Este trabalho tem por objetivo demonstrar a viabilidade do emprego da teoria de interação de substâncias no contínuo para a análise de compostos multifásicos, sendo possível considerar-se substâncias anisótropas através de sua representação via uma formulação isótropa equivalente. No campo teórico, referente à anisotropia via formulação isótropa equivalente, deduzem-se tensores de mapeamento de tensões e deformações para o espaço fictício na configuração deformada, adequados às análises com grandes deformações. Os modelos de materiais compostos e de anisotropia propostos, foram implementados no âmbito de um código de cálculo para análise dinâmica explícita com grandes deformações. Entre as aplicações do programa destacam-se o estudo de problemas de conformação de lâminas metálicas e de compostos multifásicos e a possibilidade de analisar compostos de matriz frágil reforçada por fibras curtas, considerando-se uma função simples de dano elasto-plástico. Os exemplos executados mostram boa concordância dos resultados obtidos neste trabalho com aqueles obtidos por outros autores e com alguns resultados experimentais existentes. / The aim of this work is to valuate the performance of the theory of interacting substances in the continuum (role of mixtures) applied to composites including anisotropic substances which are modeled by an isotropic equivalent formulation. In the theoretical field, with respect to the anisotropy consideration by an equivalent isotropic formulation on the deformed configuration, convenient mapping tensors for stresses and strains in the fictitious space are deduced and applied to large deformation problems. The proposed models of anisotropy and composites were implemented in an explicit code for dynamic analysis with large deformations. The code is applied to the solution of sheet metal forming processes and multiphase composites including an analysis of a brittle matrix composite reinforced by short fibers by a simple elastoplastic damage model. The numerical results of the chosen examples are in good agreement with those suggested in some references or with some reported experiments.

In the present study, we propose a computational model for the linear and nonlinear analysis of shell structures. We consider a tensor-based finite element formulation which describes the mathematical shell model in a natural and simple way by using curvilinear coordinates. To avoid membrane and shear locking we develop a family of high-order elements with Lagrangian interpolations. The approach is first applied to linear deformations based on a novel and consistent third-order shear deformation shell theory for bending of composite shells. No simplification other than the assumption of linear elastic material is made in the computation of stress resultants and material stiffness coefficients. They are integrated numerically without any approximation in the shifter. Therefore, the formulation is valid for thin and thick shells. A conforming high-order element was derived with 0 C continuity across the element boundaries. Next, we extend the formulation for the geometrically nonlinear analysis of multilayered composites and functionally graded shells. Again, Lagrangian elements with high-order interpolation polynomials are employed. The flexibility of these elements mitigates any locking problems. A first-order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the Lagrangian description. This approach takes into account thickness changes and, therefore, 3D constitutive equations are utilized. Finally, extensive numerical simulations and comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and laminated composites, as well as functionally graded shells, are found to be excellent and show the validity of the developed finite element model. Moreover, the simplicity of this approach makes it attractive for future applications in different topics of research, such as contact mechanics, damage propagation and viscoelastic behavior of shells.

