Made available in DSpace on 2014-06-11T19:28:35Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-03-21Bitstream added on 2014-06-13T20:37:41Z : No. of bitstreams: 1 rodrigues_ea_me_bauru.pdf: 1602991 bytes, checksum: 7f755b87b5be84900b2d054f02413197 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o comportamento de materiais que apresentam diferentes respostas quando solicitados à tração ou à compreensão. obtem-se uma representação constitutiva através da composição de modelos simples e específicos para tratar cada tipo de solicitação. Este modelo combinado é capaz inclusive de lidar com carregamentos alternados (tração e compreensão), envolvendo fechamento e reabertura de fissuras existentes. Para modelar o comportamento em compreensão emprega-se o modelo constitutivo que tem como critério de degradação o segundo invariante do tensor de tensão desviador (critério de Von Mises ou J2). Para simular o aparecimento de fissuras de tração, usa-se o modelo de dano com critério de degradação baseado na energia de deformação da parte positiva do tensor efetivas. A integração dos modelos é feita com base em tensões efetivas associadas a duas escalas distintas (escala grosseira e refinada). O modelo é apto para representar a formação de descontinuidades no campo de deslocamento (descontinuidades fortes) em materiais quase-frágeis. Nesse caso, a região de localização de deformação (zona de processo da fatura) pode ser descrita pelo modelo de dano combinado, com lei de abrandamento de tensões (softening) exponencial, que estabelece dissipação compatível com a energia de fratura. A região contínua pode ser descrita pelo modelo de dano J2, com parâmetros ajustados com base no comportamento não linear à compreensão. Valida-se o modelo proposto mediante testes básicos, focando a capacidade do modelo em representar os principais aspectos do comportamento de materiais quase-frágeis. A aplicabilidade do modelo é demonstrada através do estudo da capacidade de rotação plástica de vigas de concreto armado, confrontando-se os resultados numéricos com os experimentais / A combined constitutive model based on the Continuum Damage Mechanics (CDM) is presented to represent the nonlinear behavior of quasi-brittle materials, which present different response when subjected to tension or compreession. The constitutive model is a composition of two simple and specific models designed to treat each type of behavior. The combined model is able to deal with alternating load (tension-compression), involving formation, closure and reopening cracks. To model the compressive behavior, a degradation criterion based on the second invariant of the deviatoric part of the effective stress tensor (Von Miser or J2 criterion) is used. To simulate cracking, a damage model with degradation criterion based on the strain energy associated to the positive part the effective stress tensor is adopted. The combination of the models is made on the basis of the effective stresses associated to two distinct scales (coarse and fine scales) The model is able to represented the formation of discontinuities in the displacement field (strong discontinuities) for quasi-brittle materials. The region of strain localization (fracture process zone) is described by a softening law which establishes dissipation energy compatible with the fracture energy. The continuous region is described by the J2 damage model, with parameters ajusted to describle the compressive nonlinear behavior in compression. Some basic tests are performed to asses the ability of the model to represent the main aspects of the behavior of quasi-brittle materials. The applicability of the model is demonstrated by the study of the plastic rotation capacity of reinforced concrete beams, comparing the numerical responses with the experimental ones

Cette thèse porte sur la description du processus de fissuration du béton soumis à des sollicitations mécaniques. L'objectif principal est d'améliorer la description macroscopique à l'aide d'un modèle continu. Un modèle décrivant de façon cohérente le comportement à la rupture du béton devrait au moins représenter : (i) la transition continu/discret et l'effet d'écran induit par une macrofissure, (ii) la discontinuité du déplacement, (iii) l'interaction entre le processus de fissuration et un bord libre (iv) il doit aussi être capable de reproduire la réponse mécanique obtenue expérimentalement. Dans un premier temps, nous avons fait une analyse comparative entre le modèle d'endommagement non-local classique et différents modèles continus améliorés proposés dans la littérature. Des outils de comparaison ont été proposés pour cette analyse : (i) du point de vue numérique, deux exemples considérant la rupture dynamique d'une barre (barre en traction et test d'écaillage) et (ii) du point de vue expérimental, une base de données issue d'une série d'essais sur des poutres homothétiques entaillées et non-entaillées en flexion trois points. Nous avons conclu que seule une combinaison entre différentes