Dissertations / Theses on the topic 'Gradient damage'

Les modèles d'endommagement à gradient, aussi dénommés modèles à champs de phases, sont désormais largement utilisés pour modéliser la rupture fragile et ductile, depuis l'initiation de l'endommagement jusqu'à la propagation d'une fissure. Cependant, la majorité des études disponibles dans la littérature ne concerne que le cadre des petites déformations, et très peu d'études poussées ont été menées afin d'étudier leur pertinence dans un contexte de grandes déformations. Ce serait pourtant d'un intérêt primordial, notamment pour l'industrie pneumatique, qui deviendrait alors capable de prédire plus précisément l'initiation de l'endommagement dans ses structures.Dans la première partie de ce travail, nous établissons des solutions analytiques d'évolution de l'endommagement (homogène et localisée) pour des matériaux visqueux, en petites et en grandes déformations. En petites déformations, les modèles rhéologiques de Maxwell et Poynting-Thomson sont étudiés, et en grandes déformations, les modèles de Maxwell et Zener sont choisis. Une étude sur l'évolution de l'endommagement dans un cas purement hyperélastique est aussi menée.A cette première partie analytique succède une partie numérique, qui détaille l'implémentation des modèles d'endommagement à gradient dans des codes éléments finis en grandes déformations. De même qu'en petites déformations, une stratégie de minimisation alternée est adoptée pour résoudre successivement les problèmes d'endommagement et de déplacement. Le matériau suit une loi de Mooney-Rivlin quasi-incompressible, et une méthode mixte en déplacement-pression est utilisée. Des tests en 2D et 3D sont effectués, qui mettent en évidence la capacité des modèles à initier de l'endommagement en grandes déformations.Les modèles d'endommagement utilisés pour la seconde partie ne sont cependant capables d'initier de l'endommagement que dans les zones où la déformation est importante, c'est-à-dire dans les zones de forte contrainte déviatorique. Il a toutefois été montré que certains matériaux polymères, quasi-incompressibles, s'endommagent dans les zones de forte pression hydrostatique. Par conséquent, la recherche et l'étude d'un modèle d'endommagement capable d'initier de l'endommagement dans les zones de forte pression, pour des matériaux quasi-incompressibles lorsqu'ils sont sains, fait l'objet d'une troisième partie.Enfin, la croissance brusque de cavités dans un matériau hyperélastique, appelée phénomène de cavitation, est étudiée, ainsi que son interaction avec l'endommagement. Dans un premier temps, nous considérons la cavitation comme une simple bifurcation hyperélastique d'un matériau néo-hookéen compressible isotrope, et déterminons l'expression analytique de l'élongation critique pour laquelle la cavitation fait son apparition. Dans un second temps, nous montrons qu'il y a une compétition entre la cavitation et l'endommagement, et qu'en fonction de la valeur du ratio des élongations critiques respectives pour chaque phénomène, deux types de rupture apparaissent
Gradient damage models, also known as phase-field models, are now widely used to model brittle and ductile fracture, from the onset of damage to the propagation of a crack in various materials. Yet, they have been mainly studied in the framework of small deformation, and very few studies aims at proving their relevance in a finite deformation framework. This would be more helpful for the tyre industry that deals with very large deformation problems, and has to gain insight into the prediction of the initiation of damage in its structures.The first part of this work places emphasis on finding analytical solutions to unidimensional problems of damaging viscous materials in small and large deformation.In all the cases, the evolution of damage is studied, both in the homogeneous and localised cases. Having such solutions gives a suitable basis to implement these models and validate the numerical results.A numerical part naturally follows the first one, that details the specificities of the numerical implementation of these non local models in large deformation. In order to solve the displacement and damage problems, the strategy of alternate minimisation (or staggered algorithm) is used. When solved on the reference configuration, the damage problem is the same as in small deformation, and consists in a bound constraint minimisation. The displacement problem is non linear, and a mixed finite element method is used to solve a displacement-pressure problem. A quasi-incompressible Mooney-Rivlin law is used to model the behaviour of the hyperelastic material. Various tests in 2D and 3D are performed to show that gradient damage models are perfectly able to initiate damage in sound, quasi-incompressible structures, in large deformation.In the simulations depicted above, it should be noted that the damage laws combined to the hyperelastic potential results in an initiation of damage that takes place in zones of high deformation, or in other words, in zones of high deviatoric stress. However, in some polymer materials, that are known to be quasi-incompressible, it has been shown that the initiation of damage can take place in zones of high hydrostatic pressure. This is why an important aspect of the work consists in establishing a damage law such that the material be incompressible when there is no damage, and the pressure play a role in the damage criterion. Such a model is exposed in the third part.Finally, the last part focuses on the cavitation phenomenon, that can be understood as the sudden growth of a cavity. We first study it as a purely hyperelastic bifurcation, in order to get the analytical value of the critical elongation for which cavitation occurs, in the case of a compressible isotropic neo-hookean material submitted to a radial displacement. We show that there is a competition between the cavitation phenomenon and the damage, and that depending on the ratio of the critical elongation for damage and the critical elongation for cavitation, different rupture patterns can appear

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2019
Cataloged 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

Earthquake is one of the most destructive natural disasters on earth. Rapid and reliable post-quake damage assessment has an important role to reduce the drastic effects of an earthquake by setting the responsible agencies in motion. In this study, the collapsed buildings due to earthquake were detected from post-event aerial images. Two approaches were proposed to detect the collapsed buildings. These approaches were implemented in a selected urban area of Golcuk. The first approach was based on the analysis of shadow casting edges. First, the shadow casting edges of the buildings were identified and a buffer zone was generated for each building polygon along these edges. Then, the shadow regions were detected using the watershed segmentation algorithm. This was followed by measuring the agreement between the shadow producing edges of the buildings and their corresponding shadows. Of the 284 buildings analyzed, 229 were successfully labeled as collapsed or un-collapsed providing an overall accuracy of 80,63%.In the second approach, a two-branch method based on building light intensities and the gradient orientation was used. In the first branch, an intensity threshold was determined and applied to building image patches. Then, a pixel ratio was computed to categorize the buildings. In the second branch, a series of processings were carried out including the smoothing of the building image patches and the determination of the magnitude and the orientation of the gradient. Then, an optimum angle threshold was determined to label the buildings. The final decision about the condition of a building was made by integrating the two branches. Of the 284 buildings analyzed, 254 were correctly labeled providing an overall accuracy of 89,44%. The same assessments were repeated after generating a one-pixel wide buffer zone around the building polygons and an overall accuracy of 90,85% was obtained. The results of the proposed approaches prove that the collapsed buildings caused by the earthquake can be successfully detected from post-event aerial images.

Une bonne tenue mécanique des structures du génie civil en béton armé sous chargements dynamiques sévères est primordiale pour la sécurité et nécessite une évaluation précise de leur comportement en présence de propagation dynamique de fissures. Dans ce travail, on se focalise sur la modélisation constitutive du béton assimilé à un matériau élastique-fragile endommageable. La localisation des déformations sera régie par un modèle d'endommagement à gradient où un champ scalaire réalise une description régularisée des phénomènes de rupture dynamique. La contribution de cette étude est à la fois théorique et numérique. On propose une formulation variationnelle des modèles d'endommagement à gradient en dynamique. Une définition rigoureuse de plusieurs taux de restitution d'énergie dans le modèle d'endommagement est donnée et on démontre que la propagation dynamique de fissures est régie par un critère de Griffith généralisé. On décrit ensuite une implémentation numérique efficace basée sur une discrétisation par éléments finis standards en espace et la méthode de Newmark en temps dans un cadre de calcul parallèle. Les résultats de simulation de plusieurs problèmes modèles sont discutés d'un point de vue numérique et physique. Les lois constitutives d'endommagement et les formulations d'asymétrie en traction et compression sont comparées par rapport à leur aptitude à modéliser la rupture fragile. Les propriétés spécifiques du modèle d'endommagement à gradient en dynamique sont analysées pour différentes phases de l'évolution de fissures : nucléation, initiation, propagation, arrêt, branchement et bifurcation. Des comparaisons avec les résultats expérimentaux sont aussi réalisées afin de valider le modèle et proposer des axes d'amélioration
In civil engineering, mechanical integrity of the reinforced concrete structures under severe transient dynamic loading conditions is of paramount importance for safety and calls for an accurate assessment of structural behaviors in presence of dynamic crack propagation. In this work, we focus on the constitutive modeling of concrete regarded as an elastic-damage brittle material. The strain localization evolution is governed by a gradient-damage approach where a scalar field achieves a smeared description of dynamic fracture phenomena. The contribution of the present work is both theoretical and numerical. We propose a variationally consistent formulation of dynamic gradient damage models. A formal definition of several energy release rate concepts in the gradient damage model is given and we show that the dynamic crack tip equation of motion is governed by a generalized Griffith criterion. We then give an efficient numerical implementation of the model based on a standard finite-element spatial discretization and the Newmark time-stepping methods in a parallel computing framework. Simulation results of several problems are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. Specific properties of the dynamic gradient damage model are investigated for different phases of the crack evolution: nucleation, initiation, propagation, arrest, kinking and branching. Comparisons with experimental results are also performed in order to validate the model and indicate its further improvement

L'objectif de cette thèse est de proposer une démarche de modélisation à partir de niveau microstructure pour obtenir un modèle d'endommagement à gradient. Elle se fonde, d'une part, sur la méthode d'homogénéisation pour construire un milieu effectif à partir de la microstructure donnée, et d'autre part, sur la formulation variationnelle, à l'échelle macroscopique, d'une loi d'évolution d'endommagement à partir du milieu homogénéisé. Nous construisons dans un premier temps une approche basée sur le développement asymptotique et de la méthode variationnelle pour homogénéiser un milieu élastique périodique. Afin de modéliser le phénomène de localisation d'endommagement , cette approche a été étendue à un milieu hétérogène quasi périodique. Par un exemple du milieu micro fissuré quasi périodique, nous obtenons une énergie élastique qui dépend non seulement du gradient de l'endommagement mais aussi du gradient de déformation. Dans la deuxième partie, nous construisons un modèle d'endommagement à gradient à partir de l'énergie élastique homogénéisé en se basant sur la principe de minimisation d'énergie. En ajoutant des hypothèse pour simplifier le modèle, nous pouvons construit explicitement des états localisés d'endommagement et de déformation. Enfin, un schéma de résolution numérique, basé sur un algorithme de minimisation alternée, a été proposé pour le cas d'un barre en traction. A partir des résultats numériques, les avantages et les inconvénients du modèle sont discutés
The aim of this work is to propose a general framework to obtain a gradient damage model from the micro-structural level. It is based, firstly, on the homogenization method to derive an effective medium from the microstructure, and secondly, on the variational formulation of a damage evolution law from the homogenized medium. We propose, as a first step, an approach based on asymptotic expansion and the variational method for homogenizing a periodic elastic medium. To model the localization of damage, this approach has been extended to a quasi-periodic heterogeneous medium. From an example of quasi periodically micro-cracked solid, we obtain an elastic energy that not only depends on the gradient of the damage but also the strain gradients. Based on the principle of energy minimization, we propose the construction of a gradient damage model from the elastic energy homogenized in the second part. By adding some hypothesis to simplify the model, we can construct localized damage and strain solutions in closed form. Finally, a numerical resolution scheme, which is based on an alternate minimization algorithm, is proposed for the one-dimensional traction bar test. From the numerical results, the advantages and disadvantages of the model are discussed

Hyperthermia is a cancer treatment modality that raises cancerous tissue to cytotoxic temperature levels for roughly 30 to 45 minutes. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol to be used in a hyperthermia treatment. This thesis presents a method to optimize a hyperthermia treatment heating protocol. An algorithm is developed which recovers a heating protocol that will cause a desired amount of thermal damage within a region of tissue. The optimization algorithm is validated experimentally on an albumen tissue phantom.

The transient temperature distribution within the region is simulated using a two- dimensional, finite-difference model of the Pennes bioheat equation. The relationship between temperature and time is integrated to produce a damage field according to two different models; Henriques'' model and the thermal dose model (Moritz and Henriques (1947)), (Sapareto and Dewey (1984)). A minimization algorithm is developed which re duces the value of an objective function based on the squared difference between an optimal and calculated damage field. Either damage model can be used in the minimization algorithm. The adjoint problem in conjunction with the conjugate gradient method is used to minimize the objective function of the control problem.

