analogy to the existing methodology in thermomechanics of random materials, we first formulate a Hill–Mandel condition for the Darcy flow velocity and pressure gradient fields. This dictates uniform Neumann and Dirichlet boundary conditions, which, with the help of two variational principles, lead to scale-dependent hierarchies on effective (RVE level) permeability. To quantitatively assess the scaling trend towards the RVE, these hierarchies are computed for various porosities of random disc systems, where the disc centres are generated by a planar hard-core Poisson point field. Overall, it turns out that the higher is the density of random discs—or, equivalently, the narrower are the micro-channels in the system—the smaller is the size of RVE pertaining to the Darcy law.
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Liu, Jianjun, Mingyang Wu, Zhengwen Zhu, and Zuliang Shao. "A Study on the Mechanical Properties of the Representative Volume Element in Fractal Porous Media." Geofluids 2017 (2017): 1–10. http://dx.doi.org/10.1155/2017/7905218.
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Natural porous structure is extremely complex, and it is of great significance to study the macroscopic mechanical response of the representative volume element (RVE) with the microstructure of porous media. The real porous media RVE is generated by an improved quartet structure generation set (QSGS), and the connectivity of the reconstructed porous media models is analyzed. The fractal dimension of the RVE is calculated by the box-counting method, which considers the different porosity, different fractal dimension, and different mechanical properties of the matrix. Thus, the stress-strain curves of the RVE in the elastoplastic stage under different conditions are obtained. The results show that when the matrix mechanics are consistent, the mechanical properties of the porous media RVE are negatively correlated with the porosity and fractal dimension; when the difference between the porosity and fractal dimension increases, the trend is more obvious. The mechanical properties of the RVE have a positive correlation with the modulus of elasticity of the matrix, though the correlation with Poisson’s ratio of the matrix is weak. The fractal dimension of complex porous media can better predict the RVE mechanical characteristics than the porosity.
Dissertations / Theses on the topic "Representative Volume Element (RVE)"
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Fusari, Elena. "Studio e Realizzazione del Modello RVE (Representative Volume Element) per componenti polimerici realizzati in stampa 3D FDM." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/24632/.
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A fianco ai metodi più tradizionali, fin ora utilizzati, le tecnologie additive hanno subito negli ultimi anni una notevole evoluzione nella produzione di componenti. Esse permettono un ampio di range di applicazioni utilizzando materiali differenti in base al settore di applicazione. In particolare, la stampa 3D FDM (Fused Deposition Modeling) rappresenta uno dei processi tecnologici additivi più diffusi ed economicamente più competitivi. Gli attuali metodi di analisi agli elementi finiti (FEM) e le tecnologie CAE (Computer-Aided Engineering) non sono in grado di studiare modelli 3D di componenti stampati, dal momento che il risultato finale dipende dai parametri di processo e ambientali. Per questo motivo, è necessario uno studio approfondito della meso struttura del componente stampato per estendere l’analisi FEM anche a questa tipologia di componenti. Lo scopo del lavoro proposto è di creare un elemento omogeneo che rappresenti accuratamente il comportamento di un componente realizzato in stampa 3D FDM, questo avviene attraverso la definizione e l’analisi di un volume rappresentativo (RVE). Attraverso la tecnica dell’omogeneizzazione, il volume definito riassume le principali caratteristiche meccaniche della struttura stampata, permettendo nuove analisi e ottimizzazioni. Questo approccio permette di realizzare delle analisi FEM sui componenti da stampare e di predire le proprietà meccaniche dei componenti a partire da determinati parametri di stampa, permettendo così alla tecnologia FDM di diventare sempre di più uno dei principali processi industriali a basso costo.
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Hitti, Karim. "Direct numerical simulation of complex Representative Volume Elements (RVEs) : Generation, Resolution and Homogenization." Paris, ENMP, 2011. http://www.theses.fr/2011ENMP0054.