L’analyse du comportement des pieux est un problème complexe du fait de la diversité des phénomènes qui gouvernent le comportement du sol et en particulier celui se trouvant au voisinage du pieu. Ce dernier dépend particulièrement du procédé d’installation du pieu qui peut parfois engendrer des déformations de très grande amplitude dans le sol entre autre phénomènes. L’objectif de ce travail est de mettre en place un outil de modélisation pour évaluer le comportement des pieux sous chargements axiaux en développant des modèles représentant les phénomènes physiques pertinents et de les intégrer numériquement dans un logiciel aux éléments finis utilisant des algorithmes robustes et efficaces. Pour pouvoir modéliser la phase d’installation statique ou dynamique d’un pieu quelques problématiques doivent être considérées. Premièrement, étant donné que pendant l’installation d’un pieu des déformations finies (non-infinitésimal) ont lieu au niveau de l’interface, une formulation eulérienne avec un taux logarithmique des déformations a été adoptée pour prendre en compte le fait que l’hypothèse des déformations infinitésimales n’est plus valable. En plus, le modèle constitutive doit prendre en compte le comportement physique du sol lorsqu’il est soumis à des déplacements d’une magnitude élevée. Le dernier est constitué, entre autres, par le phénomène de l’écrasement des grains ce qui influence beaucoup le comportement volumique du sol et finalement sa résistance au cisaillement ou en d’autres termes le frottement mobilisé. Ce phénomène a été modélisé en introduisant une variable d’écrouissage supplémentaire au modèle de comportement élastoplastique de l’ECP. Les critères d’admissibilité thermodynamique ont été vérifiés pour le modèle constitutive original ainsi que pour le modèle révisé. Des simulations numériques ont été faites pour les deux types d’installation, monotone et pseudo-dynamique (cyclique) et les résultats ont été analysés en détail. Finalement, la dégradation de la résistance au cisaillement au niveau du fût des pieux est un phénomène typique qui se produit pendant le chargement cyclique des fondations composées par des pieux. Le modèle constitutive pour pouvoir bien reproduire ce phénomène n’est pas simple à définir car le chemin de chargement suivi par l’interface sol-pieu est très dépendant du comportement volumique du sol qui à son tours dépend de l’histoire de chargement et des conditions aux limites du problème. Une étude détaillée de toutes les composantes du comportement du pieu pendant ce type de chargement a été effectuée afin de mettre en évidence l’influence de l’histoire de chargement sur la résistance au cisaillement et l’apparition des phénomènes tels que la fatigue du frottement. / The analysis of pile behavior is a complex problem due to the diversity of the phenomena governing the soil behavior and particularly that of the neighboring soil. The objective of this work was to develop a valid modeling tool to evaluate piles’ behavior under axial loads by developing a pertinent mechanical model supported in a robust finite element program which would successfully reproduce the soil behaviour under extreme monotonic and cyclic shear strain. This is done to allow for the numerical modelling of the installation procedure of pile foundations and continued loading of high amplitude cyclic paths. In order to model the installation phase of a monotonic, jacked or dynamic pile foundation some issues must be addressed. Finite deformations take place whilst the pile is put in place requiring an adjustment in the mechanical formulation of the model at the interface level to take into account that the small deformations (rotations and strain) hypothesis is no longer valid. Moreover, the constitutive model must take into account the physical behaviour of the soil when subjected to high order of magnitude displacements. This includes the phenomenon of grain breakage, also referred to as particle crushing, which greatly influences the volumetric behaviour of soil as thus reflecting of shear stress mobilization. The elastoplastic ECP model has therefore been enhanced by introducing an internal variable taking into account the breakage mechanism. The thermodynamic admissibility criteria are verified for the original and revised constitutive models. Both monotonic and pseudo-dynamic installation procedures were numerically simulated and the results thoroughly analysed. Finally, the cyclic shear resistance degradation at the pile shaft is a commonly occurring phenomenon during continued cyclic loading of pile foundation (friction fatigue). The constitutive modelling of this phenomenon, however, is not a straightforward matter. The stress path followed by the thin layer at the soil-pile interface level is known to be directly related to the volumetric behaviour due to the boundary conditions of the problem. A comprehensive analysis of all the components of the behaviour of soil during this stage was object of study in this work.

Este trabalho tem por objetivo demonstrar a viabilidade do emprego da teoria de interação de substâncias no contínuo para a análise de compostos multifásicos, sendo possível considerar-se substâncias anisótropas através de sua representação via uma formulação isótropa equivalente. No campo teórico, referente à anisotropia via formulação isótropa equivalente, deduzem-se tensores de mapeamento de tensões e deformações para o espaço fictício na configuração deformada, adequados às análises com grandes deformações. Os modelos de materiais compostos e de anisotropia propostos, foram implementados no âmbito de um código de cálculo para análise dinâmica explícita com grandes deformações. Entre as aplicações do programa destacam-se o estudo de problemas de conformação de lâminas metálicas e de compostos multifásicos e a possibilidade de analisar compostos de matriz frágil reforçada por fibras curtas, considerando-se uma função simples de dano elasto-plástico. Os exemplos executados mostram boa concordância dos resultados obtidos neste trabalho com aqueles obtidos por outros autores e com alguns resultados experimentais existentes. / The aim of this work is to valuate the performance of the theory of interacting substances in the continuum (role of mixtures) applied to composites including anisotropic substances which are modeled by an isotropic equivalent formulation. In the theoretical field, with respect to the anisotropy consideration by an equivalent isotropic formulation on the deformed configuration, convenient mapping tensors for stresses and strains in the fictitious space are deduced and applied to large deformation problems. The proposed models of anisotropy and composites were implemented in an explicit code for dynamic analysis with large deformations. The code is applied to the solution of sheet metal forming processes and multiphase composites including an analysis of a brittle matrix composite reinforced by short fibers by a simple elastoplastic damage model. The numerical results of the chosen examples are in good agreement with those suggested in some references or with some reported experiments.