The flexibility of the minimization algorithm is proven experimentally and through a variety of simulations. With regards to the validation experiment, the optimal and recovered regions of permanent thermal damage are in good agreement for each test performed. A sensitivity analysis of the finite difference and damage models shows that the experimentally-obtained extent of damage is consistently within a tolerable error range.

Excellent agreement between the optimal and recovered damage fields is also found in simulations of hyperthermia treatments on perfused tissue. A simplified and complex model of the human skin were created for use within the algorithm. Minimizations using both the Henriques'' model and the thermal dose model in the objective function are performed. The Henriques'' damage model was found to be more desirable for use in the minimization algorithm than the thermal dose model because it is less computationally intensive and includes a mechanism to predict the threshold of permanent thermal damage. The performance of the minimization algorithm was not hindered by adding complexity to the skin model. The method presented here for optimizing hyperthermia treatments is shown to be robust and merits further investigation using more complicated patient models.
Master of Science

Hyperthermia is a cancer treatment modality that raises cancerous tissue to cytotoxic temperature levels for roughly 30 to 45 minutes. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol to be used in a hyperthermia treatment. This thesis presents a method to optimize a hyperthermia treatment heating protocol. An algorithm is developed which recovers a heating protocol that will cause a desired amount of thermal damage within a region of tissue. The optimization algorithm is validated experimentally on an albumen tissue phantom. The transient temperature distribution within the region is simulated using a two-dimensional, finite-difference model of the Pennes bioheat equation. The relationship between temperature and time is integrated to produce a damage field according to two different models; Henriques'' model and the thermal dose model (Moritz and Henriques (1947)), (Sapareto and Dewey (1984)). A minimization algorithm is developed which re duces the value of an objective function based on the squared difference between an optimal and calculated damage field. Either damage model can be used in the minimization algorithm. The adjoint problem in conjunction with the conjugate gradient method is used to minimize the objective function of the control problem. The flexibility of the minimization algorithm is proven experimentally and through a variety of simulations. With regards to the validation experiment, the optimal and recovered regions of permanent thermal damage are in good agreement for each test performed. A sensitivity analysis of the finite difference and damage models shows that the experimentally-obtained extent of damage is consistently within a tolerable error range. Excellent agreement between the optimal and recovered damage fields is also found in simulations of hyperthermia treatments on perfused tissue. A simplified and complex model of the human skin were created for use within the algorithm. Minimizations using both the Henriques'' model and the thermal dose model in the objective function are performed. The Henriques'' damage model was found to be more desirable for use in the minimization algorithm than the thermal dose model because it is less computationally intensive and includes a mechanism to predict the threshold of permanent thermal damage. The performance of the minimization algorithm was not hindered by adding complexity to the skin model. The method presented here for optimizing hyperthermia treatments is shown to be robust and merits further investigation using more complicated patient models.
Master of Science

Due to the advent of varied types of masonry systems a comprehensive failure mechanism of masonry essential for the understanding of its behaviour is impossible to be determined from experimental testing. As masonry is predominantly used in wall structures a biaxial stress state dominates its failure mechanism. Biaxial testing will therefore be necessary for each type of masonry, which is expensive and time consuming. A computational method would be advantageous; however masonry is complex to model which requires advanced computational modelling methods. This thesis has formulated a damage mechanics inspired modelling method and has shown that the method effectively determines the failure mechanisms and deformation characteristics of masonry under biaxial states of loading.

Structural health monitoring (SHM) of aerospace components is a rapidly emerging field due in part to commercial and military transport vehicles remaining in operation beyond their designed life cycles. Damage detection strategies are sought that provide real-time information of the structure's integrity. One approach that has shown promise to accurately identify and quantify structural defects is based on guided ultrasonic wave (GUW) inspections, where low amplitude attenuation properties allow for long range and large specimen evaluation. One drawback to GUWs is that they exhibit a complex multi-modal response, such that each frequency corresponds to at least two excited modes, and thus intelligent signal processing is required for even the simplest of structures. In addition, GUWs are dispersive, whereby the wave velocity is a function of frequency, and the shape of the wave packet changes over the spatial domain, requiring sophisticated detection algorithms. Moreover, existing damage quantification measures are typically formulated as a comparison of the damaged to undamaged response, which has proven to be highly sensitive to changes in environment, and therefore often unreliable. As a response to these challenges inherent to GUW inspections, this research develops techniques to locate and estimate the severity of the damage. Specifically, a phase gradient based localization algorithm is introduced to identify the defect position independent of excitation frequency and damage size. Mode separation through the filtering technique is central in isolating and extracting single mode components, such as reflected, converted, and transmitted modes that may arise from the incident wave impacting a damage. Spatially-integrated single and multiple component mode coefficients are also formulated with the intent to better characterize wave reflections and conversions and to increase the signal to noise ratios. The techniques are applied to damaged isotropic finite element plate models and experimental data obtained from Scanning Laser Doppler Vibrometry tests. Numerical and experimental parametric studies are conducted, and the current strengths and weaknesses of the proposed approaches are discussed. In particular, limitations to the damage profiling characterization are shown for low ultrasonic frequency regimes, whereas the multiple component mode conversion coefficients provide excellent noise mitigation. Multiple component estimation relies on an experimental technique developed for the estimation of Lamb wave polarization using a 1D Laser Vibrometer. Lastly, suggestions are made to apply the techniques to more structurally complex geometries.

Hot mix asphalt (HMA) is a granular composite material stabilized by the presence of asphalt binder. The behavior of HMA is highly influenced by the microstructure distribution in terms of the different particle sizes present in the mix, the directional distribution of particles, the distribution of voids, and the nucleation and propagation of cracks. Conventional continuum modeling of HMA lacks the ability to explicitly account for the effect of microstructure distribution features. This study presents the development of elastic and visco-plastic models that account for important aspects of the microstructure distribution in modeling the macroscopic behavior of HMA. In the first part of this study, an approach is developed to introduce a length scale to the elasticity constitutive relationship in order to capture the influence of particle sizes on HMA response. The model is implemented in finite element (FE) analysis and used to analyze the microstructure response and predict the macroscopic properties of HMA. Each point in the microstructure is assigned effective local properties which are calculated using an analytical micromechanical model that captures the influence of percent of particles on the microscopic response of HMA. The moving window technique and autocorrelation function are used to determine the microstructure characteristic length scales that are usedin strain gradient elasticity. A number of asphalt mixes with different aggregate types and size distributions are analyzed in this paper. In the second part of this study, an elasto-visco-plastic continuum model is developed to predict HMA response and performance. The model incorporates a Drucker- Prager yield surface that is modified to capture the influence of stress path direction on the material response. Parameters that reflect the directional distribution of aggregates and damage density in the microstructure are included in the model. The elasto-visco-plastic model is converted into a numerical formulation and is implemented in FE analysis using a user-defined material subroutine (UMAT). A fully implicit algorithm in time-step control is used to enhance the efficiency of the FE analysis. The FE model used in this study simulates experimental data and pavement section.

Ce travail porte sur la détection de l’endommagement de matériaux composites. Une première partie concerne l’élaboration de méthodes permettant d’estimer les termes sources de chaleur d’un matériau sollicité mécaniquement. Lors de ce processus, un ensemble de défauts mécaniques mènent à des productions de chaleur. La détection des sources peut permettre la détection de ces défauts. Deux principales méthodes sont présentées : une méthode dite « directe » basée sur une discrétisation du champ de température mesuré et une méthode « itérative » basée sur la méthode du gradient conjugué. A ces méthodes sont couplées des techniques de filtrages des données comme la SVD. Les équations sont résolues par différences finies sous leur forme linéaire. Des modifications sont apportées à l’algorithme itératif pour améliorer sa convergence ainsi que les résultats. Les problématiques envisagées font partie des problèmes inverses en thermique. L’objectif de la première partie est de trouver un lien entre l’apparition de macro-fissure et la localisation de termes sources de chaleur au sein d’un matériau composite. La seconde partie consiste à élaborer des méthodes d’estimation des diffusivités thermiques directionnelles. Les méthodes reposent sur une modélisation du transfert de chaleur à l’aide des quadripôles thermiques. Les estimations de paramètres sont réalisées sur des zones ciblées à risque sur un matériau déjà endommagé. Le but est de faire le lien entre un endommagement mécanique connu diffus et une dégradation des propriétés thermiques. Ce manuscrit est présenté en deux parties : une partie de validation des méthodes. Une partie expérimentale où sont analysés les composites
This work deals with the damage detection of composite materials. These materials are used in the aeronautics industry. The first part concerns the development of methods to estimate the heat sources terms of a stressed material. During this process, a set of mechanical defects leads to heat productions. The sources detection can conduct to the detection of these defects. Two main methods are presented: a "direct" method based on a discretization of the measured temperature field and an "iterative" method based on the conjugate gradient method. These methods are coupled with data filtering techniques such as SVD. In order to optimize computation time, equations are solved by finite differences in their linear form. Modifications are also made for the iterative algorithm to improve its convergence as well as the results of the estimation. These problems are considered as thermal inverse problems. The main objective of the first part is to find an experimental link between the appearance of a macro fissure and the localization of a heat source term within a composite material. The second part consists in the elaboration of methods for estimating thermal directional diffusivities. The methods are based on a modeling of heat transfer using thermal quadrupoles. Parameter estimations are made on targeted "risked" areas on a material, which is already damaged but not under stress. The aim is to link a known mechanical damage, which is called "diffuse" to thermal properties degradation in the main directions. This manuscript is presented in two parts: a validation part of the methods, and an experimental part in which composites are analyzed

Diese Dissertation beschäftigt sich mit der rigorosen Herleitung effektiver Modelle zur Beschreibung von Schädigungsprozessen. Diese effektiven Modelle werden für verschiedene raten-unabhängige Schädigungsmodelle linear elastischer Materialien hergeleitet. Den Ausgangspunkt stellt dabei ein unidirektionales Mikrostrukturevolutionsmodell dar, dessen Fundament eine Familie geordneter zulässiger Mikrostrukturen bildet. Jede Mikrostruktur dieser Familie besitzt die gleiche intrinsische Längenskala. Zur Herleitung eines effektiven Modells wird das asymptotische Verhalten dieser Längenskala mittels Techniken der Zwei-Skalen-Konvergenz untersucht. Um das Grenzmodell zu identifizieren, bedarf es einer Mikrostrukturregularisierung, die als diskreter Gradient für stückweise konstante Funktionen aufgefasst werden kann. Die Mikrostruktur des effektiven Modells ist punktweise durch ein Einheitszellenproblem gegeben, welches die Mikro- von der Makroskala trennt. Ausgehend vom Homogenisierungsresultat für die unidirektionale Mikrostrukturevolution werden effektive Modelle für Zwei-Phasen-Schädungsprozesse hergeleitet. Die aus zwei Phasen bestehende Mikrostruktur der mikroskopischen Modelle ermöglicht z.B. die Modellierung von Schädigung durch das Wachstum von Inklusionen aus geschädigtem Material verschiedener Form und Größe. Außerdem kann Schädigung durch das Wachstum mikroskopischer Hohlräume und Mikrorissen betrachtet werden. Die Größe der Defekte skaliert mit der intrinsischen Längenskala und die unidirektionale Mikrostrukturevolution verhindert, dass bei fixierter Längenskala die Defekte für fortlaufende Zeit schrumpfen. Das Material des Grenzmodells ist dann in jedem Punkt als Mischung von ungeschädigtem und geschädigtem Material durch das Einheitszellenproblem gegeben. Dabei liefert das Einheitszellenproblem nicht nur das Mischungsverhältnis sondern auch die genaue geometrische Mischungsverteilung, die dem effektiven Material des jeweiligen Materialpunktes zugrunde liegt.
This dissertation at hand deals with the rigorous derivation of such effective models used to describe damage processes. For different rate-independent damage processes in linear elastic material these effective models are derived as the asymptotic limit of microscopic models. The starting point is represented by a unidirectional microstructure evolution model which is based on a family of ordered admissible microstructures. Each microstructure of that family possesses the same intrinsic length scale. To derive an effective model, the asymptotic behavior of this intrinsic length scale is investigated with the help of techniques of the two-scale convergence. For this purpose, a microstructure-regularizing term, which can be understood as a discrete gradient for piecewise constant functions, is needed to identify the limit model. The microstructure of the effective model is given pointwisely by a so-called unit cell problem which separates the microscopic scale from the macroscopic scale. Based on these homogenization results for unidirectional microstructure evolution models, effective models for brutal damage processes are provided. There, the microstructure consists of only two phases, namely undamaged material which comprises defects of damaged material with various sizes and shapes. In this way damage progression can be modeled by the growth of inclusions of weak material, the growth of voids, or the growth of microscopic cracks. The size of the defects is scaled by the intrinsic length scale and the unidirectional microstructure evolution prevents that, for a fixed length scale, the defects shrink for progressing time. According to the unit cell problem, the material of the limit model is then given as a mixture of damaged and undamaged material. In a specific material point of the limit model, that unit cell problem does not only define the mixture ratio but also the exact geometrical mixture distribution.