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L'influence des hétérogénéités microstructurales sur le comportement d'un matériau est devenue une problématique industrielle de première importance, cet état de fait explique l'engouement actuel pour la prise en compte de ces hétérogénéités dans le cadre de la modélisation numérique. Ainsi, de nombreuses méthodes pour représenter de manière digitale un matériau virtuel statistiquement équivalent à la microstructure réelle et pour connecter cette représentation à des calculs éléments finis se sont développées ces dernières années. Les travaux réalisés durant cette thèse s'inscrivent en grande partie dans cette thématique. En effet, un générateur de microstructures virtuelles permettant de générer à la fois des microstructures polyédriques ou sphériques a été développé. Ce générateur est basé sur les diagrammes de Laguerre et une méthode frontale de remplissage, une approche level-set pour l'immersion de ces microstructures dans un maillage éléments finis et une technique d'adaptation anisotrope de maillage pour assurer une grande précision lors de cette immersion mais également lors de la réalisation de simulations éléments finis sur ces microstructures. La capacité de ces outils à respecter des données statistiques concernant les microstructures considérées est assurée par le couplage d'une méthode frontale à une méthode d'optimisation des défauts locaux selon la nature de la microstructure considérée. Une technique de coloration de graphe est également appliquée afin de limiter le nombre de fonctions level-set nécessaires à l'adaptation de maillage. En outre, le coût élevé d'une simulation micro-macro entièrement couplée peut-être significativement réduite en limitant les calculs à une analyse entièrement découplée. Dans ce contexte, la réponse d'un Volume Élémentaire Représentatif (VER) soumis à des conditions aux limites représentatives de ce que subit la matière en un point précis d'un calcul macroscopique reste l'approche la plus complète à l'heure actuelle. Dans le cadre de ce travail, nous nous sommes intéressés à deux types de VER pour deux applications différentes : la déformation de VERs de mousses polyédriques élastiques et le calcul du tenseur de perméabilité pour des VERs composés de fibres cylindriques hétérogènes mais monodirectionnelles. Plus précisément, pour la première de ces applications, des cas de compression biaxiale de mousses élastiques à cellules fermées en nids d'abeille ou irrégulières sont modélisés comme un problème d'interaction fluide structure (IFS) entre un fluide compressible (l'air à l'intérieur des cellules) et un solide élastique compressible (le squelette de la mousse). Une formulation monolithique est utilisée pour résoudre ce problème en regroupant les équations d'états régissant le solide et le fluide en un seul jeu d'équations résolu sur un maillage unique discrétisant les deux phases. Une telle stratégie donne lieu, pour la partie solide, à l'apparition d'un tenseur d'extra-contrainte dans les équations de Navier-Stokes. Ces équations sont ensuite résolues par une méthode éléments finis mixte avec une interpolation de type P1+/P1. Concernant la deuxième application, des écoulements dans des milieux fibreux sont simulés en considérant les fibres comme rigides. Ici encore, une formulation monolithique est adoptée. Ainsi, les équations de Stokes sont résolues sur l'ensemble du domaine de calcul en utilisant une méthode de pénalisation. Par homogénéisation, la loi de Darcy est utilisée pour obtenir le tenseur de perméabilité<br>The influence of microstructural heterogeneities on material processing is an issue of prime importance, which explains the need to generate a digital material, statistically equivalent to the considered microstructure, and to connect this digital description to finite element (FE) calculations. For this reason, a multi-physical virtual microstructure generator which can simultaneously generate cells and spherical particles is created. This generator is based on Laguerre tessellations and advancing front method, level-set description of interfaces and anisotropic meshing adaptation. The capability of its tools to respect statistical data could be insured by the advancing front method coupled with an optimization procedure depending on the nature of the considered microstructure. Moreover, a graph coloration technique is applied in order to reduce the number of level-set functions used in anisotropic mesh adaptation. Furthermore, the high cost of a fully coupled micro-macro simulation can be significantly reduced when restricting the attention to a fully uncoupled analysis. In this context, the response of the Representative Volume Element (RVE) when subject to a given macroscopic loading path is of the main interest. RVEs of elastic Voronoï honeycombs and fiber arrays are considered in the manuscript. The first is used to simulate the compression of an elastic foam subject to a biaxial load. In this case, a fluid structure interaction (FSI) problem occurs between a compressible fluid, the air inside the foam's cells, and an elastic compressible solid, the foam's skeleton. A monolithic formulation is used for solving this problem where a single grid is considered and one set of equations with different material properties is solved. Such strategy gives rise to an extra stress tensor in the Navier-Stokes equations, which are solved by a mixed finite element method with a P1+/P1 interpolation, coming from the presence of the structure in the fluid. The second RVE is used to compute the permeability of disordered fiber arrays. In this case, flows through unidirectional fibrous media are simulated and the fibers are considered as rigid discs. Also, a monolithic formulation is used for solving this problem. Therefore the Stokes equations are solved in the whole domain using a penalization method. After using volume average techniques, Darcy's law is obtained giving the possibility to compute the permeability tensor
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Baghbanan, Alireza. "Scale and Stress Effects on Hydro-Mechanical Properties of Fractured Rock Masses." Doctoral thesis, KTH, Teknisk geologi och geofysik, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4772.
