This work is devoted to the numerical analysis of saturated porous media, taking into accountthe damage phenomenon on the solid skeleton. The porous media is taken into poroelasticframework, in full-saturated condition, based on the Biot's Theory. A scalar damage model isassumed for this analysis. An implicit Boundary element Method (BEM) formulation, basedon time-independent fundamental solutions, is developed and implemented to couple thefluid flow and the elasto-damage problems. The integration over boundary elements isevaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case oftriangular domain cells is followed to carry out the relevant domain integrals. The non-linearsystem is solved by a Newton-Raphson procedure. Numerical examples are presented, inorder to validate the implemented formulation and to illustrate its efficiency.

Recent advances in computational mechanics have opened the potential of carrying out the analysis and design of concrete structures in a realistic manner with the use of nonlinear concrete models. This encourages the development of more capable and realistic constitutive models, based on a rigorous approach, for the analysis and design of concrete structures. This research focuses on the development of a thermodynamic approach to constitutive modelling of concrete, with emphasis on the rigour and consistency both in the formulation of constitutive models, and in the identification of model parameters based on experimental tests. The key feature of the thermodynamic framework used in this study is that all behaviour of the defined model can be derived from two specified energy potentials. In addition, the derivation of a constitutive model within this framework merely follows procedures established beforehand. The proposed constitutive model here is based on continuum damage mechanics, in combination with plasticity theory, hence enabling the macroscopic material behaviour observed in experiments to be appropriately modelled. Damage-induced softening is the cause of many problems in numerical failure simulations based on conventional continuum mechanics. The resolution of these problems requires an appropriate special treatment for the constitutive modelling which, in this study, is based on nonlocal theory, and realized through the nonlocality of energy terms in the damage loading functions. For practical applications in structural analysis, the model requires a minimum number of parameters, which can be identified from experimental tests. All the above features of the model have been incorporated in a unified and consistent thermodynamic approach, which also distinguish the approach from existing ones. Numerical implementation and application are important parts of the study. A suitable implicit scheme is adapted here for the integration of the nonlocal rate constitutive equations. For the solution of systems of nonlinear algebraic equations in finite element analysis, the arc-length method in combination with local constraint equations employing dominant displacements is implemented, and proves its reliability in this study. Application of the proposed constitutive models in the analysis and design of concrete structures is straightforward, with several numerical examples showing the practical aspects of the proposed modelling.

This work is devoted to the numerical analysis of saturated porous media, taking into account the damage phenomenon on the solid skeleton. The porous media is taken into poroelastic framework, in full-saturated condition, based on the Biot\'s Theory. A scalar damage model is assumed for this analysis. An implicit Boundary Element Method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and the elasto-damage problems. The integration over boundary elements is evaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear system is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficiency. / Este trabalho trata da análise numérica de meios porosos saturados, considerando danificação na matriz sólida. O meio poroso é admitido em regime poroelástico, em condição saturada, com base na teoria de Biot. Um modelo de dano escalar é empregado nesta análise. Uma formulação implícita do Método dos Elementos de Contorno (MEC), baseada em soluções fundamentais independentes do tempo, é desenvolvida e implementada de forma a acoplar os problemas de difusão de fluido e de elasto-dano. A integração sobre os elementos de contorno é feita através da quadratura de Gauss. Um esquema semi-analítico é aplicado sobre células triangulares para avaliar as integrais de domínio do problema. A solução do sistema não linear é obtida através de um procedimento do tipo Newton-Raphson. Apresentam-se exemplos numéricos a fim de validar a formulação implementada e demonstrar sua eficiência.

This work is devoted to the numerical analysis of saturated porous media, taking into account the damage phenomenon on the solid skeleton. The porous media is taken into poroelastic framework, in full-saturated condition, based on the Biot\'s Theory. A scalar damage model is assumed for this analysis. An implicit Boundary Element Method (BEM) formulation, based on time-independent fundamental solutions, is developed and implemented to couple the fluid flow and the elasto-damage problems. The integration over boundary elements is evaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case of triangular domain cells is followed to carry out the relevant domain integrals. The non-linear system is solved by a Newton-Raphson procedure. Numerical examples are presented, in order to validate the implemented formulation and to illustrate its efficiency. / Este trabalho trata da análise numérica de meios porosos saturados, considerando danificação na matriz sólida. O meio poroso é admitido em regime poroelástico, em condição saturada, com base na teoria de Biot. Um modelo de dano escalar é empregado nesta análise. Uma formulação implícita do Método dos Elementos de Contorno (MEC), baseada em soluções fundamentais independentes do tempo, é desenvolvida e implementada de forma a acoplar os problemas de difusão de fluido e de elasto-dano. A integração sobre os elementos de contorno é feita através da quadratura de Gauss. Um esquema semi-analítico é aplicado sobre células triangulares para avaliar as integrais de domínio do problema. A solução do sistema não linear é obtida através de um procedimento do tipo Newton-Raphson. Apresentam-se exemplos numéricos a fim de validar a formulação implementada e demonstrar sua eficiência.