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 expérimentaux
This 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

The major human activities that have transformed the Earth include agriculture and urbanization. The present study was conducted to contribute to a description of the effect on birds of urbanization and agriculture in an Indian region. Terrestrial bird assemblages were censused along a five-stage urbanisation gradient between January and April 2010-2013 near the city of Amravati, on the Deccan Plateau, Central India. Altogether, 89 species of birds were recorded, with the highest species richness in the rural areas (67 species) and lowest in the urban stage (29 species). The assemblages were significantly nested in all the five stages. Maximum cumulative species abundance (12 399 individuals over four years) was found in the urban stage, and was due to the constant presence of large groups of Rose-ringed Parakeets (Psittacula krameri). The lowest bird abundance was found in the industrial zone (4837 in total), where there was also a nearly two-fold decrease from 2010 to 2013. Thirty-six species demonstrated significant variation in their densities at least in one stage and between at least two months (p<0.05). Densities of 13.9% (n=5) of those species varied significantly in two stages, that of Copsychus saularis in three stages, and of Phoenicurus ochruros, in all five stages. Urban, suburban, periurban and forest stages were characterised by relatively stable species densities (significant changes observed only for 17.2% (n=5), 17.1% (n=6), 12.9% (n=7), and 17.8% (n=16) species, respectively). The additive diversity partitioning indicated that of the overall diversity (gamma-diversity), alpha diversity (within transects located within one stage) contributed 50.1% to the total diversity, and the controbution of within-stage variability was small (2.7%). Additionally, censuses on cultivated fields were taken. In two areas under mixed cropping systems, 53 bird species were identified in the two years period between June and December, 2011 and 2012. Out of the 53 detected species, only 14 were common (recorded at ≥50% of visits). Twenty-one species were recorded at Zadgaon in crops of tur (Cajanus cajan), cotton (Gossypium arboreum) and soybean (Glycine max). Nineteen species were recorded at Bhankhed in jawar (Sorghum bicolor), cotton and mung bean (Phaseolus aureus). At Zadgaon, territorial activity was observed in four species: the House Sparrow (Passer domesticus), Jungle Babbler (Turdoides striata), Yellow-eyed Babbler (Chrysomma sinense) and Red-wattled Lapwing (Vanellus indicus). The study indicated that four bird species were found under high risk, thirteen species at medium risk and eight species at low risk due to pesticide applications in croplands. The extent of crop damage in fields of groundnut, pearl millet, peas, sorghum, and sunflower was assessed by doing actual field censuses. The sustainable solution for reducing crop damage is a need for the farmers and such techniques will help to avoid direct or indirect effects of use of lethal bird control techniques on bird species diversity.

QC 20141022

Les châssis automobiles sont composés en majorité de pièces mécano-Soudées soumises à deschargements multiaxiaux complexes. Par leur géométrie particulière et les transformations induites par leprocédé de fabrication, les joints soudés sont des sites privilégiés d’amorçage et de propagation de fissures enfatigue. Une méthode de calcul fiable et maniable représente un enjeu majeur pour l’industrie automobile, carelle permet de détecter les points critiques dès la phase d’avant projet, d’éviter le surdimensionnement et deréduire le nombre des prototypes physiques.Afin de découpler les incertitudes et permettre l’analyse isolée des effets induits par le chargementmultiaxial lui-Même et par les caractéristiques particulières du joint soudé, cette étude est divisée en deux parties.La première partie se concentre sur le chargement multiaxial complexe. Le comportement d’un « matériauécole », l’acier C35, est étudié sous spectre de chargement de type « automobile ». Différentes méthodes deprévision de la durée de vie sont ensuite comparées sous deux critères : la qualité de prédiction et la simplicitéd’utilisation. La deuxième partie est centrée sur l’étude du comportement des assemblages soudés et lasimulation de leur durée de vie. Pour ce faire, une éprouvette représentative des pièces de liaison au sol et duprocédé de fabrication a été conçue. L’étude micrographique de l’assemblage combinée à des essais instrumentésa permis de construire un modèle EF représentatif de la structure. Deux modes de sollicitation sont utilisés lorsdes essais de fatigue dans le but d’activer différents mécanismes de dommage en amplitude constante et enspectre « automobile ».Finalement, la méthodologie « Weld Stress Gradient » est proposée pour intégrer l’effet du gradient decontraintes en proximité des points critiques du joint soudé au calcul de fatigue. Cette méthodologie, associée aucritère de Vu (prise en compte du chargement complexe) et à la règle de cumul de dommage non linéaire« DCA » (prise en compte de l’interaction entre les blocs de chargement du spectre), permet d’obtenir desrésultats encourageants pour l’assemblage étudié
Automotive chassis are composed mostly of welded parts subjected to complex multiaxial loadings.Welds are potential sites to initiation and propagation of fatigue cracks because of their particular geometry andtransformations induced by manufacturing process. A reliable and tractable fatigue design methodology is achallenge for automotive industry designers because it allows detecting the critical points from the upstreamphase, avoiding oversizing and reducing the number of physical prototypes.This study is divided into two parts allowing the distinction of effects induced by multiaxial loadingsand particular characteristics of the welded joints. The first part focuses on the complex multiaxial loading. Thebehavior of a “well known material”, the 1045 steel, is studied under "automobile" spectrum loading. Differentfatigue life prediction methods are compared under two criteria: quality of prediction and simplicity of use. Thesecond part focuses on the study of behavior and fatigue life simulation of welded structures. To achieve thisgoal, a representative specimen of chassis parts and manufacturing process has been designed. A representativeFE model is constructed, based on micrographic observations and instrumented tests. Two loading modes areused in fatigue tests in order to activate different damage mechanisms at constant amplitude and under"automobile" spectrum.Finally, the methodology "Weld Stress Gradient" is proposed to incorporate in fatigue analysis theeffect of the stress gradient at the vicinity of weld joints critical points. This methodology, combined with Vucriterion (taking into account complex loadings) and "DCA" nonlinear cumulative damage rule (taking intoaccount interaction between spectrum loading blocks), provides encouraging results for the studied specimen

Les plantes et les insectes forment l’un des principaux niveaux trophiques des écosystèmes au cours des 325 derniers millions d’années. Aujourd’hui, l’augmentation rapide et continuelle de la température principalement causée par l’activité humaine depuis les derniers siècles, perturbe la balance des écosystèmes sur Terre. En conséquence, comprendre le rôle des interactions entre les plantes et les insectes, à travers le temps mais aussi les réseaux trophiques, est essentiel. Le registre fossile est une opportunité exceptionnelle d’examiner les réponses aux interactions plante-insecte lors de longues variations climatiques et à travers des traces de réaction de la plante sachant que la Terre a déjà été soumise à de nombreux changements climatiques. Durant les derniers 3 millions d’années, des oscillations entre de longues périodes froides et de courtes périodes chaudes ont eu lieu. Les écosystèmes Européens ont particulièrement été impactés par ces oscillations. Le Langerstätte de Willershausen (Allemagne) a été particulièrement étudié. C’est un gisement contenant plus de 8000 feuilles fossiles. Ces feuilles relatent d’une paléoforêt ayant existé il y a 3- 2,6 Ma dans un climat plus chaud qu’aujourd’hui (ca.+5°C). Dans ces conditions climatiques, de nombreuses espèces d’écosystèmes Méditerranéens étaient présentes, telles que l’Érable de Montpellier ou l’Olivier. En comparaison, d’autres paléoforêts ont été prise en compte : Berga (du même âge et proche de Willershausen) et Bernasso (plus jeune que Willershausen (2,16 — 1,96 Ma) localisée dans le sud de la France près de la Méditerranée. Ces forêts sont comparables notamment du fait des nombreux taxons communs qu’elles partagent. En outre, certaines de ces espèces sont aujourd’hui endémiques de la région du Caucase, telles que le Parrotie de Perse ou encore l’orme du Caucase. Le but de cette étude a été de déterminer en quoi les différences climatiques peuvent être impliquées dans les changements des interactions plante-insecte au sein des paléoforêts Européennes de la fin du Pliocène - début du Pléistocène. Les résultats obtenus ont permis de mettre en évidence les impacts de la saisonnalité des températures et précipitations facteurs impactants les interactions plante-insecte des paléoforêts Européennes. Il est apparu que les écosystèmes sujets à d’intenses saisonnalités hydriques ont pu engendrer une plus grande spécialisation des interactions plante-insecte déduite d’un fort taux d’interactions spécialistes observées. En parallèle, les températures les plus froides durant l’année semble être un facteur important dans la faible diversité de dégâts, probablement dû à un faible métabolisme de la majorité des insectes. L’absence de corrélation convergente entre la richesse des plantes et la richesse des interactions pourrait suggérer que l’influence des facteurs climatiques surpasse l’impact potentiel des interactions biotiques locales. Pour l’ensemble de ces paramètres qui ont pu avoir un impact sur les interactions plante-insecte, nos connaissances actuelles sont encore insuffisantes. Il serait intéressant de focaliser davantage d’études sur les forêts modernes avec les méthodes appliquées dans le fossile. C’est dans cette intention qu’une partie de cette étude a étudié une espèce de plante (Parrotia persica) actuellement endémique de la forêt Hyrcanienne (Iran). Cette forêt est supposée être une forêt analogue des paléoforêts Européennes étudiées dans cette thèse. Pour le moment, les observations qui ont été faites en Iran semblent corroborer notre interprétation. Au final, les études sur les interactions plante-insecte des forêts anciennes et actuelles, combinés avec les études de changements climatiques, pourraient nous permettre de mieux caractériser les relations entre les insectes et les plantes au sein d’une forêt
Insects are the most diverse animals on Earth, and neatly associated with plants they represent two of the major groups of organisms both in species diversity and biomass quantity. The majority of their interactions involves insect feeding and insect parasitism mostly on leaves. Plant and insect compose one of the main trophic levels in ecosystems over the 325 million years. Today, the continuous and fast rising of temperature mostly due to human activities since the last century is disturbing the balance of ecosystems on Earth. Consequently, to understand the role of plant and insect interactions, through time but also trophic networks, becomes crucial. The fossil record is an exceptional opportunity to survey responses of plant-insect interaction to climate variations over long time interval through traces of plants reactions caused by interaction with insects, as Earth has already experienced many climate changes. For the last 3 million years, oscillations between long cold periods and short warm periods have occurred. Europe ecosystems has been particularly impacted. The Lagerstätte of Willershausen (Germany) was specifically study. It is an exceptional fossil outcrop that contains ca. 8000 collected fossil leaves. These leaves testify a paleoforest developed there around 3—2.6 Ma ago in a climate warmer than today (ca. +5°C). Under these conditions, many plant species typical of the Mediterranean ecosystems were settled there, such as Montpellier maple or Olive tree. For comparison, other paleoforests were studied: Berga (similar in age and geographically close to Willershausen) and Bernasso (younger than Willershausen (2.16—1.96 Ma) and located in southern France close to Mediterranean. These forests were compared as many common plant taxa were similar between each other. Furthermore, some species today endemic to the Caucasian region, such as Persian ironwood or Caucasian elm, were also present in these outcrops. The aim of this study is to determine how far the climate differences could be involved in the changes of plant-insect interactions in European paleoforests of the late Pliocene – early Pleistocene. Results highlighted the impacts of both hydric and temperature seasonality, hitherto underestimated in the fossil record, on the patterns of plant-insect interaction in the European paleoforests. It appeared that ecosystems subject to intense hydric seasonality could led to higher specialization of plant-insect interaction inferred by higher rate of observed damages due to ‘specialists insects’. In parallel, the coolest temperature during the year seems to be a major factor in the low diversity of damage in paleoforest, presumably due to lower insect metabolism. Absence of convergent correlations between plant richness and damage richness could suggested that influence of climatic factors override impact of these local biotic factors. In order to understand the whole parameters that could have an impact on plant-insect interactions, our current knowledges are still insufficient. It would be wise to make more investigations on modern forests with the methods as applied in fossil record community structure studies. These investigations could help to understand the factors potentially involved in the establishment of a pattern of plant-insect interactions. It is in this perspective that a part of this study was precisely focused on one plant species (Parrotia persica) currently endemic to the Hyrcanian forest (Iran). This forest is supposed to be an analogue forest of the European paleoforests as those studied in this thesis. For now, observations made in Iran tend to corroborate our interpretation. Finally, the studies on plant-insect interactions in past and extant ecosystems, combined with the study of climatic changes, should permit us to better characterize the relations between plants and insects in forests through time