formulations peut rendre compte de tous les mécanismes mis en jeu lors du processus de fissuration. Elle inclue à la fois la façon dont l'information non-locale est transmise, la croissance de défauts et la description des effets de bord. Nous avons mis en évidence que son implémentation 2D ou 3D reste complexe et donc la comparaison avec des données expérimentales s'avère impossible. Dans un deuxième temps, nous avons choisi de changer l'échelle d'analyse pour connaitre en détail les mécanismes ayant lieu au sein de la mésostructure du béton (pâte, granulat, interface) à l'aide d'un modèle mésoscopique basé sur des éléments lattice. Cette analyse a permis de conclure que la prise en compte des interactions entre les composants de la mésostructure du béton fournit des résultats numériques plus proches de la réalité que ceux obtenus avec le modèle non-local macroscopique classique. Le mésomodèle est capable de représenter aussi bien la charge maximale (effet d'échelle) que la phase adoucissante pour toutes les tailles de poutre et pour toutes les géométries d'entaille. Nous avons transposé la prise en compte des interactions de l'échelle mésoscopique à l'échelle macroscopique au travers de la fonction poids d'un nouveau modèle non-local. Elle est estimée en décrivant le matériau comme étant un ensemble d'inclusions qui interagissent entre elles lors du chargement. Ces inclusions sont dilatées élastiquement et successivement afin de caractériser le transfert d'information au sein du matériau et de reconstruire la fonction poids du modèle proposé. Ce nouveau modèle est capable de décrire la transition continu/discret et l'effet d'écran, la discontinuité du déplacement et de retrouver un effet de bord cohérent avec les résultats de la micromécanique. Son implémentation en 2D est présentée et les premiers résultats de calculs illustrent la démarche. Finalement, nous revenons sur la modélisation mésoscopique du comportement du béton. Sa richesse en information peut conduire à une compréhension plus fine du processus de fissuration et de la création puis l'évolution de la zone d'élaboration. / This work focuses on the description of the process of cracking of concrete subjected to mechanical stresses. The main objective is to improve the understanding of the mechanisms involved using a continuous macroscopic model. A model describing consistently the fracture behavior of concrete should at least represent: (i) the continuous / discrete transition and the shielding effect induced by a macrocrack, (ii) the discontinuity of displacement, (iii) the interaction between the cracking process and a free boundary, (iv) it must also be able to reproduce the mechanical response obtained experimentally. At first, we made a comparative analysis of the classical non-local damage model and others improved continuous models proposed in the literature. Comparison tools have been proposed for this analysis: (i) from a numerical point of view, two examples considering the dynamic rupture of a bar (tensile test and spalling test) and (ii) from an experimental point of view, a database obtained from three-point bending test on notched and unnotched geometrically similar beams made from the same concrete formulation. We found that only a combination of this formulations may account for the different mechanisms involved in the process of cracking. It includes the transmission of the non-local information, the growing of voids and the description of boundary effects. We shown that its implementation in 2D or 3D remains complex and thus comparison with experimental results are impossible. In a second step, we decided to change the scale of analysis to precise the mechanisms which are taking place within the mesostructure of concrete using a mesomodel based on lattice elements. This analysis shown that since the mesomodel intrinsically took into account the interactions evolution within the structure, it is able to provide relevant results when classical macroscopic non-local models failed. It is able to represent both the maximum load (size effect) and the softening regime whatever the beam size or the pre-notch geometry. In addition, we proposed a new non-local framework where the interactions were upscale from the mesoscale to the macroscale through a new weight function. This function is estimated by describing the material as a set of inclusions that interact upon loading. These inclusions are successively elastically dilated to characterize the transfer of information within the material and rebuild the non-local weight function. This new model is able to describe the continuous / discrete transition, the shielding effect and the discontinuity of displacement. The model has been implemented in 2D in a finite element code and first results shown its capabilities to reproduce experimental results in term of maximum loads. In a third step, the richness of the mesoscopic approach has been used to describe precisely the local process of failure in term of fracture process zone evolution.

