La thèse a pour objet la simulation numérique de divers problèmes fortement non linéaires de la mécanique des milieux continus, en particulier en formage des métaux et en géomécanique. Le formalisme théorique puis numérique de la mécanique non linéaire des milieux continus, des couplages hydromécaniques et thermomécaniques et des modèles de comportement élastoplastique et élastoviscoplastique est développé étape par étape, permettant la construction du code aux éléments finis LAGAMINE. Celui-ci est ensuite utilisé pour simuler quelques problèmes spécifiques.

Following generally accepted axioms and assumptions the authors developed a phenomenological, thermodynamically consistent material model for large anisotropic elastoplastic deformations based on a substructure concept. The material model originally includes a stress relation in rate formulation, evolutional equations for the internal variables modeling the hardening behavior, and the yield condition. Due to the necessary time discretization solving the initial value problem (IVP) this approach is associated with an incremental stress computation. It will be shown that, within this context, the accuracy of stress values essentially deteriorates with increasing load steps. Consequently, the authors substitute the usual stress relation including the symmetric plastic strain tensor of right Cauchy-Green type instead of the stress tensor into the set of unknown constitutive variables. Stresses are explicitly computed from a hyperelastic material law depending on the elastic strain tensor. Furthermore, as an alternative to the plastic strain tensor the solution of the IVP considering an evolutional equation for the plastic part of the deformation gradient has been studied. This procedure simplifies the mathematical structure of the system to be solved as well as the computation of substructure-based variables which are suitable for the analysis of texture development. The presented numerical strategies were implemented into an in-house FE-code. Some examples illustrating their accuracy, stability as well as efficiency are discussed.

Non-negligible coupled thermal and mechanical effects occur in several physical and industrial procedures, e.g. warm for ming processes. The authors present the theoretical background of a phenomenological thermoelastoplastic material model at large strains as well as its numerical realization within the context of appropriate finite element formulations. As usual, the presented thermodynamical consistent constitutive approach is based on the multiplicative decomposition of the deformation gradient, and a corresponding additive decomposition of the free Helmholtz energy density. For the numerical treatment of thermoelastoplastic problems within a finite element approach, weak formulations of the balance equation of momentum and the heat conduction equation in material description are developed. For the solution of non-linear boundary value problems the linearization of the weak formulations is presented. Within the context of the mechanical problem the temperature dependence of material parameters as well as the thermal expansion are considered. The temperature evolution will be affected by non-thermal phenomena like the thermoelastic effect and plastic dissipation. Several numerical procedures for the solution of the coupled thermomechanical problem are discussed.

This paper presents the theoretical background of a phenomenological biphasic material approach at large strains based on the theory of porous media as well as its numerical realization within the context of an adaptive mixed finite element formulation. The study is aimed at the simulation of coupled multiphysics problems with special focus on biomechanics. As the materials of interest can be considered as a mixture of two immiscible components (solid and fluid phases), they can be modeled as saturated porous media. For the numerical treatment of according problems within a finite element approach, weak formulations of the balance equations of momentum and volume of the mixture are developed. Within this context, a generalized Lagrangean approach is preferred assuming the initial configuration of the solid phase as reference configuration of the mixture. The transient problem results in weak formulations with respect to the displacement and pore pressure fields as well as their time derivatives. Therefore special linearization techniques are applied, and after spatial discretization a global system for the incremental solution of the initial boundary value problem within the framework of a stable mixed U/p-c finite element approach is defined. The global system is solved using an iterative solver with hierarchical preconditioning. Adaptive mesh evolution is controlled by a residual a posteriori error estimator. The accuracy and the efficiency of the numerical algorithms are demonstrated on a typical example.

Les élastomères présentent une diversité d’utilisation et des caractéristiques mécaniques spécifiques (grandes déformations, comportement dissipatif, ...) qui en font une famille de matériaux très utilisés dans l’industrie. Lors de leur fonctionnement, les pièces réelles subissent des sollicitations complexes. Comprendre les phénomènes induits par la fatigue multiaxiale constitue ainsi un enjeu important dans la phase de conception industrielle. Le matériau utilisé au cours de cette étude est un polychloroprène (CR), fourni par la société Hutchinson et présent dans les poulies découpleuses. Celui-ci possède une réponse dissipative en grandes déformations. Son comportement est modélisé à partir de lois de comportements viscohyperélastiques suivant deux approches : une méthode analytique impliquant un calcul simple en un point d’un cylindre et l’autre utilisant un calcul éléments finis implémenté dans ANSYS. Une campagne expérimentale en fatigue multiaxiale est alors réalisée, en traction-torsion afin de tester l’énergie dissipée comme critère de fatigue multiaxial. Celui-ci présente des résultats intéressants. Des diagramme de Haigh ont été établis afin de mettre en évidence le phénomène de cristallisation. Des analyses post-mortem ont été menés avec un microscope électronique à balayage et expose des spécificités morphologiques liées à la sollicitation vue par le matériau. / Due to their interesting mechanical behavior (large strain, dissipative behavior ...) and their diversity, elastomers are more and more used in industry. In service conditions, rubber components are subjected to complex loadings. Therefore, understanding phenomena induced by multiaxial fatigue constitutes an important issue in the industrial conception’s step. The material used in this work is a polychloroprene rubber, provided by Huchinson society and dedicated to silent-block’s applications. This elastomer possess a dissipative component at large strains. This behavior is determined following two approaches : an analytic method, implying a simple calculation at a local point of a cylinder and a finite elements analysis implemented with ANSYS software. An experimental investigation in multiaxial fatigue is then realized to test the dissipated energy density as a multiaxial fatigue criterion. This parameter obtained interesting results. Haigh diagrams has been built to point out crystallization phenomenon. Post-mortem analyses has been carried out with a scanning electronic microscope and exposes morphological specificities related to the material’s sollicitation.