Les aubes de turbine haute pression en superalliage monocristallin sont refroidies, à la fois par un réseau de canaux internes, ainsi que par des perforations débouchantes. Soumises à des cycles thermo-mécaniques complexes, elles subissent des endommagements de type fatigue, fluage et oxydation. Pour valider les chaînes de prévision de durée de vie en conditions réelles d'utilisation, il a été nécessaire d’étudier des configurations d’essais technologiques reproduisant les conditions d'un cycle moteur en laboratoire. Pour cela, une installation d'essai de fatigue à gradient thermique de paroi est développée. Le gradient thermique est généré par chauffage de la surface externe et refroidissement interne par une circulation d’air. L’installation a ainsi permis la réalisation d'essais selon une complexité croissante, allant de l’essai isotherme jusqu'au cycle thermo-mécanique complexe, sur éprouvette tubulaire lisse ou multi-perforée. Afin d’analyser finement ces essais, deux méthodes de mesures sont étudiées. La méthode du potentiel électrique pour la détection et le suivi de fissure appliquée à des géométries complexes et la corrélation d’images, dont l’utilisation est étendue à la haute température. Le point-clé de la modélisation de ces essais est l'estimation du champ thermique. L'impossibilité de le mesurer sur éprouvette, a conduit à le déterminer numériquement, notamment par des simulations couplées aéro-thermiques. La chaîne de prévision de durée de vie intégrant l'aspect non-local, a ainsi pu être confrontée aux mesures expérimentales en termes de réponse mécanique, localisation de l'endommagement et durée de vie à amorçage
Monocrystalline high pressure turbine blades are booth cooled by an internal channel network and side-wall crossing holes. As they undergo complex thermo-mechanical cycles they suffer fatigue, creep and oxidation damages. In order to validate lifetime prediction chain under real conditions of use, the study of technological test configurations reproducing turbine cycle conditions was necessary. For that, a thermal gradient mechanical fatigue facility is developed. Thermal gradient is generated through an external surface heating and an internal air cooling. As a result, tests could be conducted following a growing complexity on smooth and multi-perforated tubular specimens going from isothermal test up to thermo-mechanical complex cycle. The need of in-depth analysis of these tests led to the study of two measurement methods. The electrical potential drop method for crack detection and crack following applied to complex shapes and digital image correlation which use was extended to high temperatures. Simulation key issue is the thermal field estimation. Measurement complexity led us to numerically determine it by various methods including aero-thermal coupled calculations. Finally lifetime prediction chain including non-local coverage was confronted with experimental measurements in terms of mechanical response, damage localisation and crack initiation lifetime

In this thesis, I combined field, common-garden and greenhouse experiments to examine the ecological and evolutionary consequences of plant-herbivore interactions in the perennial herb Lythrum salicaria. More specifically I examined (1) whether resistance and tolerance to damage from herbivores vary with latitude and are positively related to the intensity of herbivory in natural populations, (2) whether effects of herbivory on plant fitness vary with latitude, (3) whether populations are locally adapted and whether herbivory influences the relative fitness of populations, and (4) whether the intensity and effects of insect herbivory on reproductive output vary locally along a disturbance gradient and are associated with differences in plant resistance. A common-garden and a greenhouse experiment demonstrated that plant resistance decreased whereas plant tolerance increased with latitude of origin among populations sampled along a latitudinal gradient in Sweden. Oviposition and feeding preference in the greenhouse and leaf damage in the common-garden experiment were negatively related to natural damage in the source populations. Experimental removal of insect herbivores in three populations sampled along the latitudinal gradient demonstrated that intensity of herbivory and its effects on plant fitness decreased towards the north. A reciprocal transplant experiment among the same three populations showed that herbivory affected the relative fitness of the three populations, but did not detect any evidence of local adaptation. Instead the southernmost population had the highest relative fitness at all three sites. A herbivore-removal experiment conducted in nine populations in an archipelago in northern Sweden demonstrated that insect herbivory strongly influenced among-population variation in reproductive output. However, variation in resistance was not related to differences in intensity of herbivory at this spatial scale. Taken together, the results demonstrate that resistance and tolerance to herbivory vary with latitude but in opposite directions, that intensity of herbivory is a major determinant of flowering and seed output, and that the strength of herbivore-mediated selection varies among populations in Lythrum salicaria. They further indicate that both physical disturbance regime and latitudinal variation in abiotic conditions may strongly influence the performance and abundance of perennial herbs because of their effects on interactions with specialized herbivores.

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 microstructure
Eine 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

Les instabilités hydrauliques et mécaniques dans les géomatériaux font référence à une variété de phénomènes non-linéaires qui peuvent être déclenchés par les hétérogénéités inhérentes à ces matériaux. Alors que les instabilités hydrauliques se manifester comme invasion hétérogène d’un fluide ‘par digitation', les instabilités mécaniques représentent des localisations de déformation et/ou des fractures. Ces instabilités potentiellement couplées constituent un obstacle majeur pour les applications impliquant des géomatériaux tels que la séquestration du dioxyde de carbone (CO2) et l'écoulement des contaminants dans les eaux souterraines. Les modèles classiques existants manquent des ingrédients nécessaires de modéliser la formation d’une microstructure dans leur formulation et sont donc stables contre toute perturbation. L'essence de cette thèse est de proposer et d'étudier des techniques de modélisation qui permettent de décrire ces instabilités. L'approche en loi de comportement adoptée est celle des milieux continus à micro-structure, en particulier celle des milieux continus équipés de lois de comportement dépendant du gradient de variables de type champ de phase.Dans la première partie de ce travail, un front fluide-fluide a été décrit comme une interface diffusée en interprétant la présence de deux fluides dans l'espace poreux comme un seul fluide non-uniforme et le degré de saturation de l'un des fluides comme le champ de phase. Alors que la relation classique bijective entre la pression capillaire et le degré de saturation décrit les propriétés de rétention du réseau poreux, une relation enrichie est obtenue en prescrivant un potentiel chimique dans l'esprit de la modélisation de type Cahn-Hilliard de fluides multiphasiques. Cette relation enrichie, associé à une contribution énergétique non-locale, fournit les ingrédients nécessaires à la description des instabilités hydrauliques. Dans un cadre unidimensionnel, le modèle proposé reproduit les profils de saturation non-monotones observés expérimentalement pendant l'infiltration. De plus, il a été démontré qu'une légère non-convexité introduite dans la fonction de perméabilité relative permet de modéliser les fronts de drainage, en plus de l'imbibition, sans employer de complexités supplémentaires. Une analyse de stabilité linéaire (ASL) révélant la croissance dans le temps de perturbations arbitraires a été réalisée, complétée par des simulations 2D montrant la capacité du modèle proposé à décrire digitation et la ségrégation des fluides.Dans la deuxième partie, le déclenchement d'une fissure dans un milieu poreux en cours de séchage a été étudié. Un paradigme de modélisation prédominant, impliquant la modélisation à gradient d'endommagement, a d'abord été testé pour sa capacité à reproduire la formation périodique de fissures telle qu'observée dans des expériences représentatives. De plus, un nouveau paradigme a été proposée en interprétant la présence d'une fissure comme une perte des propriétés capillaires, permettant ainsi le passage d'un fluide non-mouillant sous une pression capillaire évanescente. Ceci est applicable aux sols à grains fins sans cohésion et non-consolidés, où la résistance à traction est négligeable. En partant des principes de l'approche variationnelle, il a été montré que une dessiccation suffisamment forte peut amorcer l'endommagement de manière homogène sur la face de séchage tout en progressant dans le domaine dans le temps. L'apparition éventuelle de bifurcations de cette solution de base, représentant l'initiation de fissures périodiques, a été analysée toujours dans le cadre de l’ASL.Ce travail ouvre la voie à l'étude du couplage entre les instabilités mentionnées ci-dessus et l'investigation expérimentale des caractéristiques d'écoulement instables, telles que le pincement et la coalescence de la phase de mouillage. L'initiation d'endommagement induits par l'évolution du doigt de drainage présente également un intérêt particulier
Hydraulic and mechanical instabilities in geomaterials refer to a variety of non-linear phenomena that can be triggered by heterogeneities inherent to such materials. While hydraulic instabilities manifest themselves as heterogeneous fluid invasion causing `fingering' phenomenon, mechanical instabilities represent strain localizations and/or fractures. These instabilities and their associated coupling pose a major obstacle for applications involving geomaterials such as Carbon dioxide (CO2) sequestration and contaminant flow in ground waters. Existing classical models lack the required pattern-forming ingredients in their formulation and thus are stable against imposed perturbations. The essence of the current thesis work is to propose and investigate modeling techniques that allow to describe these instabilities. The constitutive approach adopted is that of micro-structured continua, in particular that of enhanced continua with a constitutive law depending on the gradient of so-called phase field variables.In the first part of this work, a fluid-fluid front has been described as a diffused interface by interpreting the presence of two fluids within the pore space as a single non-uniform fluid and the degree of saturation of one of the fluids as the corresponding phase field. While the classical one-to-one relation between capillary pressure and saturation degree describes retention properties of the porous network, an enhanced relation is obtained by prescribing a chemical potential in the spirit of Cahn-Hilliard type modeling of multi-phase fluids. This together with a non-local energy contribution provides the required ingredients required to describe hydraulic instabilites. In a one-dimensional setting, the proposed model allows to replicate experimentally observed non-monotonic saturation profiles during infiltration. Further, a slight non-convexity introduced into the flux function has been shown to allow modeling of drainage fronts, besides imbibition, without employing any additional complexities. A linear stability analysis (LSA) revealing the growth in time of arbitrary perturbations has been done, supplemented by two-dimensional simulations portraying the ability of the proposed model to describe fluid fingering and segregation.In the second part, triggering of a fracture within a drying porous medium has been studied. A prevailing modeling perspective, involving gradient damage modeling, has been first tested for its ability to replicate periodic fracture formation as observed in representative experiments. Further, a new paradigm has been introduced by interpreting the presence of a fracture as a loss of capillary properties, thus allowing passage of non-wetting fluid under vanishing capillary pressure. This is applicable to cohesion-less and unconsolidated fine-grained soils, where resistance against tensile loading is negligible and thus fracturing induced due to development of tensile stresses is not the prevailing phenomenon. Starting from the principles of variational approach, it has been shown that for sufficiently strong desiccation, damage initiates homogeneously on the drying face while progressing into the body with time. The possible occurrence of bifurcations of this base solution, representing initiation of periodic fractures, has been analyzed again in the framework of LSA.This work sets the stage for the study of coupling between the above mentioned instabilities and experimental investigation of unstable flow features such as pinching and coalescence of the wetting phase. Initiation of damage induced due to evolving drainage finger is also of particular interest in the context of earlier mentioned applications