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In this thesis, the effects of size and stress on permeability, deformability and strength of fractured rock masses are investigated. A comparison study was carried out to examine the effects of considering, or not considering, the correlation between distributions of fracture apertures and fracture trace lengths on the hydro-mechanical behavior of fractured rocks. The basic concepts used are the fundamental principles of the general theory of elasticity, Representative Elementary Volume (REV), the tensor of equivalent permeability, and the strength criteria of the fractured rocks. Due to the size and stress dependence of the hydro-mechanical properties of rock fractures, the overall effective (or equivalent) hydro-mechanical properties of the fractured rocks are also size and stress-dependent. However, such dependence cannot be readily investigated in laboratory using small samples, and so numerical modeling becomes a necessary tool for estimating their impacts. In this study, a closed-form relation is established for representing the correlation between a truncated lognormal distribution of fracture apertures and a truncated power law distribution of trace lengths, as obtained from field mapping. Furthermore, a new nonlinear algorithm is developed for predicting the relationship between normal stress and normal displacement of fractures, based on the Bandis model and the correlation between aperture and length. A large number of stochastic Discrete Fracture Network (DFN) models of varying sizes were extracted from some generated large-sized parent realizations based on a realistic fracture system description from a site investigation programme at Sellafield, UK, for calculating the REV of hydro-mechanical properties of fractured rocks. Rotated DFN models were also generated and used for evaluation of the distributions of directional permeabilities, such that tensors of equivalent permeability could be established based on stochastically established REVs. The stress-dependence of the permeability and the stress-displacement behaviour were then investigated using models of REV sizes. The Discrete Element Method (DEM) was used for numerical simulation of the fluid flow, deformability properties and mechanical strength behavior of fractured rocks. The results show significant scale-dependency of rock permeability, deformability and strength, and its variation when the correlation between aperture and trace length of fractures are concerned, with the overall permeability and deformability more controlled by dominating fractures with larger apertures and higher transmissivity and deformability, compared with fracture network models having uniform aperture. As the second moment of aperture distribution increases, a fractured rock mass shows more discrete behavior and an REV is established in smaller value of second moment with much larger model size, compared with the models with uniform fracture aperture. When the fracture aperture pattern is more scattered, the overall permeability, Young’s modulus and mechanical strength change significantly. The effect of stress on permeability and fluid flow patterns in fractured rock is significant and can lead to the existence or non-existence of a permeability tensor. Stress changes the fluid flow patterns and can cause significant channeling and the permeability tensor, and REV may be destroyed or re-established at different applied stress conditions. With an increase in the confining stress on the DEM models, the strength is increased. Compared with the Hoek-Brown criterion, the Mohr-Coulomb strength envelope provides a better fit to the results of numerical biaxial compression tests, with significant changes of the strength characteristic parameters occurring when the second moment of the aperture distribution is increased.<br>QC 20100702
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Noorian-Bidgoli, Majid. "Strength and deformability of fractured rocks." Doctoral thesis, KTH, Mark- och vattenteknik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-155719.
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This thesis presents a systematic numerical modeling framework to simulate the stress-deformation and coupled stress-deformation-flow processes by performing uniaxial and biaxial compressive tests on fractured rock models with considering the effects of different loading conditions, different loading directions (anisotropy), and coupled hydro-mechanical processes for evaluating strength and deformability behavior of fractured rocks. By using code UDEC of discrete element method (DEM), a series of numerical experiments were conducted on discrete fracture network models (DFN) at an established representative elementary volume (REV), based on realistic geometrical and mechanical data of fracture systems from field mapping at Sellafield, UK. The results were used to estimate the equivalent Young’s modulus and Poisson’s ratio and to fit the Mohr-Coulomb and Hoek-Brown failure criteria, represented by equivalent material properties defining these two criteria. The results demonstrate that strength and deformation parameters of fractured rocks are dependent on confining pressures, loading directions, water pressure, and mechanical and hydraulic boundary conditions. Fractured rocks behave nonlinearly, represented by their elasto-plastic behavior with a strain hardening trend. Fluid flow analysis in fractured rocks under hydro-mechanical loading conditions show an important impact of water pressure on the strength and deformability parameters of fractured rocks, due to the effective stress phenomenon, but the values of stress and strength reduction may or may not equal to the magnitude of water pressure, due to the influence of fracture system complexity. Stochastic analysis indicates that the strength and deformation properties of fractured rocks have ranges of values instead of fixed values, hence such analyses should be considered especially in cases where there is significant scatter in the rock and fracture parameters. These scientific achievements can improve our understanding of fractured rocks’ hydro-mechanical behavior and are useful for the design of large-scale in-situ experiments with large volumes of fractured rocks, considering coupled stress-deformation-flow processes in engineering practice.<br><p>QC 20141111</p>
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Kanit, Toufik. "Notion of representative volume element for heterogeneous materials: statistical and numerical approach." Phd thesis, École Nationale Supérieure des Mines de Paris, 2003. http://tel.archives-ouvertes.fr/tel-00005751.
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Hill, Richard Lee Sr. "Development of a representative volume element of lithium-ion batteries for thermo-mechanical integrity." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/67781.
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Thesis (Nav. E. and S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2011.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (p. 67-69).<br>The importance of Lithium-ion batteries continues to grow with the introduction of more electronic devices, electric cars, and energy storage. Yet the optimization approach taken by the manufacturers and system designers is one of test and build, an approach that nearly every other industry has long abandoned. A computational model is required to reduce the expensive build-test cycle and allow safer, cheaper batteries to be built. The path to building this computational model will involve many different processes and one of those processes dictates the homogenizing of the interior of the battery casing by treating the interior as a homogenized Representative Volume Element. This study explains this process and outlines a procedure for the development of this particular model for both cylindrical and prismatic / pouch cells. Over twenty different mechanical tests were performed on fully-discharged cylindrical and pouched / prismatic lithium-ion batteries, in casings and without casings under multiple loading conditions. These included lateral indentation by a rod, axial compression, through-thickness compression, in-plane unconfined compression, in-plane confined compression, hemispherical punch indentation and three-point bending. Extensive testing on the battery cell and jelly roll of 18650 lithium ion cylindrical cell, combined with the use of analytical solutions to estimate material properties of the cell, yielded the development of a finite element model. It was found that the suitably calibrated model of high density compressible foam provided a very good prediction of the crash behavior of cylindrical battery cell subjected to high intensity lateral and axial loads. For the prismatic / pouch cell, the measured load-displacement data allowed calculation of the individual compression stress-strain curves for the separator, the active anode and cathode materials. The average stress-volumetric strain relation was derived from averaging the properties of individual layers as well as from direct measurement on the bare cell. This information was then used as an input to the FE model of the cell. The model was composed of shell elements representing the Al and Cu foil and solid elements for the active material with a binder lumped together with the separator. Very good correlation was obtained between LS-Dyna numerical simulation and test results for the through-thickness compression, punch indentation and confined compression. Closed form solutions were also derived for the latter three problems which helped explain the underlying physics and identified important groups of parameters. It was also demonstrated that a thin Mylar pouch enclosure provided considerable reinforcement and in some cases changed the deformation and failure mechanism. This paper reports on the results generated for the Li-ion Battery Consortium at MIT.<br>by Richard Lee Hill, Sr.<br>Nav.E.and S.M.