La méthode isogéométrique (IGA) récemment proposée en tant que méthode numérique générique offre de réelles perspectives dans l’unification des modèles géométriques et computationnel. La méthode isogéométrique est intiment liée à la méthode des éléments finis (FEM) étant donné que la méthode est basée sur le même cadre variationnel. Cette méthode a montré dans de nombreuses circonstances de très bonne qualités numériques notamment avec des maillages grossiers (précision numérique, capacité à supporter de grandes déformations…). Notre objectif final dans ce travail est de fournir un environnement de base, numérique et logiciel, pour la simulation de problèmes à champs et physiques multiples pour des pièces élastomériques de type industriel. Dans ce contexte, les points numériques à développer pour l’IGA sont le traitement de l’incompressibilité et le caractère multi-champs du problème thermique dans la formulation de Galerkin. Ainsi dans ce travail nous proposons en premier, un paradigme objet de l’IGA intégré au sein d’une architecture orientée objet en Java, initialement con?ue pour résoudre des problèmes multi-champs couplés en transformations finies. L’approche proposée s’appuie pleinement sur le contexte variationnel existant dans le code dans le cadre des éléments finis pour réduire les développements pour MEF et IGA (une formulation développée en IGA tourne en MEF et vice versa). Dans un second temps, nous avons étudié le problème de l’incompressibilité pour notamment réduire le verrouillage numérique existant toujours sur l’IGA standard. Par un souci de simplicité, nous adoptons des formulations mixtes à 2 champs (déplacement/pression). Afin d’essayer de satisfaire la condition inf-sup en relachant la contrainte sur le déplacement, nous avons développé deux idées de la littérature (naturelle en NURBS) qui consiste à soit dupliquer une fois les n?uds intérieurs du patch des déplacements ou subdiviser les éléments du patch des déplacements. Nous avons étendu ce type d’éléments aux transformations finies. Enfin, et de manière originale, nous avons adopté la même stratégie pour les problèmes à 2-champs pour la thermomécanique. Différentes simulations à petites et grandes déformations confirment le potentiel de l’approche. Enfin, nous évaluons l’ensemble sur un modèle quasi-incompressible thermo-visco-élastique de type Zener sur des éprouvettes classiques dans un contexte physique complexe. / Recently proposed as a general purpose numerical method, the Isogeometric Analysis (IGA) offers great perspective to bridge the gap between CAD and CAE. The IGA is closely related to the finite element method (FEM) as the method is based on the same variational framework. Moreover, this method has shown in many circumstances to be have a better accuracy than the FEM (large mesh distortions…). Our final aim in this work is to simulate complex multiphysics problems for elastomers industrial parts. As matter of fact, the two main numerical issues in this context is the incompressibility/quasi-incompressibility of the material and the thermochemical coupling in Galerkin formulations. First, we propose, a programming paradigm of the IGA in an existing Java object-oriented hierarchy initially designed for solving multi-fields coupled problems at finite strains. We develop an approach that fully take benefit of the original architecture to reduce developments for both FEM and IGA (one problem developed in FEM can be run in IGA and vice versa). Second, we investigate volumetric locking issues persisting for low order NURBS element observed with standard displacement formulation as finite elements. To cure the problem, we adopt two-fields mixed formulation (displacement/pressure) for the sake of simplicity and target at assessing different discretizations in stability (inf-sup condition). The basic idea is to first to increase the internal knot’s multiplicity or to subdivide the patch for displacements. These ideas that are directly inspired from patches properties, have been found in the literature for the Stokes problem and extended to large strain in solid mechanics. The comparison between the two-fields mixed formulation and a strain projection method is lead at small and large strains. At last, we originally adopt a similar strategy for thermomechanical problem at small and large strains. In the context two-fields formulation, displacement/temperature, the LBB stability condition must be fulfilled to guaranty stability. Thus, we investigate the choices of patches for two-fields formulation displacement/temperature fields for IGA applied to thermoelasticity. Several numerical results for thermomechanical problems at small and finite strains, linear and nonlinear have been presented. At last, an incompressible viscous thermo-hyperelastic model is evaluated in the IGA framework with the proposed approach.