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The adoption of different ecological strategies is an important factor to determine the establishment and persistence of species in local communities. In general, the Cerrado is characterized by high fire frequency and poor soils. Generally under conditions of low fertility and high fire frequency the filtered species tend to have characteristics that represent adaptations to these environmental stresses. Considering that savanna species evolved under severe environmental filters, our aim was to evaluate how the adoption of different ecological strategies can determine the performance of the functional traits, the structure of the communities, and the relationship between a focal plant and its neighborhood. In this thesis work, which is divided into three chapters, we use three different scales to evaluate how species ecological strategies can determine the performance and establishment in local communities. In the first chapter, which is based on habitat scale, we evaluated how ecological strategies of generalist and specialist species of seasonal forest and savannas are fundamental for the establishment and persistence of the species in these habitats with marked differences in frequency in fire frequency and nutrient availability. In this chapter, we discuss that the different strategies adopted by species are in accordance to the limiting factors of the species occurrence in each of these environments. In the second chapter, which is based on community scale, we seek to understand how environmental gradients can determine different ecological strategies related to functional traits and density of individuals. We showed that the changes in trait values and density of individuals were more evident in the fertility gradient than toxicity, and that seasonal forest communities were more sensitive to changes savanna communities in both gradients. We also observed that species with conservative traits were associated with poor soils and species with acquisitive traits with more fertile soils. In the third chapter, which was developed at the individual scale, we discussed whether the characteristics and phylogenetic relationship of the neighboring plants influence leaf damage in trees and shrubs of savannas. In this chapter, we showed that the ecological and evolutionary distance between individual plants and neighboring plants does not determine the level of leaf damage by herbivores. We discussed that the dominance of generalist herbivores, co-evolution between plants and specialist herbivores, and preferential consumption of young leaves may be more important to determine the level of leaf damage than the neighboring context in which a given plant is inserted.
A adoção de diferentes estratégias ecológicas é um fator importante para determinar o estabelecimento e a persistência de espécies em comunidades locais. De maneira geral, o cerrado é caracterizado por uma alta frequência de fogo e solos pobres em nutrientes. Geralmente em condições de baixa fertilidade e alta frequência de fogo as espécies filtradas tendem a possuir características que representam adaptações a estes estresses ambientais. Considerando que as espécies de Cerrado se desenvolvem sob a atuação destes filtros ambientais, nosso objetivo foi avaliar como a adoção de diferentes estratégias ecológicas podem determinar a performance dos atributos funcionais, a estrutura das comunidades e a relação entre uma planta focal e sua vizinhança. Neste trabalho de tese, que está dividido em três capítulos, nós utilizamos três diferentes escalas para avaliar como estratégias ecológicas das espécies podem determinar seu desempenho e estabelecimento em comunidades locais. No primeiro capítulo que está baseado em uma escala de habitat, nós avaliamos como as estratégias ecológicas de espécies generalistas e especialistas de floresta estacional e cerrado sentido restrito são fundamentais para o estabelecimento e a persistência das espécies nestes habitats com diferenças marcantes em relação à frequência de fogo e disponibilidade de nutrientes. Neste capítulo, nós discutimos que as diferentes estratégias adotadas pelas espécies estão de acordo com os fatores limitantes da ocorrência de espécies em cada um destes ambientes. No segundo capítulo, que está baseado em escala de comunidades, nós buscamos compreender como os gradientes ambientais podem determinar diferentes estratégias ecológicas relacionadas aos atributos funcionais e a densidade de espécies. Nós demonstramos que as mudanças nos valores de atributos e densidade de espécies foram mais claras no gradiente de fertilidade do que toxicidade, e que comunidades de floresta estacional foram mais sensíveis a mudanças do que comunidades de cerrado sentido restrito em ambos os gradientes. Nós observamos também que espécies com atributos conservativos foram associados à solos pobres e espécies com atributos aquisitivos associado à solos mais férteis. Já no terceiro capítulo, que foi desenvolvido na escala de indivíduo, nós discutimos se as características e relação filogenética das plantas vizinhas influenciam o dano foliar em árvores e arbustos do cerrado. Neste capítulo, demonstramos que a distância ecológica e evolutiva entre plantas individuais e as plantas vizinhas não determina o nível de consumo foliar por herbívoros. Nós discutimos que a dominância de herbívoros generalistas, a co-evolução entre plantas e herbívoros especialistas, e o consumo preferencial de folhas jovens podem ser mais importante para determinar o nível de dano foliar do que o contexto de vizinhança em que uma dada planta está inserida.

Les simulations numériques des fissures fragiles par les modèles d’endommagement à gradient deviennent main- tenant très répandues. Les résultats théoriques et numériques montrent que dans le cadre de l’existence d’une pre-fissure la propagation suit le critère de Griffith. Alors que pour le problème à une dimension la nucléation de la fissure se fait à la contrainte critique, cette dernière propriété dimensionne le paramètre de longueur interne.Dans ce travail, on s’attarde sur le phénomène de nucléation de fissures pour les géométries communément rencontrées et qui ne présentent pas de solutions analytiques. On montre que pour une entaille en U- et V- l’initiation de la fissure varie continument entre la solution prédite par la contrainte critique et celle par la ténacité du matériau. Une série de vérifications et de validations sur diffèrent matériaux est réalisée pour les deux géométries considérées. On s’intéresse ensuite à un défaut elliptique dans un domaine infini ou très élancé pour illustrer la capacité du modèle à prendre en compte les effets d’échelles des matériaux et des structures.Dans un deuxième temps, ce modèle est étendu à la fracturation hydraulique. Une première phase de vérification du modèle est effectuée en stimulant une pré-fissure seule par l’injection d’une quantité donnée de fluide. Ensuite on étudie la simulation d’un réseau parallèle de fissures. Les résultats obtenus montrent qu’il a qu’une seule fissure qui se propage et que ce type de configuration minimise mieux l’énergie la propagation d’un réseau de fractures. Le dernier exemple se concentre sur la stabilité des fissures dans le cadre d’une expérience d’éclatement à pression imposée pour l’industrie pétrolière. Cette expérience d’éclatement de la roche est réalisée en laboratoire afin de simuler les conditions de confinement retrouvées lors des forages.La dernière partie de ce travail se concentre sur la rupture ductile en couplant le modèle à champ de phase avec les modèles de plasticité parfaite. Grâce à l’approche variationnelle du problème on décrit l’implantation numérique retenue pour le calcul parallèle. Les simulations réalisées montrent que pour une géométrie légèrement entaillée la phénoménologie des fissures ductiles comme par exemple la nucléation et la propagation sont en concordances avec ceux reportées dans la littérature
Phase-field models, sometimes referred to as gradient damage, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’s criterion. For a one- dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter is identified with the material’s internal characteristic length.In this work, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from the one predicted by a strength criterion to the one of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification of numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.In a second movement, this model is extended to hydraulic fracturing. We present a validation of the model by simulating a single fracture in a large domain subject to a control amount of fluid. Then we study an infinite network of pressurized parallel cracks. Results show that the stimulation of a single fracture is the best energy minimizer compared to multi-fracking case. The last example focuses on fracturing stability regimes using linear elastic fracture mechanics for pressure driven fractures in an experimental geometry used in petroleum industry which replicates a situation encountered downhole with a borehole called burst experiment.The last part of this work focuses on ductile fracture by coupling phase-field models with perfect plasticity. Based on the variational structure of the problem we give a numerical implementation of the coupled model for parallel computing. Simulation results of a mild notch specimens are in agreement with the phenomenology of ductile fracture such that nucleation and propagation commonly reported in the literature

Pour étendre l'utilisation des composites dans des applications plus variées (applications intelligentes et multifonctionnelles), l'une des barrières est leur faible conductivité électrique et thermique. Dans le cas de composites renforcés par des fibres de carbone, la matrice organique est responsable des propriétés isolantes du composite résultant. L'une des solutions pour améliorer les conductivités des matériaux est l'utilisation des nanocharges conductrices. L'amélioration des propriétés électriques et thermiques des polymères nanochargés est une problématique récurrente dans la littérature. Cependant, étudier les propriétés des composites à fibre de carbone continue et nanochargés est moins abordée. Ce travail porte sur la fabrication et la caractérisation des composites nanochargés par du noir de carbone et des nanotubes de carbone. Tout d'abord, un intérêt particulier a été accordé à la phase délicate de la fabrication. Comme mentionné ci-dessus, la mise en œuvre des composites à renfort continu et matrice nanochargée implique des problèmes liés à l'agglomération et à la dispersion inhomogène des nanocharges dans le composite final. Pour résoudre ces problèmes, le choix de la matrice thermoplastique (Polyamide 6) était judicieux. En fait, la dispersion des nanocharges a été faite par extrusion bi-vis qui est connue comme l'une des voies les plus efficaces de séparation d'agglomérats. De plus, la méthode de fabrication à base de films de Polyamide 6, appelée film stacking, assure une partition homogène dès le début du processus. Des observations MEB ont été effectuées pour localiser les nanoparticules. Ceux-là ont montré que les particules pénétraient dans la zone des fibres. En effet, en atteignant le cœur des torons, les nano-charges ont créé un réseau de connectivité entre les fibres pour le passage de courant. Ceci explique l'amélioration constatée de la conductivité électrique des composites en présence de noir de carbone et des nanotubes de carbone. Ces essais ont été réalisés avec la méthode à 4 points. La conductivité électrique du composite à matrice « pure » est passée de 20S / cm à 80S / cm en ajoutant 8% en poids de noir de carbone et à 15S / cm en ajoutant 18% en poids de la même charge nanométrique. Pour les nanotubes de carbone, avec 2,5% en poids, la conductivité était d'environ 150S / cm. Pour les propriétés thermiques, des tests basés sur l'effet Joule ont été réalisés. L'augmentation de la température a été enregistrée en utilisant une caméra IR. Les résultats obtenus sont en accord avec ceux de la conductivité électrique, montrant une amélioration du comportement thermique en présence de nanocharges. Grâce à ces résultats, l'utilisation de ces composites comme outil de suivi d’endommagement était possible. Par ailleurs, la méthode de variation de la résistance électrique a été effectuée. Les matériaux nanochargés ont montré une meilleure sensibilité aux endommagements. Les résultats ont été comparés aux outils classiques de suivi d’endommagement. A la fin, plusieurs applications « intelligentes » ont été testées telles que : le composite à gradients de propriétés et des matériaux nanochargés cousus
To extend the use of composites in more varied application (smart applications, multifunctional issues), one of the actual barrier is their poor electrical and thermal conductivities. In the case of carbon fiber reinforced composites, organic matrix are in charge of the insulating properties of the resulting composite. One of the solutions to enhance conductivities of materials is the use of conductive nanofillers. Improving the electrical and thermal properties of nanofilled polymers has been investigated in several studies. However, studiing the properties of continuous carbon fiber nano-filled composites is less approached. This work tends to fabricate and characterize carbon black and carbon nanotubes nano-filled composites. First of all, special interest was given to the delicate phase of manufacturing. As mentioned before, processing continuous fiber reinforced nanofilled polymers implies issues related to nanofillers agglomeration and inhomogeneous dispersion in the final composite. To resolve these problems, the choice of the thermoplastic (Polyamide6) matrix seemed preferable. In fact, the dispersion of nanofillers was made by twin screw extrusion which is known as one of the most effective agglomeration separation ways. Adding to this, the fabrication method based on Polyamide 6 shects called film stacking, ensure a homogeneous partition at the beginning of the process. SEM observations were performed to localize the nano-particles. It showed that particles penetrated on the fiber zone. In fact, by reaching the fiber zone, the nano-fillers created network connectivity between fibers which means an easy pathway for the current. It explains the noticed improvement of the electrical conductivity of the composites by adding carbon black and carbon nanotube. This test was performed with the 4 points electrical circuit. It shows that electrical conductivity of 'neat' matrix composite passed from 20S/cm to 80S/cm by adding 8wt% of carbon black and to 15S/cm by adding 18wt% of the same nano-filler. For carbon nanotubes, with '2.5wt% the conductivity was around 150S/cm. For the thermal properties, tests based on Joule's effect were performed. The rise of temperature was recorded using IR camera. Results obtained are in agreement with the electrical conductivity ones, showing enhancement of the thermal behavior in presence of nanofillers. Thanks to these results, the use of these composites as a damage-monitoring tool was possible. By the way, the electrical resistance change method was performed. Nanofilled materials showed better sensitivity to damage. Results were compared with classical damage monitoring tools. At the end, several 'smart' applications were tested such as graded functionalities composite and stitched nanofilled materials

Experiments were conducted to determine the effects of applying fill soil around existing trees and mechanisms for species tolerance to soil compaction, both common site disturbances in urban forestry. Groups of 22-year-old white oak (Quercus alba) and 13-year-old sweetgum (Liquidambar styraciflua) were subjected to one of three treatments: a control, fill (20 cm of subsoil spread over the root zones), and compacted fill (same as fill soil, but compacted). Additionally, individual trees had tree wells (fill soil pulled away from trunks), or not. After three years, treatments had no consistent effect on tree growth, chlorophyll fluorescence, or soil respiration. However, soil treatments disrupted normal soil moisture patterns at both sites. Roots of white oak grew into fill layers, although overall root growth was not significantly affected by treatment. Sweetgum roots grew very little into fill soils. However, root distribution shifted upward in the original soil under uncompacted fill. Other factors associated with raising the soil grade, such as soil trafficking and root severance, may be largely responsible for the tree decline often attributed to construction fill. Another experiment investigated the relationship between tolerance of wet soils and the ability to grow in compacted soils. It was hypothesized that tree species tolerant of wet soils would have opportunities for root growth in compacted soil when high soil moisture reduced soil strength. Seedlings of flowering dogwood (Cornus florida), a species intolerant of inundation, and silver maple (Acer saccharinum), a bottomland species, were grown in a loam soil maintained at various combinations of soil strength and soil matric potential. In moderately compacted soil (1.5 g cm-3 bulk density), maple seedlings, but not dogwoods, had greater root growth rate, root length per plant, and ratio of root length to root dry weight in the wet soil (0.006 MPa soil matric potential) than in the moist and dry soils (0.026 and 0.06 MPa, respectively). No such effect was detected in highly compacted soil (1.7 g cm-3). It can be concluded that silver maple roots can grow in moderately compacted soil when high soil water content decreases soil strength, whereas dogwood is unable to take advantage of this opportunity.
Ph. D.