Resumo: No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o comportamento de materiais que apresentam diferentes respostas quando solicitados à tração ou à compreensão. obtem-se uma representação constitutiva através da composição de modelos simples e específicos para tratar cada tipo de solicitação. Este modelo combinado é capaz inclusive de lidar com carregamentos alternados (tração e compreensão), envolvendo fechamento e reabertura de fissuras existentes. Para modelar o comportamento em compreensão emprega-se o modelo constitutivo que tem como critério de degradação o segundo invariante do tensor de tensão desviador (critério de Von Mises ou J2). Para simular o aparecimento de fissuras de tração, usa-se o modelo de dano com critério de degradação baseado na energia de deformação da parte positiva do tensor efetivas. A integração dos modelos é feita com base em tensões efetivas associadas a duas escalas distintas (escala grosseira e refinada). O modelo é apto para representar a formação de descontinuidades no campo de deslocamento (descontinuidades fortes) em materiais quase-frágeis. Nesse caso, a região de localização de deformação (zona de processo da fatura) pode ser descrita pelo modelo de dano combinado, com lei de abrandamento de tensões (softening) exponencial, que estabelece dissipação compatível com a energia de fratura. A região contínua pode ser descrita pelo modelo de dano J2, com parâmetros ajustados com base no comportamento não linear à compreensão. Valida-se o modelo proposto mediante testes básicos, focando a capacidade do modelo em representar os principais aspectos do comportamento de materiais quase-frágeis. A aplicabilidade do modelo é demonstrada através do estudo da capacidade de rotação plástica de vigas de concreto armado, confrontando-se os resultados numéricos com os experimentais / Abstract: A combined constitutive model based on the Continuum Damage Mechanics (CDM) is presented to represent the nonlinear behavior of quasi-brittle materials, which present different response when subjected to tension or compreession. The constitutive model is a composition of two simple and specific models designed to treat each type of behavior. The combined model is able to deal with alternating load (tension-compression), involving formation, closure and reopening cracks. To model the compressive behavior, a degradation criterion based on the second invariant of the deviatoric part of the effective stress tensor (Von Miser or J2 criterion) is used. To simulate cracking, a damage model with degradation criterion based on the strain energy associated to the positive part the effective stress tensor is adopted. The combination of the models is made on the basis of the effective stresses associated to two distinct scales (coarse and fine scales) The model is able to represented the formation of discontinuities in the displacement field (strong discontinuities) for quasi-brittle materials. The region of strain localization (fracture process zone) is described by a softening law which establishes dissipation energy compatible with the fracture energy. The continuous region is described by the J2 damage model, with parameters ajusted to describle the compressive nonlinear behavior in compression. Some basic tests are performed to asses the ability of the model to represent the main aspects of the behavior of quasi-brittle materials. The applicability of the model is demonstrated by the study of the plastic rotation capacity of reinforced concrete beams, comparing the numerical responses with the experimental ones / Orientador: Osvaldo Luís Manzoli / Coorientador: André Luís Gamino / Banca: Leonardo José do Nascimento Guimarães / Banca: Edson Antonio Capello Sousa / Mestre

Pour l'analyse de durabilité et la conception économique (moins de matériel) de structures en matériaux ressemblant à du béton, la modélisation de la rupture est essentielle. Dans le cadre de la mécanique des milieux continus, une longueur interne est introduite dans les modèles non locaux pour remédier au problème lié à la sensibilité du maillage qui est une pathologie des modèles d'endommagement classiques , lorsqu'il s'agit de matériaux adoucissantes. Toutefois, l'évaluation de la longueur interne de hétérogénéités du matériau est toujours une question difficile, ce qui rend un problème obscur en utilisant des modèles non locaux. Nos travaux portent sur le développement