Shape memory polymers (SMPs) are a relatively new class of active materials that can store a temporary shape and return to the original configuration upon application of a stimulus such as temperature. This shape changing ability has led to increased interest in their use for biomedical and aerospace applications. A major challenge, however, in the advancement of these applications is the ability to accurately predict the material behavior for complex geometries and boundary conditions. This work addresses this challenge by developing an experimentally calibrated and validated constitutive model that is implemented as a user material subroutine in Abaqus ? a commercially available finite element software package. The model is formulated in terms of finite deformations and assumes the SMP behaves as a thermoelastic material, for which the response is modeled using a compressible neo-Hookean constitutive equation. An internal state variable, the glassy volume fraction, is introduced to account for the phase transformation and associated stored deformation upon cooling from the rubbery phase to the glassy phase and subsequently recovered upon heating. The numerical implementation is performed such that a system of equations is solved using a Newton-Raphson method to find the updated stress in the material. The conductive heat transfer is incorporated through solving Fourier's law simultaneously with the constitutive equations. To calibrate and validate the model parameters, thermomechanical experiments are performed on an amorphous, thermosetting polyurethane shape memory polymer. Strains of 10-25% are applied and both free recovery (zero load) and constrained displacement recovery boundary conditions are considered for each value of applied strain. Using the uniaxial experimental data, the model is then calibrated and compared to the 1-D experimental results. The validated finite element analysis tool is then used to model biomedical devices, including cardiovascular tubes and thrombectomy devices, fabricated from shape memory polymers. The effects of heat transfer and complex thermal boundary conditions are evaluated using coupled thermal-displacement analysis, for which the thermal material properties were experimentally calibrated.

The analysis of pile behavior is a complex problem due to the diversity of the phenomena governing the soil behavior and particularly that of the neighboring soil. The objective of this work was to develop a valid modeling tool to evaluate piles' behavior under axial loads by developing a pertinent mechanical model supported in a robust finite element program which would successfully reproduce the soil behaviour under extreme monotonic and cyclic shear strain. This is done to allow for the numerical modelling of the installation procedure of pile foundations and continued loading of high amplitude cyclic paths. In order to model the installation phase of a monotonic, jacked or dynamic pile foundation some issues must be addressed. Finite deformations take place whilst the pile is put in place requiring an adjustment in the mechanical formulation of the model at the interface level to take into account that the small deformations (rotations and strain) hypothesis is no longer valid. Moreover, the constitutive model must take into account the physical behaviour of the soil when subjected to high order of magnitude displacements. This includes the phenomenon of grain breakage, also referred to as particle crushing, which greatly influences the volumetric behaviour of soil as thus reflecting of shear stress mobilization. The elastoplastic ECP model has therefore been enhanced by introducing an internal variable taking into account the breakage mechanism. The thermodynamic admissibility criteria are verified for the original and revised constitutive models. Both monotonic and pseudo-dynamic installation procedures were numerically simulated and the results thoroughly analysed. Finally, the cyclic shear resistance degradation at the pile shaft is a commonly occurring phenomenon during continued cyclic loading of pile foundation (friction fatigue). The constitutive modelling of this phenomenon, however, is not a straightforward matter. The stress path followed by the thin layer at the soil-pile interface level is known to be directly related to the volumetric behaviour due to the boundary conditions of the problem. A comprehensive analysis of all the components of the behaviour of soil during this stage was object of study in this work.