Cette thèse traite d’une approche pragmatique de l'endommagement par fatigue des structures sous un chargement cyclique. Un modèle anisotrope de dommage par fatigue a été développé. L'évolution de la dégradation des propriétés du matériau dépend d’un critère de fatigue (choisi) et de ses gradients. La dégradation du matériau anisotrope guidera la propagation des dommages. La propagation des dommages dépend principalement des crêtes de la «surface» du critère (gradients zéro). L'approche proposée décrit l'amorçage, la propagation des dommages et la rupture structurale sous un chargement multiaxial en fatigue. Pour chaque élément fini, des distributions anisotropes non homogènes des propriétés du matériau sont associées. Schématiquement, il apparaît comme un «surfer» matériel sur la «surface» du critère et les dommages suivent la crête de la «surface» du critère (niveau et gradient). Un critère d'approche globale, basé sur des invariants du tenseur des contraintes, est adopté. La réduction des propriétés des matériaux est affectée à un certain nombre de cycles et à un niveau global de contraintes, en utilisant une courbe de Wöhler expérimentale. Deux formes simplifiées du modèle sont proposées et les résultats sont comparés avec un exemple de référence expérimental (plaque cruciforme) et un cas industriel (pale d’une éolienne d’EDF). Une cartographie avec le critère de Dang Van est également calculée pour analyser les résultats numériques
A new practical engineering methodology for the analysis of structures under cyclic loading is proposed in this work . A new anisotropic fatigue damage model is developed. The evolution of material properties degradation depends on a failure criterion and its gradient. The anisotropic material degradation will guide the damage propagation. The propagation of damage is mainly depending on the ridges of the criterion’s « surface » (zero gradients). The proposed approach can describe the initiation and propagation of the damage until the structural failure under fatigue loading. For each finite element, non-homogeneous anisotropic distributions of material properties are associated. Schematically, it seems like a material « surfing » on the criterion’s « surface » and damages follow the crest of the criterion’s « surface » (level and gradient). A global approach criterion, based on invariants of the stress tensor, is adopted. The reduction of material properties is assigned to a number of cycles and a global level of stresses, using an experimental Wöhler curve. Two simplified forms of the model are proposed and results are compared with a cruciform experimental reference example and an industrial case. A mapping with Dang Van criterion is also computed to analyze the numerical results

The thesis presents a novel computational method for analysing the static and dynamic behaviour of a multi-damaged beam using local and non-local elasticity theories. Most of the lumped damage beam models proposed to date are based on slender beam theory in classical (local) elasticity and are limited by inaccuracies caused by the implicit assumption of the Euler-Bernoulli beam model and by the spring model itself, which simplifies the real beam behaviour around the crack. In addition, size effects and material heterogeneity cannot be taken into account using the classical elasticity theory due to the absence of any microstructural parameter. The proposed work is based on the inhomogeneous Euler-Bernoulli beam theory in which a Dirac's delta function is added to the bending flexibility at the position of each crack: that is, the severer the damage, the larger is the resulting impulsive term. The crack is assumed to be always open, resulting in a linear system (i.e. nonlinear phenomena associated with breathing cracks are not considered). In order to provide an accurate representation of the structure's behaviour, a new multi-cracked beam element including shear effects and rotatory inertia is developed using the flexibility approach for the concentrated damage. The resulting stiffness matrix and load vector terms are evaluated by the unit-displacement method, employing the closed-form solutions for the multi-cracked beam problem. The same deformed shapes are used to derive the consistent mass matrix, also including the rotatory inertia terms. The two-node multi-damaged beam model has been validated through comparison of the results of static and dynamic analyses for two numerical examples against those provided by a commercial finite element code. The proposed model is shown to improve the computational efficiency as well as the accuracy, thanks to the inclusion of both shear deformations and rotatory inertia. The inaccuracy of the spring model, where for example for a rotational spring a finite jump appears on the rotations' profile, has been tackled by the enrichment of the elastic constitutive law with higher order stress and strain gradients. In particular, a new phenomenological approach based upon a convenient form of non-local elasticity beam theory has been presented. This hybrid non-local beam model is able to take into account the distortion on the stress/strain field around the crack as well as to include the microstructure of the material, without introducing any additional crack related parameters. The Laplace's transform method applied to the differential equation of the problem allowed deriving the static closed-form solution for the multi-cracked Euler-Bernoulli beams with hybrid non-local elasticity. The dynamic analysis has been performed using a new computational meshless method, where the equation of motions are discretised by a Galerkin-type approximation, with convenient shape functions able to ensure the same grade of approximation as the beam element for the classical elasticity. The importance of the inclusion of microstructural parameters is addressed and their effects are quantified also in comparison with those obtained using the classical elasticity theory.

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This study aimed to evaluate the relationship among seed size and their physical and physiological attributes in three soybean cultivars (NK 7059 RR, SYN 3358 RR and BMX POTÊNCIA RR). Samples were collected from the Seed Processing Unit C.Vale in Abelardo Luz-SC, and the following analyzes were performed: seed germination , seed vigor, mechanical damage, screen retention and weight of 1000 seeds. The analyzes were performed at the Laboratory of Seeds Analysis C.Vale- Cooperativa Agroindustrial in Palotina-PR, and the following cultivars and screens were used: NK 7059 RR (5.75 and 6.75 mm), SYN 3358 RR (5.5 and 6.5mm) and BMX POTÊNCIA RR (5.75 and 6.75mm). The analysis of seed germination was performed according to the Brazilian Rules for Seed Analysis; the seed vigor test was based on the accelerated aging and the test with sodium hypochlorite was used for the evaluation of mechanical damage. Two replicates of 100 seeds were used for the screen retention test, which was determined by retention in specified screen and in screen without perforations. The weight of 1000 seeds was measured in eight replications of 100 seeds. The following conclusions were obtained: 1-Physiological seed quality is independent of seed size 2-There is higher seed retention on the superior screen, reaching more than 10%, and 3-Large seeds tend to have higher mechanical damage.
O presente trabalho teve como objetivo avaliar a relação do tamanho das sementes de soja em três cultivares (NK 7059 RR, SYN 3358 RR e BMX POTÊNCIA RR), sobre os atributos físicos e fisiológicos da semente na qualidade das sementes. As amostras foram coletadas da Unidade de Beneficiamento Sementes da C.Vale, em Abelardo Luz-SC, sendo feito as seguintes análises: Germinação, Vigor, Dano mecânico, Retenção de peneiras e peso de mil sementes. As análises foram conduzidas no Laboratório de Análise de Sementes da C.Vale-Cooperativa Agroindustrial, em Palotina-PR, para os seguintes cultivares e peneiras: NK 7059 RR(5,75 e 6,75), SYN 3358 RR(5,5 e 6,5) e BMX POTÊNCIA RR(5,75 e 6,75). A análise de germinação seguiu as normas da Regra de Análise de Sementes; A análise de vigor foi feita com base no Teste de Envelhecimento Acelerado e a avaliação do dano mecânico foi feita aplicando-se o teste com hipoclorito de sódio. A retenção de peneiras foi determinada através da retenção na peneira especificada em duas repetições de 100 sementes e outra peneira com um fundo cego. Por último, foi determinado o peso de 1000 sementes com oito repetições com 100 sementes de cada. As seguintes conclusões foram obtidas: 1 A qualidade fisiológica independe do tamanho das sementes; 2 Há uma maior retenção de sementes na peneira superior, podendo alcançar mais de 10%; e 3 As sementes grandes tendem a apresentar maior danificação mecânica.

Les études de faisabilité concernant le stockage géologique profond des déchets radioactifs ont conduit un intérêt accru concernant la modélisation géomécanique de la roche hte. En France, une roche hte potentielle est l'argilite du Callovo-Oxfordien du site de Meuse/Haute Marne. Etant donné que le principe de stockage géologique profond repose fortement sur la capacité de confinement de la formation hte, sa faible perméabilité est d'une importance clé. La perméabilité étant dépendante de la microstructure du matériau et de son évolution sous chargement, le comportement couplé hydro-mécanique de l'argilite est important. En effet, des modifications mécaniques sont induites par le creusement de la galerie d'entreposage, générant une zone endommagée (EDZ), pouvant conduire une modification de la perméabilité dans le voisinage de la galerie. Dans les matériaux microstructure complexe comme l'argilite du Callovo-Oxfordien, le comportement macroscopique trouve son origine dans l'interaction des constituants micro-mécaniques. En plus du couplage entre le comportement hydraulique et mécanique, un couplage entre les échelles micro et macro existe. Par le biais de l'élaboration d'un cadre d'homogénéisation du couplage hydro-mécanique, une approche de modélisation deuxéchelles est développée dans ce travail, dans laquelle la relation constitutive macroscopique découle directement du comportement à l'échelle microscopique. Un modèle existant du couplage hydro-mécanique, reposant sur l'identification de grains et d'espaces poreux intergranulaires à l'échelle micro est adopté comme point de départ. Ce modèle repose sur une homogénéisation numérique du comportement à la petite échelle afin d'obtenir à l'échelle macroscopique la réponse en contrainte et de transport du fluide interstitiel. Ce modèle est basé sur un VER périodique qui permet de déduire le comportement macroscopique local de l'argilite. En réponse, en un point d'intégration macro donné, à un incrément de la déformation et du gradient de pression, la réponse du VER permet d'exprimer l'incrément de contrainte et de flux associé, constituant de fait un équivalent numérique de la relation constitutive. Les problèmes aux conditions limites macro et micro sont traités simultanément par la méthode élément fini. Pour obtenir les opérateurs tangents consistants à l'échelle macro, la méthode d'homogénéisation par condensation statique des opérateurs tangeants micro est étendu au cas avec couplage hydro-mécanique. L'implémentation du modèle double échelle et la mise en uvre des développements théoriques d'homogénéisation ont été effectués dans le code élément fini Lagamine (Université de Liège). Pour la modélisation de la localisation de la déformation à l'échelle macro, qui, dans un formalisme de milieu continu classique, souffre de la dépendance au maillage, l'approche double-échelle a été utilisée dans un formalisme de milieu enrichi de type milieu de second gradient pour matériau poreux saturé. Les capacités du modèle homogénéisé numériquement, utilisé dans un cadre de milieu de second gradient, sont ensuite démontrées par des simulations d'essais dométriques et d'essais de compression biaxiaux. L'approche se confirme être un moyen puissant pour modéliser l'anisotropie initiale et induite du comportement mécanique et du comportement hydraulique. Pour la modélisation du comportement de l'argilite du Callovo-Oxfordien, des VER sont construits en tenant compte des travaux de caractérisation de la géométrie des inclusions microscopiques et des résultats expérimentaux d'essais macroscopiques.La loi de comportement homogénéisée numériquement ainsi calibrée est utilisée dans des simulations de creusement de galerie jusqu'à des niveaux d'endommagement générant une localisation de la déformation.Ces calculs montrent à la fois la pertinence et l'applicabilité du concept double échelle pour l'évaluation du comportement hydromécanique des EDZ dans un contexte du stockage des déchets radioactifs
Feasibility studies for deep geological radioactive waste disposal facilities have led to an increased interest in the geomechanical modelling of its host rock. In France, a potential host rock is the Callovo-Oxfordian claystone. The low permeability of this material is of key importance, as the principal of deep geological disposal strongly relies on the sealing capacity of the host formation. The permeability being coupled to the mechanical material state, hydromechanical coupled behaviour of the claystone becomes important when mechanical alterations are induced by gallery excavation in the so-called excavation damaged zone (EDZ). In materials with microstructure such as the Callovo-Oxfordian claystone [Robinet et al., 2012], the macroscopic behaviour has its origin in the interaction of its mi- cromechanical constituents. In addition to the coupling between hydraulic and mech- anical behaviour, a coupling between the micro (material microstructure) and macro will be made. By means of the development of a framework of computational homo- genization for hydromechanical coupling, a doublescale modelling approach is formu- lated, for which the macroscale constitutive relations are derived from the microscale by homogenization. An existing model for the modelling of hydromechanical coupling based on the distinct definition of grains and intergranular pore space [Frey, 2010] is adopted and modified to enable the application of first order computational homogenization for obtaining macroscale stress and fluid transport responses. This model is used to constitute a periodic representative elementary volume (REV) that allows the rep- resentation of the local macroscopic behaviour of the claystone. As a response to deformation loading, the behaviour of the REV represents the numerical equivalent of a constitutive relation at the macroscale. For the required consistent tangent operators, the framework of computational homogenization by static condensation [Kouznetsova et al., 2001] is extended to hy- dromechanical coupling. The theoretical developments of this extension are imple- mented in the finite element code Lagamine (Li` ege) as an independent constitutive relation. For the modelling of localization of deformation, which in classical FE meth- ods suffers from the well-known mesh dependency, the doublescale approach of hy- dromechanical coupling is combined with a local second gradient model [Collin et al., 2006] to control the internal length scale of localized deformation. By accepting the periodic boundary conditions as a regularization of the microscale deformation, the use of the multiscale model in combination with the local second gradient model can be used for modelling localization phenomena in HM-coupled settings with material softening. The modelling capacities of the approach are demonstrated by means of simula- tions of oedometer tests and biaxial compression tests. The approach is demonstrated to be a powerful way to model anisotropy in the mechanical as well as the hydraulic behaviour of the material both in the initial material state and as an effect of hy- dromechanical alterations. For the application to the modelling of Callovo-Oxfordian claystone, microstructural REVs are calibrated to geometrical characteristics of the inclusion that form the microstructure under consideration and to macroscale ex- perimental results of the mechanical behaviour. The calibrated constitutive relation is used in the simulation of gallery excavation processes. These computations give a proof of concept of the doublescale assessment of the hydromechanical behaviour of the excavation damaged zones around galleries in the context of nuclear waste disposal