d'un outil numérique basée sur la méthode des éléments en treillis (LEM) qui est un modèle discret pour la simulation et la prévision de la rupture des structures en béton. En utilisant le modèle de réseau à l'échelle mésoscopique, il n'est pas nécessaire d'introduire une longueur interne dans la loi de comportement, comme cela se fait dans les modèles non locaux, et nous pouvons affranchir ce paramètre en introduisant explicitement la mesotructure matérielle via une description géométrique. Basé sur l'outil numérique développé, nous avons étudié, en effectuant des tests numériques de traction uniaxiale, l'influence géométrique de la mesotructure du matériau ainsi que l'influence des conditions aux limites et de tailles d'échantillons (qui se traduisent par le gradient de sollicitation et le champ de rotation de matériel différents) sur le taille de la FPZ (fracture process zone) et sur la longueur caractéristique du matériau quasi-fragile homogénéisé. Ces études fournissent des recommandations/avertissements lors de l'extraction d'une longueur interne nécessaire pour les modèles nonlocaux à partir de la microstructure du matériau. Par ailleurs, les études contribuent un aperçu direct de l'origine mésoscopic de la taille FPZ et la longueur de la caractéristique du matériau, et par conséquent sur l'origine et la nature du comportement non linéaire du matériau. Ensuite, nous avons implanté le modèle du treillis dans la bibliothèque de SOFA développé par l'INRIA pour réaliser le couplage avec la méthode des éléments finis (MEF) afin de faire face avec des structures à grande échelle. Nous avons proposé un algorithme de couplage entre une approche macroscopique représentée par MEF et une approche mésoscopique infligés par LEM au sein d'une manière adaptative. Le modèle de couplage est d'abord utilisée pour valider l'approche multi-échelle proposée sur des simulations heuristiques. Et à long terme, il fournit un outil prometteur pour des simulations de grandes structures en matériaux quasi-fragiles de la vie réelle. / For durability analysis and economic design (less material) of structures made of concrete-like materials, modeling of cracking process and failure is essential. In the framework of continuum mechanics, an internal length is introduced in nonlocal models to remedy the problem related to mesh sensitivity which is a pathology of classical damage models, when dealing with softening materials. However, the assessment of the internal length from heterogeneities of the material is still a difficult question, which makes an obscure issue in using nonlocal models. Our work concerns developing of a numerical tool based on the Lattice Element Method (LEM) which is a discrete model for simulating and predicting fracture in concrete(-like) material. Using the lattice model at the mesoscopic scale, there is no need to introduce any internal length in the constitutive law, as done in nonlocal models, and we can enfranchise this parameter by explicitly introducing the material mesotructure via geometric description. Based on the developed numerical tool, we studied, by performing numerical uniaxial tensile tests, the geometric influence of the material mesotructure as well as the influence of the boundary conditions and specimen sizes (that result in different stress gradient and material rotation field) on the size of the FPZ (Fracture Process Zone) and on the characteristic length of the homogenized quasi-brittle material. These studies provide recommendations/warnings when extracting an internal length required for nonlocal damage models from the material microstructure. Moreover, the studies contribute a direct insight into the mesoscale origin of the FPZ size and the material characteristic length, and consequently into the origin and nature of the nonlinear behavior of the material. Then, we implemented the lattice model into SOFA library developed by INRIA for realizing the coupling with the Finite Element Method (FEM) in order to deal with large-scale structures. We proposed a strong coupling algorithm between a macroscopic approach represented by FEM and a mesoscopic approach dealt by LEM within an adaptive manner. The coupling model is first used to validate the multiscale approach proposed on heuristic simulations. And in the long term, it provides a promising tool for simulations of large-scale structures made of quasi-brittle materials of real life.