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Willoughby, Natasha. "Dynamic homogenization for the elastic properties of periodic and random composites." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/dynamic-homogenization-for-the-elastic-properties-of-periodic-and-random-composites(da82e607-bc1f-40e9-8e62-ec5fbca1f68f).html.
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In this thesis we are interested in the propagation of low-frequency linear elastic waves through composite materials. We use a variety of dynamic homogenization techniques to find the effective elastic properties of some composites. We consider composites with isotropic phases for ease of exposition but the theory could easily be extended to anisotropic inclusions or host.We use a Representative Volume Element approach with the Method of Asymptotic Homogenization to model a random fibre-reinforced composite. The fibres are all aligned in the same direction and are taken to be of infinite extent, so the composite is essentially two-dimensional. For a random composite we have considered the anti-plane case for SH wave propagation and the in-plane case for P and SV elastic wave propagation, extending the previous published work of Parnell and Abrahams (2006), (2008a), in which a periodic fibre-reinforced composite was studied. We also show, for a simple example, that it is possible to extend the Representative Volume Element method to a three-dimensional particulate composite.In this thesis an Integral Equation Method for homogenization is also studied, with application to periodic fibre-reinforced composites. We have extended the work of Parnell and Abrahams (2008b), which considered SH wave propagation only, to the case of P and SV wave propagation.
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Zhou, Zhiqiang. "Multiple-Scale Numerical Analysis of Composites Based on Augmented Finite Element Method." Scholarly Repository, 2010. http://scholarlyrepository.miami.edu/oa_dissertations/75.
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Advanced composites are playing a rapidly increasing role in all fields of material and structural related engineering practices. Damage tolerance analysis must be a critical integral part of composite structural design. The predictive capabilities of existing models have met with limited success because they typically can not account for multiple damage evolution and their coupling. As a result, current composite design is heavily dependent upon lengthy and costly test programs and empirical design methods. There is an urgent need for efficient numerical tools that are capable of analyzing the progressive failure caused by nonlinearly coupled, multiple damage evolution in composite materials. Such numerical tools are a necessity in achieving virtual testing of composites and other heterogeneous materials. In this thesis, an advanced finite element method named augmented finite element method (A-FEM) has been developed. This method is capable of incorporating nonlinear cohesive damage descriptions for major damage modes observed in composite materials. It also allows for arbitrary nucleation and propagation of such cohesive damages upon satisfactory of prescribed initiation and propagation criterion. Major advantages of the A-FEM include: 1) arbitrary cohesive cracking without the need of remeshing; 2) full compatibility with existing FEM packages; and 3) easy inclusion of intra-element material heterogeneity. The numerical capabilities of the A-FEM have been demonstrated through direct comparisons between prediction results and experimental observations of typical composite tests including 3-point bending of unidirectional laminates, open-hole tension of quasi-isotropic laminates, and double-notched tension of orthogonal laminates. In all these tests, A-FEM can predict not only the qualitative damage patterns but also quantitatively the nonlinear stress-strain curves and other history-dependent results. The excellent numerical capability of A-FEM in accurately accounting for multiple cracking in composites enables the use of A-FEM as a multi-scale numerical platform for virtual testing of composites. This has been demonstrated by a series of representative volume element (RVE) analyses which explicitly considered microscopic matrix cracking and fiber matrix interface debonding. In these cases the A-FEM successfully predicted the cohesive failure descriptions which can be used for macroscopic composite failure analyses. At the sublaminate scale, the problem of a transverse tunneling crack and its induced local delamination has been studied in detail. Two major coupling modes, which depends on the mode-I to mode-II fracture toughness ratio and cohesive strength values, has been revealed and their implications in composite engineering has been fully discussed. Finally, future improvements to the A-FEM so that it can be more powerful in serving as a numerical platform for virtual testing of composites are discussed.
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Min, Ki-Bok. "Determination of equivalent hydraulic and mechanical properties of fractured rock masses using the distinct element method." Licentiate thesis, KTH, Land and Water Resources Engineering, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-1550.