Die rheumatoide Arthritis ist eine chronisch-entzündliche Bindegewebserkrankung mit symmetrischem Befall der Gelenke. Die genaue Ätiologie ist bisher unbekannt. Aktivierte synoviale Fibroblasten sollen durch gesteigerte Adhäsion und Produktion von proinflammatorischen Zytokinen und Matrix-lysierenden Proteasen maßgeblich an der Gelenkdestruktion beteiligt sein. Ziel dieser Arbeit war es, ein neues in-vivo-Knorpeldestruktions-Modell zu etablieren, in welchem unter immunkompetenten Bedingungen, die Invasion und Destruktion von Gelenkknorpel durch die Fibroblasten-Zelllinie LS48 über einen längeren Zeitraum simuliert werden kann. Die am Institut für klinische Immunologie der Medizinischen Fakultät der Universität Leipzig etablierte Zelllinie LS48 wurde in die ipsilateralen Kniegelenke von BALB/c-Mäusen injiziert. Die dadurch induzierte Gewebsdestruktion wurde über zehn Wochen in zweiwöchigem Abstand histopathologisch beurteilt und klassifiziert. Als vergleichende Fibroblasten-Zelllinie wurden nicht-invasive NIH/3T3-Zellen eingesetzt. An Hand der Score-Parameter Zellinvasion, Pannusformation und Knorpeldestruktion wurde eine mäßige bis schwer-wiegende Gewebsdestruktion durch die LS48-Zellen bereits ab der zweiten Untersuchungswoche lichtmikroskopisch nachgewiesen, ohne dass dabei pathologische Effekte in den kontralateralen Kniegelenken aufgetreten sind. Polarisationsmikroskopisch wurden für den Parameter Knorpeldestruktion vergleichbare Ergebnisse erzielt. Damit wurde gezeigt, dass das Modell BALB/c LS48 ein erfolgversprechendes Instrument darstellt, das zur Testung neuer therapeutischer Strategien gegen die Gelenkdestruktion verwendet werden kann. Inwieweit die Auseinandersetzung der LS48-Zellen mit dem spezifischen Immunsystem der BALB/c-Maus Auswirkungen auf den Verlauf der Gewebsdestruktion hat, sollte in weiterführenden Experimenten untersucht werden.

Das Wissen über Mechanismen, die einen Einfluss auf Muster der Artenvielfalt und biotische Interaktionen haben, ist grundlegend für den Schutz von Biodiversität. Darüber hinaus kann es von direktem ökonomischem Nutzen sein, zum Beispiel im biologischen Pflanzenschutz oder bei Bestäubungsdienstleistungen. Die Größe eines Organismus kann ein solcher Faktor sein, der die Artenzahl und Interaktionen der assoziierten Organismen beeinflusst, denn große Organismen sind auffälliger als kleine und ihr Angebot an Ressourcen und Nischen für mit ihnen assoziierte Organismen ist oft reicher. Bezogen auf Pflanzen könnte daher die Größe einer Pflanze einen erheblichen Einfluss auf die Artenzahl der mit ihr assoziierten Arthropoden und ihre biotischen Interaktionen wie Herbivorie oder Bestäubung haben. Trotzdem ist der Einfluss der Pflanzengröße auf mutualistische und antagonistische Interaktionspartner der Pflanze und der sich daraus ergebende Einfluss auf die reproduktive Fitness der Pflanze bisher nicht umfassend und unter standardisierten Bedingungen untersucht worden. In der vorliegenden Studie wurden die Auswirkungen der Pflanzengröße auf die Artenzahl von Herbivoren, deren Gegenspielern und Bestäubern untersucht, sowie die Auswirkungen dieser Interaktionspartner auf die Pflanzenfitness. Dabei wurde zusätzlich zwischen endophagen und ektophagen Herbivoren und deren Gegenspielern unterschieden. Außerdem wurden die Herbivoren einzelner Pflanzenkompartimente und deren Gegenspieler separat analysiert. Des Weiteren wurde der Einfluss der Pflanzengröße auf den Herbivorieschaden an den verschiedenen Pflanzenkompartimenten und deren Einfluss auf die reproduktive Fitness der Pflanze, d.h. auf ihre Samenzahl, Tausendkorngewicht und Samengesamtgewicht, untersucht. Zuletzt wurde besonderes Augenmerk auf den Einfluss der Pflanzengröße auf mutualistische und antagonistische Blütenbesucher und deren Einfluss auf die reproduktive Fitness gelegt und untersucht, ob und inwiefern die reproduktive Fitness letztendlich von der Pflanzengröße abhängig ist. Zur Untersuchung dieser Fragen wurde ein „Common Garden“-Experiment angelegt. Um einen interspezifischen Pflanzengrößengradienten zu erzeugen, wurden 21 annuelle Pflanzenarten aus der Familie der Kreuzblütler (Brassicaceae) ausgewählt, deren Größe von 10 bis 130 cm reichte (gemessen als Pflanzenhöhe vom Boden bis zur Spitze). So konnten die Einflüsse des Habitats und der umgebenden Landschaft für alle Pflanzenarten standardisiert und trotzdem ein breiter Gradient realisiert werden. Dadurch hebt sich diese Studie von den bisherigen ab, die den Effekt von meist intraspezifischer Pflanzengröße auf die assoziierten Tiere anhand wild wachsender Pflanzen untersucht haben. Pflanzengröße sowie Zahl, Biomasse und Größe der unterschiedlichen überirdischen Pflanzenkompartimente (Blüten, Schoten, Blätter, Stängel) sowie Blütendeckung und -farbe wurden aufgenommen. Der Herbivorieschaden an diesen Pflanzenkompartimenten und die reproduktive Fitness (Samenzahl, Tausendkorngewicht und Gesamtsamengewicht) wurden gemessen. An und in Blüten, Schoten, Blättern und Stängeln wurden herbivore, räuberische, parasitäre und bestäubende Arthropoden gezählt. Die Pflanzengröße hatte einen positiven Einfluss auf die Artenzahl von Herbivoren, deren Gegenspielern und Bestäubern. Das traf ebenso auf endophage und ektophage sowie auf mit Blättern und Schoten assoziierte Herbivore und deren Gegenspieler zu. Des Weiteren konnte ein Anstieg des Herbivorieschadens an Blüten und Schoten mit zunehmender Pflanzengröße festgestellt werden, wohingegen der Schaden an Blättern und Stängeln von der Biomasse des entsprechenden Kompartiments positiv beeinflusst wurde. Der Schaden an Blüten hatte den stärksten Einfluss auf die reproduktive Fitness und reduzierte neben der Samenzahl auch das Tausendkorngewicht und das Gesamtsamengewicht der Pflanze. Die genaue Analyse der blütenbesuchenden Insekten ergab einen positiven Einfluss der Pflanzengröße auf die Abundanz und Artenzahl von Bestäubern (allerdings nicht bei extrem großem Blütenangebot), wie auch auf die Abundanz der adulten und juvenilen Rapsglanzkäfer und deren Parasitierungsrate. Steigende Rapsglanzkäferzahlen verringerten die Samenzahl sowie das Tausendkorngewicht, während die Bestäuber sich lediglich auf die Samenzahl positiv auswirkten. Insgesamt führte ein Anstieg der Pflanzenhöhe zu einer Abnahme des Tausendkorngewichts, aber nicht zu einer Veränderung der Samenzahl oder des Gesamtsamengewichts, was auf einen Ausgleich der Effekte von zunehmender Antagonistenzahl und zunehmender Mutualistenzahl hindeutet. Großen Pflanzen entstehen also durch ihre Auffälligkeit und Attraktivität für Herbivore hohe Fitnesskosten, wobei insbesondere der Blütenschaden durch Rapsglanzkäfer einen starken negativen Einfluss auf Samenzahl, Tausendkorngewicht und Gesamtsamengewicht hat. Diesen Fitnesskosten großer Pflanzen wirkt der Nutzen durch ihre Auffälligkeit und Attraktivität für Bestäuber entgegen, die die Samenzahl positiv beeinflussen. Hinsichtlich der Samenzahl sollten also große Pflanzen gegenüber kleineren im Vorteil sein, wenn die Insektengemeinschaft des Habitats von Bestäubern dominiert wird. Wird sie aber von herbivoren Blütenbesuchern dominiert, sollten kleine Pflanzen gegenüber großen einen Vorteil haben. Im Gegensatz dazu sollten große Pflanzen immer einen Nachteil bezüglich des Tausendkorngewichts haben, das von Antagonisten, nicht aber von Mutualisten beeinflusst wurde. Der Einfluss der Pflanzengröße auf biotische Interaktionen wurde bisher oft unterschätzt, obwohl er sich auf komplexe Weise über die mutualistischen und antagonistischen Insekten auf die reproduktive Fitness der Pflanze auswirkt.