The accurate description of the nonlinear structural behaviour is an important issue in engineering science. Usually, classic nonlinear theories, such as fracture and damage mechanics, applied to finite element programmes are used to fulfil that purpose. Classic fracture mechanics describes the structural deterioration process by a few discrete cracks. This theory presents good precision for structures with simple geometries, few cracks and homogeneous materials. Classic damage mechanics measures the deterioration process by an internal variable called damage. This theory has been successful in the description of several deterioration mechanisms in continuum media. Despite their accuracy, classic fracture and damage mechanics present some drawbacks. Firstly, regarding civil engineering problems, both theories are not suitable for some practical applications. Secondly, fracture mechanics demands the consideration of initial cracks to begin the analysis. Lastly, classic damage models may present an issue known as localisation, what essentially leads to ill-posed problems and mesh-dependent numerical algorithms. Alternatively, a recent theory, called lumped damage mechanics, was proposed in order to achieve good accuracy in actual engineering problems. Such theory applies key concepts from fracture and damage mechanics in plastic hinges. In the light of the foregoing, the main goal of this thesis is the extension of the lumped damage mechanics framework to analyse different engineering problems. So far, lumped damage mechanics was characterised as a simplified methodology to analyse reinforced concrete frames under seismic and monotonic loadings; even with a few contributions on the analysis of local buckling in metallic structures. Therefore, this work extends the lumped damage mechanics framework to analyse reinforced concrete arches, unreinforced concrete structures, high cycle fatigue and continuum problems. The application examples show the accuracy of the proposed methodologies. / A descrição acurada do comportamento não linear de estruturas é um problema importante na engenharia. Usualmente, teorias não lineares clássicas, tais como as mecânicas da fratura e do dano, aplicadas a programas de elementos finitos são utilizadas a fim de cumprir aquele propósito. A mecânica da fratura clássica descreve o processo de deterioração estrutural por meio de um pequeno número de fissuras discretas. Esta teoria apresenta boa precisão para estruturas com geometrias simples, poucas fissuras e materiais homogêneos. A mecânica do dano clássica tem sido exitosa na descrição de diversos mecanismos de deterioração em meios contínuos. Apesar de precisas, as abordagens clássicas em fratura e dano apresentam alguns entraves. Primeiramente, tratando-se de problemas da engenharia civil, ambas teorias não são adequadas para aplicações práticas. Em segundo lugar, os modelos clássicos de fratura demandam a consideração de fissuras iniciais para iniciar a análise. Por fim, os modelos clássicos de dano podem apresentar um problema conhecido como localização, o que essencialmente implica em problemas mal colocados e algoritmos com dependência de malha. Alternativamente, uma teoria recente, chamada teoria do dano concentrado, foi proposta a fim de obter boa precisão em problemas reais de engenharia. Tal teoria aplica conceitos-chave das mecânicas da fratura e do dano em rótulas plásticas. À luz do exposto, o principal objetivo desta tese é a extensão da teoria do dano concentrado para analisar diferente problemas da engenharia. Até então, a teoria do dano concentrado era caracterizada como uma metodologia simplificada para analisar pórticos de concreto armado sob solicitações monotônicas ou sísmicas; mesmo com algumas poucas contribuições na análise de instabilidade local em estruturas metálicas. Desta forma, este trabalho estende a teoria do dano concentrado a fim de analisar arcos de concreto armado, estruturas de concreto simples, fadiga de alto ciclo e problemas contínuos. Os exemplos de aplicação mostram a acurácia das metodologias propostas.

[pt] O processo de fraturamento de materiais quase-frágeis requer atenção especial para a predição da direção de propagação de fraturas. A simulação do fraturamento com o método dos elementos finitos (MEF) tem como desvantagem a dependência da trajetória da fratura com respeito à malha adotada. Além disso, há certa dificuldade para os modelos numéricos representarem a fratura em modo misto por conta dos parametros envolvidos. O Método dos Elementos Finitos Estendido (XFEM) é uma técnica que combina o MEF com funções de enriquecimento para representar descontinuidades no campo de deslocamentos. Neste contexto, discutem-se nesta dissertação os critérios para a nucleação e propagação de fraturas e sua implementação no contexto do XFEM. As implementações foram feitas no framework GeMA, um software desenvolvido no Tecgraf / PUC-Rio. Os critérios de propagação de fraturas implementados baseiamse na abordagem das tensões e permitem controlar diferentes geometrias e tamanhos da área de avaliação na ponta da trinca. Um estudo paramétrico é apresentado para modelar uma viga de concreto sob carregamento não proporcional com fratura em modo misto. Foram consideradas diferentes questões como: discretização da malha, zona de avaliação, iniciação e propagação de fraturas e técnicas de controle de solução. Além disso, outros modelos com diferentes condições de contorno foram analisados para validar os critérios em situações complexas. As constatações paramétricas obtidas através do estudo da viga se monstraram válidas para os demais modelos avaliados. As implementações dos critérios de propagação de fraturas no XFEM, demonstraram excelentes concordâncias nas simulações das trajetórias de fraturamento, comparado com os dados