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<p>The equivalent continuum approach uses equivalent propertiesof rock mass as the input data for a continuum analysis. Thisis a common modeling method used in the field of rock mechanicsand hydrogeology. However, there are still unresolvedquestions; how can the equivalent properties be determined andis the equivalent continuum approach suitable for modeling thediscontinuous fractured rock mass.</p><p>The purpose of this paper is to establish a methodology todetermine the equivalent hydraulic and mechanical properties offractured rock masses by explicit representations of stochasticfracture systems, to investigate the scale-dependency of theproperties, and to investigate the conditions for theapplication of the equivalent continuum approach for thefractured rock masses. Geological data used for this study arefrom the site characterization of Sellafield, Cumbria, UK. Aprogram for the generation of stochastic Discrete FractureNetwork (DFN) is developed for the realization of fractureinformation and ten parent DFN models are constructed based onthe location, trace length, orientation and density offractures. Square models with the sizes varying from 0.25 m× 0.25 m to 10 m × 10 m are cut from the center ofthe each parent network to be used for the scale dependencyinvestigation. A series of the models in a parent network arerotated in 30 degrees interval to be used for investigation oftensor characteristic. The twodimensional distinct elementprogram, UDEC, was used to calculate the equivalentpermeability and compliance tensors based on generalizedDarcys law and general theory of anisotropic elasticity.Two criteria for the applicability of equivalent continuumapproach were established from the investigation: i) theexistence of properly defined REV (Representative ElementaryVolume) and ii) existence of the tensor in describing theconstitutive equation of fractured rock The equivalentcontinuum assumption cannot be accepted if any one of the abovetwo criteria is not met. Coefficient of variation and meanprediction error is suggested for the measures toquantitatively evaluate the errors involved in scale dependencyand tensor characteristic evaluation.</p><p>Equivalent permeability and mechanical properties (includingelastic modulus and Poissons ratios) determined onrealistic fracture network show that the presence of fracturehas a significant effect on the equivalent properties. Theresults of permeability, elastic moduli and Poisson's ratioshow that they narrow down with the increase of scale andmaintain constant range after a certain scales with someacceptable variation. Furthermore, Investigations of thepermeability tensor and compliance tensor in the rotated modelshow that their tensor characteristics are satisfied at acertain scale; this would indicate that the uses of theequivalent continuum approach is justified for the siteconsidered in this study.</p><p>The unique feature of the thesis is that it gives asystematic treatment of the homogenization and upscaling issuesfor the hydraulic and mechanical properties of fractured rockswith a unified approach. These developments established a firmfoundation for future application to large-scale performanceassessment of underground nuclear waste repository byequivalent continuum analysis.</p><p><b>Keywords :</b>Equivalent continuum approach, Equivalentproperty, Representative Elementary Volume (REV), DistinctElement Method, Discrete Fracture Network (DFN)</p>
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Kouach, Mona. "Methods for modelling lattice structures." Thesis, KTH, Hållfasthetslära (Avd.), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-260498.
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The application of lattice structures have become increasingly popular as additive manufacturing (AM) opens up the possibility to manufacture complex configurations. However, modelling such structures can be computationally expensive. The following thesis has been conducted in order for the department of Structural Analysis, at SAAB in Järfälla, to converge with the future use of AM and lattice structures. An approach to model lattice structures using homogenization is presented where three similar methods involving representative volume element (RVE) have been developed and evaluated. The stiffness matrices, of the RVEs, for different sizes of lattice structures, comprising of BCC strut-based units, have been obtained. The stiffness matrices were compared and analysed on a larger solid structure in order to see the deformational predictability of a lattice-based structure of the same size. The results showed that all methods were good approximations with slight differences in terms of boundary conditions (BCs) at the outer edge. The comparative analyses showed that two of the three methods matches the deformational predictability. The BCs in all methods have different influences which makes it pivotal to establish the BCs of the structure before using the approach presented in this thesis.<br>Ökad implementering av gitterstrukturer i komponenter är ett resultat av utvecklingen inom additiv tillverkning. Metoden öppnar upp för tillverkning av komplexa strukturer med färre delmoment. Dock så uppkommer det svårigheter vid simulering av dessa komplexa strukturer då beräkningar snabbt tyngs ner med ökad komplexitet. Följande examensarbete har utförts hos avdelningen Strukturanalys, på SAAB i Järfälla, för att de ska kunna möta upp det framtida behovet av beräkningar på additivt tillverkade gitterstrukturer. I det här arbetet presenteras ett tillvägagångsätt för modellering av gitterstrukturer med hjälp av represantiva volymselement. Styvhetsmatriser har räknats fram, för en vald gitterkonfiguration, som sedan viktats mot tre snarlika representativa volymselement. En jämförelseanalys mellan de olika styvhetsmatriserna har sedan gjorts på en större och solid modell för att se hur väl metoderna förutsett deformationen av en gitterstruktur i samma storlek. Resultaten har visat att samtliga metoder är bra approximationer med tämligen små skillnader från randeffekterna. Vid jämförelseanalysen simulerades gitterstrukturen bäst med två av de tre metoder. En av slutsatserna är att det är viktigt att förstå inverkan av randvillkoren hos gitterstrukturer innan implementering görs med det tillvägagångssätt som presenterats i det här examensarbetet.
Books on the topic "Representative Volume Element (RVE)"
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Anter, Andreas, ed. Die normative Kraft des Faktischen. Nomos Verlagsgesellschaft mbH & Co. KG, 2020. http://dx.doi.org/10.5771/9783748900481.