The classical Cauchy-Boltzmann theory of continuum mechanics requires that the dimension, over which macroscopic gradients occur, are much larger than characteristic length scales of the microstructure. For this reason, the classical continuum theory comes to its limits for very small specimens or if material degradation leads to a localisation of deformations into bands, whose width is determined by the microstructure itself. Deviations from the predictions of the classical theory of continuum mechanics are referred to as size effects. It is well-known, that generalised continuum theories can describe size effects in principle. Especially micromorphic theories gain increasing popularity due its favorable numerical implementation. However, the formulation of the additionally necessary constitutive equations is a problem. For linear-elastic behavior, the number of material parameters increases considerably compared to the classical theory. The experimental determination of these parameters is thus very difficult. For nonlinear and history-dependent processes, even the qualitative structure of the constitutive equations can hardly be assessed solely on base of phenomenological considerations. Homogenisation methods are a promising approach to solve this problem. The present thesis starts with a critical review on the classical theory of homogenisation and the approaches on micromorphic homogenisation which are available in literature. On this basis, a theory is developed for the homogenisation of a classical Cauchy-Boltzmann continuum at the microscale towards a micromorphic continuum at the macroscale. In particular, the micro-macro-relations are specified for all macroscopic kinetic and kinematic field quantities. On the microscale, the corresponding boundary-value problem is formulated, whereby kinematic, static or periodic boundary conditions can be used. No restrictions are imposed on the material behavior, i. e. it can be linear or nonlinear. The special cases of the micropolar theory (Cosserat theory), microstrain theory and microdilatational theorie are considered. The proposed homogenisation method is demonstrated for several examples. The simplest example is the uniaxial case, for which the exact solution can be specified. Furthermore, the micromorphic elastic properties of a porous, foam-like material are estimated in closed form by means of Ritz' method with a cubic ansatz. A comparison with partly available exact solutions and FEM solutions indicates a qualitative and quantitative agreement of sufficient accuracy. For the special cases of micropolar and microdilatational theory, the material parameters are specified in the established nomenclature from literature. By means of these material parameters the size effect of an elastic foam structure is investigated and compared with corresponding results from literature. Furthermore, micromorphic damage models for quasi-brittle and ductile failure are presented. Quasi-brittle damage is modelled by propagation of microcracks. For the ductile mechanism, Gurson's limit-load approach on the microscale is extended by microdilatational terms. A finite-element implementation shows, that the damage model exhibits h-convergence even in the softening regime and that it thus can describe localisation.:1 Introduction 2 Literature review: Micromorphic theory and strain-gradient theory 2.1 Variational approach 2.1.1 Cauchy-Boltzmann continuum 2.1.2 Second gradient theory / Strain gradient theory 2.1.3 Micromorphic theory 2.1.4 Method of virtual power 2.2 Homogenisation approaches 2.2.1 Classical theory of homogenisation 2.2.2 Strain-gradient theory by Gologanu, Kouznetsova et al. 2.2.3 Micromorphic theory by Eringen 2.2.4 Average field theory by Forest et al. 2.3 Scope of the present thesis 3 Homogenisation towards a micromorphic continuum 3.1 Thermodynamic considerations and generalized Hill-Mandel lemma 3.2 Surface operator and kinetic micro-macro relations 3.3 Kinematic micro-macro relations 3.4 Porous material 3.5 Kinematic and periodic boundary conditions 3.6 Special cases 3.6.1 Strain-gradient theory / Second gradient theory 3.6.2 Micropolar theory 3.6.3 Microstrain theory 3.6.4 Microdilatational theory 4 Elastic Behaviour 4.1 Uniaxial case 4.2 Upper bound estimates by Ritz' Method 4.3 Isotropic porous material 4.4 Micropolar theory 4.5 Microdilatational theory 4.6 Size effect in simple shear 5 Damage Models 5.1 Quasi-brittle damage 5.2 Microdilatational extension of Gurson’s model of ductile damage 5.2.1 Limit load analysis for rigid ideal-plastic material 5.2.2 Phenomenological extensions 5.2.3 FEM implementation 5.2.4 Example 6 Discussion
Die klassische Cauchy-Boltzmann-Kontinuumstheorie setzt voraus, dass die Abmessungen, über denen makroskopische Gradienten auftreten, sehr viele größer sind als charakteristische Längenskalen der Mikrostruktur. Aus diesem Grund stößt die klassische Kontinuumstheorie bei sehr kleinen Proben ebenso an ihre Grenzen wie bei Schädigungsvorgängen, bei denen die Deformationen in Bändern lokalisieren, deren Breite selbst von der Längenskalen der Mikrostruktur bestimmt wird. Abweichungen von Vorhersagen der klassischen Kontinuumstheorie werden als Größeneffekte bezeichnet. Es ist bekannt, dass generalisierte Kontinuumstheorien Größeneffekte prinzipiell beschreiben können. Insbesondere mikromorphe Theorien erfreuen sich auf Grund ihrer vergleichsweise einfachen numerischen Implementierung wachsender Beliebtheit. Ein großes Problem stellt dabei die Formulierung der zusätzlich notwendigen konstitutiven Gleichungen dar. Für linear-elastisches Verhalten steigt die Zahl der Materialparameter im Vergleich zur klassischen Theorie stark an, was deren experimentelle Bestimmung sehr schwierig macht. Bei nichtlinearen und lastgeschichtsabhängigen Prozessen lässt sich selbst die qualitative Struktur der konstitutiven Gleichungen ausschließlich auf Basis phänomenologischer Überlegungen kaum erschließen. Homogenisierungsverfahren stellen einen vielversprechenden Ansatz dar, um dieses Problem zu lösen. Die vorliegende Arbeit gibt zunächst einen kritischen Überblick über die klassische Theorie der Homogenisierung sowie die im Schrifttum verfügbaren Ansätze zur mikromorphen Homogenisierung. Auf dieser Basis wird eine Theorie zur Homogenisierung eines klassischen Cauchy-Boltzmann-Kontinuums auf Mikroebene zu einem mikromorphen Kontinuum auf der Makroebene entwickelt. Insbesondere werden Mikro-Makro-Relationen für alle makroskopischen kinetischen und kinematischen Feldgrößen angegebenen. Auf der Mikroebene wird das entsprechende Randwertproblem formuliert, wobei kinematische, statische oder periodische Randbedingungen verwendet werden können. Das Materialverhalten unterliegt keinen Einschränkungen, d. h., dass es sowohl linear als auch nichtlinear sein kann. Die Sonderfälle der mikropolaren Theorie (Cosserat-Theorie), Mikrodehnungstheorie und mikrodilatationalen Theorie werden erarbeitet. Das vorgeschlagene Homogenisierungsverfahren wird für eine Reihe von Beispielen demonstriert. Als einfachstes Beispiel dient der einachsige Fall, für den die exakte Lösung angegebenen werden kann. Weiterhin werden die mikromorphen, elastischen Eigenschaften eines porösen, schaumartigen Materials mittels des Ritz-Verfahrens mit einem kubischen Ansatz in geschlossener Form abgeschätzt. Ein Vergleich mit teilweise verfügbaren exakten Lösungen sowie FEM-Lösungen weist eine qualitative und quantitative Übereinstimmung hinreichender Genauigkeit aus. Für die Sonderfälle mikropolaren und mikrodilatationalen Theorien werden die Materialparameter in der im Schrifttum üblichen Nomenklatur angegebenen. Mittels dieser Materialparameter wird der Größeneffekt in einer elastischen Schaumstruktur untersucht und mit entsprechenden Ergebnissen aus dem Schrifttum verglichen. Desweiteren werden mikromorphe Schädigungsmodelle für quasi-sprödes und duktiles Versagen vorgestellt. Quasi-spröde Schädigung wird durch das Wachstum von Mikrorissen modelliert. Für den duktilen Mechanismus wird der Ansatz von Gurson einer Grenzlastanalyse auf Mikroebene um mikrodilatationale Terme erweitert. Eine Finite-Elemente-Implementierung zeigt, dass das Schädigungsmodell auch im Entfestigungsbereich h-Konvergenz aufweist und die Lokalisierung beschreiben kann.:1 Introduction 2 Literature review: Micromorphic theory and strain-gradient theory 2.1 Variational approach 2.1.1 Cauchy-Boltzmann continuum 2.1.2 Second gradient theory / Strain gradient theory 2.1.3 Micromorphic theory 2.1.4 Method of virtual power 2.2 Homogenisation approaches 2.2.1 Classical theory of homogenisation 2.2.2 Strain-gradient theory by Gologanu, Kouznetsova et al. 2.2.3 Micromorphic theory by Eringen 2.2.4 Average field theory by Forest et al. 2.3 Scope of the present thesis 3 Homogenisation towards a micromorphic continuum 3.1 Thermodynamic considerations and generalized Hill-Mandel lemma 3.2 Surface operator and kinetic micro-macro relations 3.3 Kinematic micro-macro relations 3.4 Porous material 3.5 Kinematic and periodic boundary conditions 3.6 Special cases 3.6.1 Strain-gradient theory / Second gradient theory 3.6.2 Micropolar theory 3.6.3 Microstrain theory 3.6.4 Microdilatational theory 4 Elastic Behaviour 4.1 Uniaxial case 4.2 Upper bound estimates by Ritz' Method 4.3 Isotropic porous material 4.4 Micropolar theory 4.5 Microdilatational theory 4.6 Size effect in simple shear 5 Damage Models 5.1 Quasi-brittle damage 5.2 Microdilatational extension of Gurson’s model of ductile damage 5.2.1 Limit load analysis for rigid ideal-plastic material 5.2.2 Phenomenological extensions 5.2.3 FEM implementation 5.2.4 Example 6 Discussion

Die Arbeit widmet sich der Entwicklung und numerischen Implementierung eines nichtlokalen kontinuumsmechanischen Schädigungsmodells zur Beschreibung des duktilen Versagens eines austenitischen TRIP-Stahlgusses. Dieser weist eine martensitische Phasenumwandlung während der Verformung auf. Das Umwandlungs- und Verfestigungsverhalten des Untersuchungswerkstoffs hängt stark von Temperatur und Spannungszustand ab. Deshalb wird ein vollständig thermomechanisch gekoppeltes Viskoplastizitätsmodell zugrunde gelegt, welches die temperaturabhängige Zug-Druck-Asymmetrie von Verfestigung und verformungsinduzierter Martensitentwicklung abbildet. Bei erhöhter Dehnrate können experimentell beobachtete Kreuzungseffekte der Fließkurven vorhergesagt werden. Die Schädigungsmodellierung baut auf dem viskoplastischen Grundmodell auf, wobei das netzunabhängige Verhalten durch eine Gradientenerweiterung im Rahmen der mikromorphen Theorie erreicht wird. Im Modell können verschiedene Ansätze für Schädigungsinitiierung und -entwicklung kombiniert werden. Die Einflüsse der Modellparameter auf die Ergebnisse von Risswachstumssimulationen werden für ausgewählte Modellvarianten untersucht und bewertet. Mithilfe erarbeiteter Kalibrierungsstrategien können die qualifizierten Varianten erfolgreich an experimentelle Ergebnisse von Kerbzugversuchen und bruchmechanischen Kompaktzugproben angepasst werden.
The present thesis comprises the development and numerical implementation of a non-local damage model in order to describe ductile failure of a cast austenitic TRIP-steel. The TRIP-steel shows a martensitic phase transformation during deformation. The transformation and strain hardening behavior is strongly dependent on temperature and stress state. For this reason, a fully thermomechanically coupled viscoplasticity model is proposed, which exhibits the temperature dependent tension-compression-asymmetry of strain hardening and deformation-induced martensite evolution. Experimentally observed crossing effects of the flow curves can be predicted at increased strain rates. The damage modeling is based on the viscoplastic basic model, whereby the mesh-independent behavior is achieved by a gradient extension within the framework of micromorphic theory. Different approaches for damage initiation and evolution can be combined within the model. The influences of the model parameters on results of crack growth simulations are investigated and evaluated for selected model variants. With the help of developed calibration strategies the qualified variants can be successfully adapted to experimental results of notched tensile tests and compact tension tests.

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 microstructure.:1 Introduction 7 2 Generalised Continua - a journey 9 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Principal classes of generalised continua . . . . . . . . . . . . . . . . . 10 2.2.1 Polar field theories and their relatives . . . . . . . . . . . . . . 10 2.2.2 Non-local continua . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Generalised continua by explicit homogenisation . . . . . . . . . . . . 15 2.3.1 Random micro-structures . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Periodic micro-structures . . . . . . . . . . . . . . . . . . . . . 18 2.3.3 Generalised homogenisation based on polynomials . . . . . . 20 3 Modelling of quasi-brittle failure 25 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Discussion of main results . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Bibliography 29 4 Collection of articles reflecting the author’s contribution 35
Eine 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.:1 Introduction 7 2 Generalised Continua - a journey 9 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Principal classes of generalised continua . . . . . . . . . . . . . . . . . 10 2.2.1 Polar field theories and their relatives . . . . . . . . . . . . . . 10 2.2.2 Non-local continua . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 Generalised continua by explicit homogenisation . . . . . . . . . . . . 15 2.3.1 Random micro-structures . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Periodic micro-structures . . . . . . . . . . . . . . . . . . . . . 18 2.3.3 Generalised homogenisation based on polynomials . . . . . . 20 3 Modelling of quasi-brittle failure 25 3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Discussion of main results . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Bibliography 29 4 Collection of articles reflecting the author’s contribution 35

The thesis is devoted to study of continuum mechanics and thermodynamics and the related mathematical analysis. It consists of four self-contained chapters dealing with different aspects. The first chapter focuses on peridynamics, a non-local theory of continuum mechanics, and its relation to conventional local theory of Cauchy-Green elasticity. Similar compar- isons has been used for proving consistency and for determining some of the material coefficients in peridynamics, provided the material parameters in the local theory are known. In this chapter the formula for the non-local force-flux is computed in terms of the peridynamic interaction, relating the fundamental concepts of these two theories and establishing hence a new connection, not present in the previous works. The second and third chapters are both devoted to Rate-Independent Systems (RIS) and their applications to continuum mechanics. RIS represents a suitable approximation when the internal, viscous, and thermal effects can be neglected. RIS has been proven to be useful in modeling hysteresis, phase transitions in solids, elastoplasticity, damage, or fracture in both small and large strain regimes. In the second chapter the existence of solutions to an evolutionary rate-independ- ent model of Shape Memory Alloys (SMAs) is proven. The model...