Ce travail est consacré à l'analyse numérique des milieux poreux saturés, en tenant comptele phénomène d'endommagement sur le squelette solide. Le milieu poreux est pris dans lecadre poro-élastique, dans un état complètement saturé, d'après la théorie de Biot. Unmodèle scalaire d'endommagement est supposé pour cette analyse. Une formulationimplicite de la Méthode des éléments de frontière, basée sur des solutions fondamentalesindépendantes du temps, est développé et implantée numeriquement pour coupler lesproblèmes de l'écoulement de fluide et de l'elasticité endommageable. L'intégration sur deséléments de frontière est realisée en utilisant la méthode numérique de Gauss. Un schémasemi-analytique pour le cas des cellules triangulaires de domaine est suivie pour évaluer lesintégrales de domaine pertinentes. Le systéme non-linéaire est résolu par une procédure deNewton-Raphson. Des exemples numériques sont présentés, afin de valider la formulationimplantée et pour illustrer son efficacité. / This work is devoted to the numerical analysis of saturated porous media, taking into accountthe damage phenomenon on the solid skeleton. The porous media is taken into poroelasticframework, in full-saturated condition, based on the Biot’s Theory. A scalar damage model isassumed for this analysis. An implicit Boundary element Method (BEM) formulation, basedon time-independent fundamental solutions, is developed and implemented to couple thefluid flow and the elasto-damage problems. The integration over boundary elements isevaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case oftriangular domain cells is followed to carry out the relevant domain integrals. The non-linearsystem is solved by a Newton-Raphson procedure. Numerical examples are presented, inorder to validate the implemented formulation and to illustrate its efficiency. / Este trabalho trata da análise numérica de meios porosos saturados, considerandodanificação na matriz sólida. O meio poroso é admitido em regime poroelástico, emcondição saturada, com base na teoria de Biot. Um modelo de dano escalar é empregadonesta análise. Uma formulação implícita do Método dos Elementos de Contorno (MEC),baseada em soluções fundamentais independentes do tempo, é desenvolvida eimplementada de forma a acoplar os problemas de difusão de fluido e de elasto-dano. Aintegração sobre os elementos de contorno é feita através da quadratura de Gauss. Umesquema semi-analítico é aplicado sobre células triangulares para avaliar as integrais dedomínio do problema. A solução do sistema não linear é obtida através de um procedimentodo tipo Newton-Raphson. Apresentam-se exemplos numéricos a fim de validar a formulaçãoimplementada e demonstrar sua eficiência.

La modélisation numérique des structures bois dans des conditions d’incendie nécessite la connaissance : de la variation des propriétés physiques du bois telles que la conductivité thermique, la chaleur spécifique et la densité en fonction de la température ; de la dégradation thermique du bois au cours des phases de séchage, de pyrolyse et de combustion. En particulier, nous nous sommes intéressés à l’étude du comportement thermomécanique du matériau bois. La loi thermique est décrite par l’équation de la chaleur. Le modèle choisi intègre les trois modes du transfert de chaleur : la conduction, le rayonnement et la convection. La loi mécanique est modélisée dans le cadre de la thermodynamique des processus irréversibles utilisant la notion des variables d’état. Elle tient compte du couplage entre le comportement élastique orthotrope, plastique anisotrope à écrouissage non linéaire isotrope et un endommagement isotrope. L’intégration numérique de la loi mécanique par un schéma implicite itératif combinant la technique du retour radial avec la réduction du nombre des équations est présentée. Le couplage thermomécanique est réalisé, selon l’approche réglementaire de l’Eurocode 5 relatif à la résistance au feu des structures en bois, en appliquant le facteur de réduction Kθ sur la résistance mécanique d’un résineux. Les aspects théoriques et les conditions aux limites associés au modèle thermomécanique sont abordés. L’identification des paramètres du modèle est réalisée sur des données expérimentales obtenues sur des tests réels d’incendie disponibles dans la littérature. À ce titre, plusieurs comparaisons avec différentes applications sont réalisées. Le modèle éléments finis reproduit avec précision la distribution du champ de température dans l’épaisseur des panneaux en bois, la formation du charbon ainsi que l’évolution de la résistance mécanique au cours de l’exposition au feu / Numerical modelling of timber structures in fire conditions requires the knowledge of the variation with temperature of the physical properties of the wood material (the thermal conductivity, the specific heat and the density) in order to take into account the thermal degradation of wood under high temperatures during the drying, pyrolysis and combustion phases, as well as the temperature profiles in the thickness of the surfaces exposed to fire. In particular, this work focusses on the thermomechanical behaviour of timber. The heat transfer analysis is described by the standard equations of heat conduction. It includes the three modes of heat transfer: conduction, radiation and convection. The structural response is modelled within the framework of thermodynamics of irreversible processes using the notion of state variables. It takes into account the coupling between the orthotropic elastic behaviour, the anisotropic plastic behaviour with isotropic nonlinear hardening, and isotropic damage. The numerical integration of the equilibrium equations is carried out with an iterative implicit scheme combining the technique of radial re- turn with the reduction of the number of equations. The thermomechanical coupling is carried out according to the approach recommended by Eurocode 5 for the fire resistance of timber structures by applying the reduction factor Kθ to the strength of a softwood. The theoretical aspects and boundary conditions associated with the thermomechanical model are also discussed. The parameters of the model are identified with experimental data obtained from actual fire tests available in the literature. Several comparative applications are carried out. The finite element model accurately reproduces the distribution of the temperature profile in the thickness of timber planks, the formation of the charred layer, and the evolution of the mechanical resistance during exposure to fire