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Georg Jellinek was the most important representative of constitutional theory of his time. Up to now, his conceptions have been discussed in international state theory. Whether a two-sided theory, a three-element doctrine or a four-status doctrine—Jellinek imposed himself on the history of constitutional theory with concise numerical formulas. For a long time, his concept of the ‘normative force of the factual’ has been part of the fixed vocabulary of constitutional and political theory. Celebrated as a masterpiece on its publication, his opus magnum ‘Allgemeine Staatslehre’ was quickly translated into all the world’s languages. For Max Weber, Jellinek was the only representative of constitutional theory of worldwide standing. The contributions in this volume discuss the central aspects of Jellinek’s political and constitutional theory, examining its relevance for the solution of today's problems, not least the questions of statehood and the syndicate nature of the European Union. Andreas Anter’s fields of research include state theory, the history of political ideas and constitutional politics. With contributions by Andreas Anter, Hans Boldt, Stefan Breuer, André Brodocz, Jens Kersten, Dieter Koop, Oliver Lepsius, Walter Pauly, Martin Siebinger
Book chapters on the topic "Representative Volume Element (RVE)"
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Jeulin, Dominique, Toufik Kanit, and Samuel Forest. "Representative Volume Element: A Statistical Point of View." In Continuum Models and Discrete Systems. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2316-3_5.
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Eraslan, Sinan, Inna M. Gitman, Mingxiu Xu, Harm Askes, and René de Borst. "Representative Volume Element Size and Length Scale Identification in Generalised Magneto-Elasticity." In Advanced Structured Materials. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-26186-2_11.
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El Houdaigui, F., S. Forest, A. F. Gourgues, and D. Jeulin. "On the Size of the Representative Volume Element for Isotropic Elastic Polycrystalline Copper." In IUTAM Symposium on Mechanical Behavior and Micro-Mechanics of Nanostructured Materials. Springer Netherlands, 2007. http://dx.doi.org/10.1007/978-1-4020-5624-6_17.
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Nguyen, Trung-Kien. "On the Representative Volume Element of Dense Granular Assemblies Made of 2D Circular Particles." In Lecture Notes in Civil Engineering. Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-0945-9_41.
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Munde, Yashwant S., Ravindra B. Ingle, Avinash S. Shinde, and Siva Irulappasamy. "Micromechanical Modelling and Evaluation of Pineapple Leaves Fibre (PALF) Composites Through Representative Volume Element Method." In Pineapple Leaf Fibers. Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1416-6_12.
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Ostoja-Starzewski, Martinos, X. Du, Z. F. Khisaeva, and W. Li. "On the Size of Representative Volume Element in Elastic, Plastic, Thermoelastic and Permeable Random Microstructures." In THERMEC 2006. Trans Tech Publications Ltd., 2007. http://dx.doi.org/10.4028/0-87849-428-6.201.
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Rauch, Łukasz, Krzysztof Bzowski, Danuta Szeliga, and Maciej Pietrzyk. "Development and Application of the Statistically Similar Representative Volume Element for Numerical Modelling of Multiphase Materials." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-50433-5_30.
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Pise, M., D. Brands, J. Schröder, G. Gebuhr, and S. Anders. "Macroscopic model based on application of representative volume element for steel fiber reinforced high performance concrete." In Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems. CRC Press, 2022. http://dx.doi.org/10.1201/9781003348443-212.
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Pise, M., D. Brands, J. Schröder, G. Gebuhr, and S. Anders. "Macroscopic model based on application of representative volume element for steel fiber reinforced high performance concrete." In Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems. CRC Press, 2022. http://dx.doi.org/10.1201/9781003348450-212.
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Clendennen, Crystal Rae, and Pedro Romero. "Evaluating the Representative Volume Element of Asphalt Concrete Mixture Beams for Testing in the Bending Beam Rheometer." In Multi-Scale Modeling and Characterization of Infrastructure Materials. Springer Netherlands, 2013. http://dx.doi.org/10.1007/978-94-007-6878-9_2.
Full textConference papers on the topic "Representative Volume Element (RVE)"
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Wu, Xuehai, and Assimina A. Pelegri. "Deep 3D Convolution Neural Network Methods for Brain White Matter Hybrid Computational Simulations." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-24664.
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Abstract Material properties of brain white matter (BWM) show high anisotropy due to the complicated internal three-dimensional microstructure and variant interaction between heterogeneous brain-tissue (axon, myelin, and glia). From our previous study, finite element methods were used to merge micro-scale Representative Volume Elements (RVE) with orthotropic frequency domain viscoelasticity to an integral macro-scale BWM. Quantification of the micro-scale RVE with anisotropic frequency domain viscoelasticity is the core challenge in this study. The RVE behavior is expressed by a viscoelastic constitutive material model, in which the frequency-related viscoelastic properties are imparted as storage modulus and loss modulus for the composite comprised of axonal fibers and extracellular glia. Using finite elements to build RVEs with anisotropic frequency domain viscoelastic material properties is computationally very consuming and resource-draining. Additionally, it is very challenging to build every single RVE using finite elements since the architecture of each RVE is arbitrary in an infinite data set. The architecture information encoded in the voxelized location is employed as input data and is consequently incorporated into a deep 3D convolution neural network (CNN) model that cross-references the RVEs’ material properties (output data). The output data (RVEs’ material properties) is calculated in parallel using an in-house developed finite element method, which models RVE samples of axon-myelin-glia composites. This novel combination of the CNN-RVE method achieved a dramatic reduction in the computation time compared with directly using finite element methods currently present in the literature.