No description available.

No description available.

O objetivo precípuo deste estudo é a implementação computacional de modelos constitutivos elásticos e elastoplásticos para materiais com gradação funcional em regime de grandes deslocamentos e elevadas deformações. Para simular numericamente um problema estrutural, são empregados aqui elementos finitos sólidos (tetraédrico e hexaédrico) com ordem de aproximação polinomial qualquer. Grandezas da Mecânica Não Linear do Contínuo, como deformação e tensão, são utilizadas na formulação deste estudo. Para reproduzir os grandes deslocamentos, é empregada a análise não linear geométrica. A descrição adotada aqui é a Lagrangiana total, e o equilíbrio da estrutura é expresso pelo Princípio da Mínima Energia Potencial Total. Com relação à resposta elástica do material, são usadas leis constitutivas hiperelásticas, nas quais a relação tensão-deformação é obtida a partir de um potencial escalar. O comportamento elastoplástico do material é definido pela decomposição da deformação nas parcelas elástica e plástica, pelo critério de plastificação de von-Mises, pela lei de fluxo associativa, pelas condições de consistência e de complementaridade, pelo parâmetro de encruamento isotrópico e pelo tensor das tensões inversas, relacionado ao encruamento cinemático. Duas formulações elastoplásticas são utilizadas aqui: a de Green-Naghdi, na qual a deformação é decomposta de forma aditiva; e a hiperelastoplástica, em que o gradiente é decomposto de forma multiplicativa. É empregado também o conceito de material com gradação funcional (GF), a qual é definida como a variação gradual (contínua e suave) das propriedades constitutivas do material. A solução numérica do equilíbrio de forças é feita via método iterativo de Newton-Raphson. Para satisfazer o critério de plastificação, são utilizadas as estratégias de previsão elástica, e de correção plástica via algoritmos de retorno. Basicamente foram desenvolvidos cinco programas computacionais: o gerador automático das funções de forma; o gerador de malhas de elementos finitos sólidos; o código para análise de materiais em regime elástico; o código para análise de materiais em regime elastoplástico; e o programa de pós-processamento. Além desses, o aluno teve contato com os programas EPIM3D e DD3IMP ao longo de seu estágio de doutorado na Universidade de Coimbra (Portugal). Os programas EPIM3D e DD3IMP são empregados para analisar, respectivamente, materiais em regime elastoplástico, e processos de conformação de metais. Para o problema da barra sob tração uniaxial uniforme, são descritas equações e soluções analíticas para materiais homogêneos e com GF em regime elastoplástico. Para reduzir o tempo de simulação, foi empregada a programação em paralelo. De acordo com os resultados das simulações numéricas, as principais conclusões são: o refinamento da malha de elementos finitos melhora a precisão dos resultados para materiais em regimes elástico e elastoplástico; as formulações elastoplásticas de Green-Naghdi e hiperelastoplástica parecem ser equivalentes para pequenas deformações; a formulação hiperelastoplástica é equivalente ao modelo mecânico dos programas EPIM3D e DD3IMP para materiais em regime de pequenas deformações elásticas; foram constatados ganhos significativos, em termos de tempo de simulação, com a paralelização dos códigos computacionais de análise estrutural; e os programas desenvolvidos são capazes de simular - com precisão - problemas complexos, como a membrana de Cook e o cilindro fino transversalmente tracionado. / The main objective of this study is the computational implementation of elastic and elastoplastic constitutive models for functionally graded materials in large deformation regime. In order to numerically simulate a structural problem, the finite elements used are solids (tetrahedric and hexahedric) of any order of approximation. Entities from Nonlinear Continnum Mechanics, as strain and stress, are used in the present formulation. To reproduce the finite displacements, the geometrically nonlinear analysis is employed. The description adopted here is the total Lagrangian, and the structural equilibrium is expressed by means of the Principal of Minimum Total Potential Energy. Regarding the elastic material response, hyperelastic constitutive laws are used, in which the stress-strain relation is obtained from a scalar potential. The elastoplastic material behavior is defined by the strain decomposition in the elastic and plastic parts, by the von-Mises yield criterion, by the associative flow law, by the consistency and complementarity conditions, by the isotropic hardening parameter, and by the backstress tensor, related to the kinematic hardening. Two elastoplastic formulations are used here: the Green-Naghdi one, in which the strain is additively decomposed; and the hyperelastoplasticiy, in which the gradient is multiplicatively decomposed. The concept of functionally graded (FG) material, in which the constitutive properties vary gradually (continuous and smoothly), is also used. The numerical solution of the forces equilibrium is obtained via Newton-Raphson iterative procedure. In order to satisfy the yield criterion, the strategies of elastic prediction and plastic correction (via return algorithms) are used. Basically, five computer codes have been developed: the automatic shape functions generator; the solid mesh generator; the code for analysis of materials in the elastic regime; the code for analysis of materials in the elastoplastic regime; and the post-processor. Besides these, the student had contact with the programs EPIM3D and DD3IMP during his doctoral stage in the University of Coimbra (Portugal). The programs EPIM3D and DD3IMP are employed to analyze, respectively, materials in the elastoplastic regime, and sheet-metal forming processes. For the problem of the bar under uniform uniaxial tension, equations and analytical solutions are described for homogeneous and FG materials. To reduce the simulation time, the parallel programming has been employed. According to the numerical simulation results, the main conclusions are: the results accuracy is improved with mesh refinement for materials in the elastic and elastoplastic regimes; the Green-Naghdi elastoplastic formulation and the hyperelastoplasticity appear to be equivalent for small strains; the hyperelastoplastic formulation is equivalent to the mechanical model of the programs EPIM3D and DD3IMP for materials the small elastic strains regime; simulation time reduction has been obtained with the parallelization of the computer codes for structural analysis; the developed programs are capable of simulating, precisely, complex problems, such as the Cook\'s membrane and the pulled thin cylinder.