Une nouvelle approche appelée “Approche Pseudo Inverse” (API) est développée pour la modélisation du procédé de forgeage à froid des pièces axisymétriques. L'API est basée sur la connaissance de la forme de la pièce finale. Certaines configurations intermédiaires « réalistes » ont été introduites dans l'API pour considérer le chemin de déformations. Elles sont créées géométriquement sans traitement de contact et ensuite corrigées par la méthode de surface libre afin de respecter l'équilibre, les conditions aux limites et la condition d'incompressibilité. Un nouvel algorithme direct de plasticité est développé, conduisant à une méthode d'intégration plastique très rapide, précise et robuste même dans le cas de très grands incréments de déformations. Un modèle d'endommagement en déformation, est couplé à la plasticité et implémenté dans l'API. Les validations numériques montrent que l'API donne des résultats très proches des résultats de l'approche incrémentale mais en utilisant beaucoup moins de temps de calcul.L'API est adoptée comme solveur du forgeage pour la conception et l'optimisation des préformes du forgeage multi-passes. La rapidité et la robustesse de l'API rendent la procédure d'optimisation très performante. Une nouvelle technique est développée pour générer automatiquement le contour initial d'un outil de préforme pour la procédure d'optimisation. Les variables de conception sont les positions verticales des points de contrôle des courbes B-spline définissant les formes des outils de préforme. Notre optimisation multi-objectif consiste à minimiser la variation de la déformation plastique équivalente dans la pièce finale et la force du poinçon au cours du forgeage. Un algorithme génétique et un algorithme de recuit simulé sont utilisés pour trouver les points d'optimum de Pareto. Pour réduire le nombre de simulations de forgeage, un méta-modèle de substitution basé sur la méthode de krigeage est adopté pour établir une surface de réponse approximative. Les résultats obtenus par l'API en utilisant les outils de préforme optimaux issues de l'optimisation sont comparés à ceux obtenus par les approches incrémentales classiques pour montrer l'efficacité et les limites de l'API. La procédure d'optimisation combinée avec l'API peut être un outil numérique rapide et performant pour la conception et l'optimisation des outillages de préforme. / A new method called “Pseudo Inverse Approach” (PIA) is developed for the axi-symmetrical cold forging modelling. The PIA is based on the knowledge of the final part shape. Some « realistic » intermediate configurations are introduced in the PIA to consider the deformation path. They are created geometrically without contact treatment, and then corrected by using a free surface method in order to satisfy the equilibrium, the boundary conditions and the metal incompressibility. A new direct algorithm of plasticity is proposed, leading to a very fast, accurate and robust plastic integration method even in the case of very large strain increments. An isotropic damage model in deformation is coupled with the plasticity and implemented in the PIA. Numerical tests have shown that the Pseudo Inverse Approach gives very close results to those obtained by the incremental approach, but using much less calculation time.The PIA is adopted as forging solver for the design and optimization of preform tools in the multi-stage forging process. The rapidity and robustness of the PIA make the optimization procedure very powerful. A new method is developed to automatically generate the initial preform tool shape for the optimization procedure. The design variables are the vertical positions of the control points of B-spline curves describing the preform tool shape. Our multi-objective optimization is to minimize the equivalent plastic strain in the final part and the punch force during the forging process. The Genetic algorithm and Simulated Annealing algorithm are used to find optimal Pareto points. To reduce the number of forging simulations, a surrogate meta-model based on the kriging method is adopted to build an approximate response surface. The results obtained by the PIA using the optimal preform tools issued from the optimization procedure are compared to those obtained by using the classical incremental approaches to show the effectiveness and limitations of the PIA. The optimization procedure combined with the PIA can be a rapid and powerful tool for the design and optimization of the preform tools.