No presente trabalho é descrita uma formulação para modelos constitutivos elastoviscoplásticos, considerando deformações infinitesimais e finitas. Os modelos são formulados em um contexto da termodinâmica de variáveis internas usando fundamentos de análise convexa. As equações de evolução são obtidas a partir do princípio da máxima dissipação, o qual desempenha um importante papel na abordagem adotada, a qual consiste na generalização do modelo reológico de Bingham. O problema constitutivo de valor inicial local é solucionado por um esquema de integração implícita combinado a um algoritmo de mapeamento de retorno. O problema de valor no contorno e inicial global, considerando casos quasi-estáticos, é solucionado por meio do método dos elementos finitos (MEF) empregando também um método de integração implícita. Esta estratégia é implementada empregando os modelos constitutivos viscoplásticos linear e não linear de Perzyna e o modelo de Perié. A implementação computacional é avaliada por meio da comparação dos resultados numéricos a soluções analíticas e também a problemas padrões disponíveis na literatura. Os resultados obtidos são importantes para avaliar o comportamento e as características dos modelos viscoplásticos na análise dos fenômenos de dependência da taxa de deformação e de relaxação de tensão. Embora os três modelos se mostrem adequados à captura destes fenômenos, uma atenção especial deve ser dada ao modelo não linear de Perzyna, pois este não recupera o modelo invíscido como um caso limite, além disso, apresenta mal condicionamento no algoritmo de mapeamento de retorno. / In this work an elastic-viscoplastic constitutive formulation is described, considering infinitesimal and finite deformations. The models are formulated inside a thermodynamic with internal variables framework using fundamentais from convex analysis. The evolution equations are obtained from the maximum dissipation principie, which plays an important role on the approach adopted, which is the generalization of the Bingham rheological model. The local initial value problem is solved by an implicit integration scheme with a return mapping algorithm. The global initial boundary value problem is solved by the finite element method (FEM) also employing an implicit integration method. The strategy is implemented employing the linear and nonlinear Perzyna and the Perié viscoplastic models. The computational implementation is evaluated by comparing the numerical results with analytical solutions and with benchmarks available in the literature. The results obtained are important to evaluate the behavior and the characteristics of the models on the analysis of rate-dependency and stress relaxation. The three models were suitable to predict these phenomena. However, a special attention is needed on the nonlinear Perzyna model, because it does not recover the inviscid model as a limit case. Further, it presents ill-conditioning in the return mapping algorithm.

No presente trabalho é descrita uma formulação para modelos constitutivos elastoviscoplásticos, considerando deformações infinitesimais e finitas. Os modelos são formulados em um contexto da termodinâmica de variáveis internas usando fundamentos de análise convexa. As equações de evolução são obtidas a partir do princípio da máxima dissipação, o qual desempenha um importante papel na abordagem adotada, a qual consiste na generalização do modelo reológico de Bingham. O problema constitutivo de valor inicial local é solucionado por um esquema de integração implícita combinado a um algoritmo de mapeamento de retorno. O problema de valor no contorno e inicial global, considerando casos quasi-estáticos, é solucionado por meio do método dos elementos finitos (MEF) empregando também um método de integração implícita. Esta estratégia é implementada empregando os modelos constitutivos viscoplásticos linear e não linear de Perzyna e o modelo de Perié. A implementação computacional é avaliada por meio da comparação dos resultados numéricos a soluções analíticas e também a problemas padrões disponíveis na literatura. Os resultados obtidos são importantes para avaliar o comportamento e as características dos modelos viscoplásticos na análise dos fenômenos de dependência da taxa de deformação e de relaxação de tensão. Embora os três modelos se mostrem adequados à captura destes fenômenos, uma atenção especial deve ser dada ao modelo não linear de Perzyna, pois este não recupera o modelo invíscido como um caso limite, além disso, apresenta mal condicionamento no algoritmo de mapeamento de retorno. / In this work an elastic-viscoplastic constitutive formulation is described, considering infinitesimal and finite deformations. The models are formulated inside a thermodynamic with internal variables framework using fundamentais from convex analysis. The evolution equations are obtained from the maximum dissipation principie, which plays an important role on the approach adopted, which is the generalization of the Bingham rheological model. The local initial value problem is solved by an implicit integration scheme with a return mapping algorithm. The global initial boundary value problem is solved by the finite element method (FEM) also employing an implicit integration method. The strategy is implemented employing the linear and nonlinear Perzyna and the Perié viscoplastic models. The computational implementation is evaluated by comparing the numerical results with analytical solutions and with benchmarks available in the literature. The results obtained are important to evaluate the behavior and the characteristics of the models on the analysis of rate-dependency and stress relaxation. The three models were suitable to predict these phenomena. However, a special attention is needed on the nonlinear Perzyna model, because it does not recover the inviscid model as a limit case. Further, it presents ill-conditioning in the return mapping algorithm.