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Pochanard, Pandhita, and Anil Saigal. "Prediction of Rice Husk Particulate-Filled Polymer Composite Properties Using a Representative Volume Element (RVE) Model." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51145.
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In this study, a numerical representative volume element (RVE) model was used to predict the mechanical properties of a Rice Husk Particulate (RHP)-Epoxy composite for use as an alternative material in non-critical applications. Seven different analytical models Counto, Ishai-Cohen, Halpin-Tsai, Nielsen, Nicolais, Modified Nicolais and Pukanszky were used as comparison tools for the numerical model. The mechanical properties estimated for 0%, 10% and 30% RHP-Epoxy composites using the numerical and analytical models are in general agreement with each other. Using the analytical models, it was calculated that an increase in volume percentage of RHP to 30% led to continual reduction in elastic Young’s modulus and ultimate tensile strength of the composite. The numerical RVE models also predicted a similar trend between filler volume percentage and material properties. Overall, the results of this study suggest that RHP can be used to reduce the composite raw material costs by replacing the more expensive polymer content with agricultural waste products with limited compromise to the composite’s mechanical properties.
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Karami, G. "An Equivalent Continuum-Atomistic Characterization Model for Nanographitic Materials." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-81858.
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An equivalent continuum-atomistic algorithm is proposed for carbon-based structures such as nano-scale graphene platelets (NGPs) and carbon nanotubes (CNTs) individually or as stiffeners with polymers. This equivalent continuum-atomistic model will account for the nonlocal effect at the atomistic level and will be a highly accurate mean to determine the bulk properties of graphene-structured materials from its atomistic parameters. In the model, the equivalent continuum and atomic domains are analyzed by finite elements and molecular dynamics finite element-based where atoms stand as nodes in discretized form. Micromechanics idea of representative volume elements (RVE) will be used to determine averaged homogenized properties. In the procedure, a unit hexagonal cell will be the RVE. A minimum volume of material containing this RVE and the neighboring hexagonal cells will be chosen. The size of this volume should cover all the atoms, which have bonded, and nonbonded interaction with the atoms of the RVE unit cell. This minimum volume will be subjected to several load cases. Determination of the response of the RVE hexagonal unit cell contained within the minimum volume, and its potential energy density under the defined load cases, will lead to the determination of mechanical parameters of an equivalent, continuum geometrical shape. For a single layer NGP the thickness of the hexagonal continuum plate is assumed to be 0.34 nm, while in three-dimension and multilayered the actual thickness of layers can be implemented. Under identical loading on the minimum volumes, identical potential (strain) energies for both models will be assumed. Through this equivalence a linkage between the molecular force field constants and the structural elements stiffness properties will be established.
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Xu, Hongyi, Hua Deng, Catherine Brinson, et al. "Stochastic Reassembly for Managing the Information Complexity in Multilevel Analysis of Heterogeneous Materials." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70668.
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Efficient and accurate analysis of materials behavior across multiple scales is critically important in designing complex materials systems with exceptional performance. For heterogeneous materials, apparent properties are typically computed by averaging stress-strain behavior in a statistically representative cell. To be statistically representative, such cells must be larger and are often computationally intractable, especially with standard computing resources. In this research, a stochastic reassembly approach is proposed for managing the information complexity and reducing the computational burden, while maintaining accuracy, of apparent property prediction of heterogeneous materials. The approach relies on a hierarchical decomposition strategy that carries the materials analyses at two levels, the RVE (representative volume element) level and the SVE (statistical volume element) level. The hierarchical decomposition process uses clustering methods to group SVEs with similar microstructure features. The stochastic reassembly process then uses t-testing to minimize the number of SVEs to garner their own apparent properties and fits a random field model to high-dimensional properties to be put back into the RVE. The RVE thus becomes a coarse representation, or “mosaic,” of itself. Such a mosaic approach maintains sufficient microstructure detail to accurately predict the macro-property but becomes far cheaper from a computational standpoint. A nice feature of the approach is that the stochastic reassembly process naturally creates an apparent-SVE property database. Thus, material design studies may be undertaken with SVE-apparent properties as the building blocks of a new material’s mosaic. Some simple examples of possible designs are shown. The approach is demonstrated on polymer nanocomposites.
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Pan, Yi, Vivak Patel, Assimina A. Pelegri, and David I. Shreiber. "Pseudo 3D RVE Based Finite Element Simulation on White Matter." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-89808.
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Axonal injury represents a critical target for traumatic brain and spinal cord injuries prevention and treatment. Finite element head models are often used to predict brain injury caused by mechanical loading exerted on the head. Many studies have been attempted to understand injury mechanisms and to define mechanical parameters of axonal injury. Mechanical strain has been identified as the proximal cause of axonal injury. Since the microstructure of the brain white matter is locally oriented, the stress and strain fields are highly axon orientation dependent. The accuracy of the finite element simulations depends not only on correct determination of the material properties but also on precise depiction of the tissues’ microstructure (microscopic level). We applied a finite element method and a mircomechanics approach to simulate the kinematics of axon, which was developed according to experimental data, and found that the degree of coupling between the axons and surrounding cells within the tissue will affect the behavior of the tissue. In this study, the finite element model and the kinematic axonal model are applied to the Representative Volume Element (RVE) of central nervous system (CNS) white matter to investigate the tissue level mechanical behavior. The uniaxial tensile test on the white matter tissue will be presented as an example using the RVE.