experimentais. / [en] The fracture process of quasi-brittle materials requires special attention for the prediction of the direction of fracture propagation. The fracture simulation with the finite element method (FEM) has as its disadvantage the dependence of the fracture trajectory with respect to the mesh adopted. Besides, there is some difficulty for numerical models to represent the fracture in mixed mode because of the parameters involved. The Extended Finite Element Method (XFEM) is a technique which combines the FEM with enrichment functions to represent discontinuities in the displacement field. In this context, this dissertation discusses the criteria for nucleation and propagation of fractures and their implementation in the context of XFEM. The implementations were made in the GeMA framework, a software developed at Tecgraf / PUC-Rio. The implemented crack growth criteria is based on the stress approach and allows to control different geometries and sizes of the evaluation area in the crack tip. A parametric study is presented for modeling a concrete beam under nonproportional loading with mixed-mode fracture. Different situations were taken into account such as mesh refinement, geometry and size of the evaluation region, crack initiation and propagation and solution control techniques. Also, several models with different loading and boundary conditions were made to validate the criteria under complex situations. The parametric findings obtained through the study of the beam proved to be valid for the other models. The implementations of the fracture propagation criteria in the XFEM demonstrated excellent agreement in the simulations of the fracture trajectories compared to the experimental data.

The accurate description of the nonlinear structural behaviour is an important issue in engineering science. Usually, classic nonlinear theories, such as fracture and damage mechanics, applied to finite element programmes are used to fulfil that purpose. Classic fracture mechanics describes the structural deterioration process by a few discrete cracks. This theory presents good precision for structures with simple geometries, few cracks and homogeneous materials. Classic damage mechanics measures the deterioration process by an internal variable called damage. This theory has been successful in the description of several deterioration mechanisms in continuum media. Despite their accuracy, classic fracture and damage mechanics present some drawbacks. Firstly, regarding civil engineering problems, both theories are not suitable for some practical applications. Secondly, fracture mechanics demands the consideration of initial cracks to begin the analysis. Lastly, classic damage models may present an issue known as localisation, what essentially leads to ill-posed problems and mesh-dependent numerical algorithms. Alternatively, a recent theory, called lumped damage mechanics, was proposed in order to achieve good accuracy in actual engineering problems. Such theory applies key concepts from fracture and damage mechanics in plastic hinges. In the light of the foregoing, the main goal of this thesis is the extension of the lumped damage mechanics framework to analyse different engineering problems. So far, lumped damage mechanics was characterised as a simplified methodology to analyse reinforced concrete frames under seismic and monotonic loadings; even with a few contributions on the analysis of local buckling in metallic structures. Therefore, this work extends the lumped damage mechanics framework to analyse reinforced concrete arches, unreinforced concrete structures, high cycle fatigue and continuum problems. The application examples show the accuracy of the proposed methodologies. / A descrição acurada do comportamento não linear de estruturas é um problema importante na engenharia. Usualmente, teorias não lineares clássicas, tais como as mecânicas da fratura e do dano, aplicadas a programas de elementos finitos são utilizadas a fim de cumprir aquele propósito. A mecânica da fratura clássica descreve o processo de deterioração estrutural por meio de um pequeno número de fissuras discretas. Esta teoria apresenta boa precisão para estruturas com geometrias simples, poucas fissuras e materiais homogêneos. A mecânica do dano clássica tem sido exitosa na descrição de diversos mecanismos de deterioração em meios contínuos. Apesar de precisas, as abordagens clássicas em fratura e dano apresentam alguns entraves. Primeiramente, tratando-se de problemas da engenharia civil, ambas teorias não são adequadas para aplicações práticas. Em segundo lugar, os modelos clássicos de fratura demandam a consideração de fissuras iniciais para iniciar a análise. Por fim, os modelos clássicos de dano podem apresentar um problema conhecido como localização, o que essencialmente implica em problemas mal colocados e algoritmos com dependência de malha. Alternativamente, uma teoria recente, chamada teoria do dano concentrado, foi proposta a fim de obter boa precisão em problemas reais de engenharia. Tal teoria aplica conceitos-chave das mecânicas da fratura e do dano em rótulas plásticas. À luz do exposto, o principal objetivo desta tese é a extensão da teoria do dano concentrado para analisar diferente problemas da engenharia. Até então, a teoria do dano concentrado era caracterizada como uma metodologia simplificada para analisar pórticos de concreto armado sob solicitações monotônicas ou sísmicas; mesmo com algumas poucas contribuições na análise de instabilidade local em estruturas metálicas. Desta forma, este trabalho estende a teoria do dano concentrado a fim de analisar arcos de concreto armado, estruturas de concreto simples, fadiga de alto ciclo e problemas contínuos. Os exemplos de aplicação mostram a acurácia das metodologias propostas.