No presente trabalho é descrita uma formulação para modelos constitutivos elastoviscoplásticos, considerando deformações infinitesimais e finitas. Os modelos são formulados em um contexto da termodinâmica de variáveis internas usando fundamentos de análise convexa. As equações de evolução são obtidas a partir do princípio da máxima dissipação, o qual desempenha um importante papel na abordagem adotada, a qual consiste na generalização do modelo reológico de Bingham. O problema constitutivo de valor inicial local é solucionado por um esquema de integração implícita combinado a um algoritmo de mapeamento de retorno. O problema de valor no contorno e inicial global, considerando casos quasi-estáticos, é solucionado por meio do método dos elementos finitos (MEF) empregando também um método de integração implícita. Esta estratégia é implementada empregando os modelos constitutivos viscoplásticos linear e não linear de Perzyna e o modelo de Perié. A implementação computacional é avaliada por meio da comparação dos resultados numéricos a soluções analíticas e também a problemas padrões disponíveis na literatura. Os resultados obtidos são importantes para avaliar o comportamento e as características dos modelos viscoplásticos na análise dos fenômenos de dependência da taxa de deformação e de relaxação de tensão. Embora os três modelos se mostrem adequados à captura destes fenômenos, uma atenção especial deve ser dada ao modelo não linear de Perzyna, pois este não recupera o modelo invíscido como um caso limite, além disso, apresenta mal condicionamento no algoritmo de mapeamento de retorno. / In this work an elastic-viscoplastic constitutive formulation is described, considering infinitesimal and finite deformations. The models are formulated inside a thermodynamic with internal variables framework using fundamentais from convex analysis. The evolution equations are obtained from the maximum dissipation principie, which plays an important role on the approach adopted, which is the generalization of the Bingham rheological model. The local initial value problem is solved by an implicit integration scheme with a return mapping algorithm. The global initial boundary value problem is solved by the finite element method (FEM) also employing an implicit integration method. The strategy is implemented employing the linear and nonlinear Perzyna and the Perié viscoplastic models. The computational implementation is evaluated by comparing the numerical results with analytical solutions and with benchmarks available in the literature. The results obtained are important to evaluate the behavior and the characteristics of the models on the analysis of rate-dependency and stress relaxation. The three models were suitable to predict these phenomena. However, a special attention is needed on the nonlinear Perzyna model, because it does not recover the inviscid model as a limit case. Further, it presents ill-conditioning in the return mapping algorithm.

Cette étude s'intéresse au vieillissement thermique d'élastomères synthétiques, amorphes, vulcanisés et additionnés de charges (noir de carbone). Sur la base d'une même formulation matériau, on étudie plus particulièrement, l'impact du procédé initial (conditions de vulcanisation), les conséquences de l'évolution physico-chimique des matériaux sur le comportement mécanique et l'influence d'un chargement mécanique permanent durant le vieillissement. Des caractérisations mécaniques (essais cycliques, relaxations par paliers, essais de compressibilité) et physico-chimiques (suivi des variation de dimension et de masse, essais de gonflement dans un solvant) sont réalisées afin de quantifier l'impact du vieillissement. Le phénomène dominant étant une augmentation de la densité de réticulation (maturation des ponts polysulfures en ponts disulfures ou monosulfures). D'une manière générale la partie expérimentale a permis de formuler un certain nombre d'hypothèses (isotropie, insensibilité de certaines caractéristiques physiques aux vieillissement, etc.) qui ont guidé le développement d'un modèle multiphysique. Ce modèle s'appuie sur une approche thermo-chimio-mécanique formulée dans le cadre de la thermodynamique des processus irréversibles avec introduction de variables internes afin de traduire d'une part les non-linéarités de comportement de ce type de matériau (grandes déformations, viscoélasticité non-linéaire et effet Payne), et d'autre part de décrire l'évolution physico-chimique du réseau macromoléculaire (qui dépend de la température et de l'état mécanique). Cette modélisation a permis d'introduire un couplage réciproque entre les états physico-chimique et mécanique / This study mainly concerns the thermal aging phenomenon in amorphous synthetic rubbers, initially vulcanized and filled with carbon blacks. On the basis of one material formulation, we study: the impact of the process (vulcanization condition), the influence of the chemo-physical evolution of the cross-linked network on the mechanical behavior and the influence of a permanent mechanical load during aging. Mechanical characterizations (cyclic, relaxation and hydrostatic tests) and chemo-physical ones (variation of mass and volume, swelling in solvent) are realized in order to quantify the impact of ageing. The main phenomena observed is an increase of the crosslink density (maturation of polysulfides to monosulfide or disulfide crosslinks). From a general point of view, we can formulate many hypothesis from the experimental characterizations (isotropy, non-dependence of some physical properties on ageing, etc.). For the modeling, we have adopted a themo-chemo-mechanical approach that is based on the thermodynamics of irreversible processes and the introduction of internal variables in order to phenomelogically describe on one hand the nonlinear mechanical behavior at finite strain (nonlinear viscoelasticty, Payne effect, etc.) and on the other hand the chemo-physical evolution of the macromolecular network (which depends on temperature and mechanical state). This approach has permitted to introduce a reciprocal coupling between chemo-physical and mechanical states