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Studer, Michel, and Kara Peters. "Multi-Scale Embedded Sensing for Damage Identification." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33947.
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This paper presents an efficient technique to uniquely identify damage through the creation of a multi-scale map of material deformations and behavior within a representative volume element (RVE) of the host structure. Optimally distributed, embedded fiber optic sensors provide strain, strain gradient, and integrated strain fields throughout the RVE. As a demonstration, an isotropic, homogeneous RVE is modeled instrumented with an evenly spaced grid of sensing elements. The multi-scale damage identification technique and an equivalent single-scale method are evaluated on the basis of damage detection and identification. A large number of induced, stochastic damage cases are analyzed, generated by introducing a crack defined by three random variables: center location, length, and orientation angle. The multi-scale sensing capability is shown to provide a higher quality strain map of the RVE from the distributed sensors, resulting in significantly improved damage identification.
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Pan, Yi, and Assimina A. Pelegri. "Response of Random Chopped Fiber Reinforced Composite to Uniaxial Tensile Load." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-11440.
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Recent interests of application of random chopped fiber reinforced composites in manufacturing lightweight components in the automotive industry motivate active research on the material behaviors of this kind of materials. A representative volume element is generated numerically based on microscopic observation on the realistic samples. It captures the complex meso-structure of random chopped fiber composites. A finite element model is developed for the RVE of random chopped fiber composite. The elastic stiffness properties of the composite material thus can be derived with homogenization scheme. The representative volume element was verified by Young’s modulus obtained from experimental measurements and analytical calculation of the modulus by other methods. Furthermore, damages deboning of fiber/matrix interface is simulated using the representative volume element.
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Chiu, Tz-Cheng, and Huang-Chun Lin. "On the Multiscale Finite Element Analysis for Interfacial Fracture in Cu/Low-K Interconnects." In ASME 2007 InterPACK Conference collocated with the ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ipack2007-33204.
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The interface crack problem in integrated circuit devices was considered by using global and local modeling approach. In the global analysis the thin film interconnect was modeled by a homogenized layer with material constants obtained from representative volume element (RVE) analysis. Local analyses were then considered to determine fracture mechanics parameters. It was shown that the multiscale model with RVE approach gives accurate fracture mechanics parameters for an interface crack under either thermal or mechanical loads; while significant error was observed when the thin film layers are ignored in the global analysis. The problem of an interface crack between low-k dielectric and etch-stop thin film in a flip-chip package under thermal loading was also investigated as an application example of the multiscale modeling.
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Saavedra Flores, Erick I., Senthil Murugan, Michael I. Friswell, and Eduardo A. de Souza Neto. "Fully Coupled Three-Scale Finite Element Model for the Mechanical Response of a New Bio-Inspired Composite." In ASME 2011 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2011. http://dx.doi.org/10.1115/smasis2011-4946.
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This paper proposes a fully coupled three-scale finite element model for the mechanical description of an alumina/magnesium alloy/epoxy composite inspired in the mechanics and architecture of wood cellulose fibres. The constitutive response of the composite (the large scale continuum) is described by means of a representative volume element (RVE, corresponding to the intermediate scale) in which the fibre is represented as a periodic alternation of alumina and magnesium alloy fractions. Furthermore, at a lower scale the overall constitutive behavior of the alumina/magnesium alloy fibre is modelled as a single material defined by a large number of RVEs (the smallest material scale) at the Gauss point (intermediate) level. Numerical material tests show that the choice of the volume fraction of alumina based on those volume fractions of crystalline cellulose found in wood cells results in a maximisation of toughness in the present bio-inspired composite.
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RIVERA, ADRIAN XAVIER, SATCHI VENKATARAMAN, HYONNY KIM, EVAN PINEDA, and ANDREW BERGAN. "FINITE ELEMENT MODELING FOR COMPRESSION STRENGTH PREDICTION OF HONEYCOMB CORES WITH GEOMETRIC IMPERFECTIONS MEASURED USING X-RAY CT IMAGING." In Proceedings for the American Society for Composites-Thirty Seventh Technical Conference. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/asc37/36497.
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Aluminum honeycomb cores are used in composite sandwich panels to achieve high bending rigidity while maintaining low weight. Geometric imperfections arise in the walls of metallic honeycomb cores during manufacturing, which affects their compression and impact response. This paper presents finite element modeling of metallic honeycomb cores with measured geometric imperfections. The honeycomb cores are modeled using shell geometry reconstructions of images of cores obtained using X-ray Computer Tomography. Flatwise compression responses of the cores are computed using finite element analyses of honeycomb cores for different representative volume element (RVE) sizes and boundary conditions. It is found that the compression response of the 10x11 cells RVE models can be predicted by the average of single RVE cell models sampled from the 10x11 cells RVE domain. However, this requires appropriate choice of boundary conditions. The non-periodic nature of the imperfection and the variation in geometric imperfection in the double and single thickness walls of the honeycomb core cells lead to interactive buckling of these walls and mode jumping during the amplification of initial imperfections under compression. These interactions play a significant role in the compression response and, therefore, the RVE size and boundary condition choices made should ensure this interaction are accurately captured.