Dans ce travail, nous avons souhaité étudier l'impact de la structure sur les propriétés adhésives enexplorant différentes architectures dont des étoiles à trois branches de longueur importante, elles-mêmesramifiées par des branches longues, synthétisées en plusieurs étapes par polymérisation radicalaire contrôlée.Nous avons également étudié des polymères linéaires et des copolymères à bloc. Ils sont en particulier constituésde poly(acrylate de n-butyle) naturellement collant à température ambiante, permettant ainsi une étude despropriétés adhésives sans formulation. Toutefois, la masse molaire entre enchevêtrements élevée du PnBA s'estavérée être un frein car les techniques de polymérisation choisies n’ont pas permis la synthèse de massesmolaires suffisamment élevées pour obtenir le comportement typique d'une étoile possédant les niveaux decomplaisance visés. Etant donné qu'une grande part de l'énergie dissipée lors du décollement est due à laformation et à l'extension d'une structure fibrillaire, nous avons proposé d'explorer les propriétés rhéologiquesdans le domaine linéaire mais également aux grandes déformations par des tests d'élongation. Par ailleurs, destests de tack avec une visualisation par caméra rapide des phénomènes ayant lieu au sein des échantillons durantle décollement ont été mis en place. Nous avons confronté les propriétés rhéologiques et les performancesadhésives pour toutes les structures analysées. Des mélanges de polymères linéaires avec une très haute massemolaire peuvent présenter du rhéodurcissement, et nous avons confirmé que les conditions d'apparition sontlimitées si la polymolécularité devient trop importante. Pour les polymères en étoile, nous avons plusparticulièrement analysé l’importance de la complaisance d’équilibre sur les performances adhésives. Lescopolymères à bloc présentant une tenue suffisante pour être analysés en élongation ont montré un fortrhéodurcissement, mais une propagation de fissure interfaciale lors des tests de tack, par manque dedéformabilité, empêchant de bénéficier de l'apport du rhéodurcissement. / In this work, we studied the effect of polymer structure on adhesive properties exploring variousarchitectures including stars having three very long arms and branched themselves, synthesized with severalsteps by controlled radical polymerization. We also studied linear polymers and block copolymers. They havebeen made with poly(n-butyl acrylate) naturally sticky at room temperature, allowing to work withoutformulation. However, high molecular weight between entanglements of PnBA has shown to be a brake becausechosen polymerization techniques did not allow the synthesis of sufficient high molecular weights to obtaintypical behavior of star having targeted compliance levels. Considering that a large part of the energy dissipatedduring debonding is due to the formation and extension of a fibrillar structure, we proposed to explore linearrheological properties but also at large strains with elongational tests. Furthermore, tack tests with high-speedcamera display of phenomena occurring within samples during debonding have been set up. We comparedrheological properties with adhesive performances for all analyzed structures. Linear polymers blended with veryhigh molecular weight could exhibit strain hardening, and we confirmed that appearance conditions are limitedwith polydispersity. For star-shaped polymers, we particularly analyzed the impact of the compliance on adhesiveperformances. Block copolymers having a sufficient holding to be analyzed in elongation have shown a strongstrain hardening, but propagation of interfacial fracture during tack tests, because of a deformability lack,preventing the strain hardening benefit.