Les modèles de comportement mécanique, dits macroscopiques, sont développés à la fois pour leur légèreté, permettant le calcul d’éléments structuraux pouvant atteindre d’importantes dimensions, et pour leur finesse de représentation des phénomènes mécaniques observés par le matériau à des échelles plus fines. Le développement de tels modèles est ici effectué dans le cadre de la sollicitation sismique, donc des chargements cycliques alternés, appliquée à des ouvrages en matériaux quasi-fragiles, et plus précisément en béton. À ce jour, les modèles macroscopiques, effectivement applicables au calcul de structures, et représentatifs du comportement cyclique du béton sont encore rares. En conséquence de la complexité du problème de fissuration à homogénéiser, les modèles macroscopiques existants affichent une robustesse limitée ou ne permettent pas de reproduire l’ensemble des phénomènes mécaniques observés par le matériau. Une des barrières à la résolution de ces deux problématiques est le manque de données expérimentales relatives aux phénomènes à modéliser. En effet, en cause de la difficulté technique de les réaliser, peu de résultats d’essais cycliques alternés sur du béton sont disponibles dans la littérature.
 Une démarche d’expérimentation numérique a donc été élaborée sur la base d’un modèle fin du matériau, dit microscopique, capable de fournir les résultats nécessaires à la formulation et à l’identification d’un modèle macroscopique. Dans le modèle microscopique le matériau est considéré comme une structure à part entière, il a été développé afin de ne nécessiter qu’une quantité réduite de résultats d’essais, maîtrisés, pour être mis en oeuvre. Le modèle microscopique, un modèle particulaire lattice, a été développé sur la base d’un modèle lattice existant, enrichi pour être en mesure de simuler le comportement des matériaux quasi-fragiles sous chargements multi-axiaux et cycliques. Le modèle microscopique a alors été validé en tant qu’outil d’expérimentation numérique, et exploité afin d’établir les équations constitutives du modèle macroscopique fondées sur les théories de l’endommagement et de la plasticité. La régularité de la relation de comportement proposée, intégrant un effet unilatéral progressif, a notamment été garantie par l’utilisation d’un modèle d’élasticité non-linéaire. Le modèle macroscopique a finalement été calibré, entièrement, à l’aide du modèle microscopique, et mis à l’oeuvre dans la simulation de la réponse d’un voile en béton armé soumis à un chargement de cisaillement cyclique alterné. Cette simulation a permis de mettre en avant la robustesse numérique du modèle développé, ainsi que la contribution significative du comportement uni-axial cyclique alterné du béton à l’amortissement de telles structures. / Macroscopic mechanical behavior models are developed for their light computational costs, allowing the simulation of large structural elements, and the precise description of mechanical phenomena observed by the material at lower scales. Such constitutive models are here developed in the seismic solicitation framework, therefore implying cyclic alternate loadings at the material scale, and applied to civil engineering buildings, often made of concrete, or more generally of quasi-brittle materials. To date, macroscopic models applicable to structural computations, while representing the cyclic mechanical behavior are rare. In consequence of the intricacy of the fracture processes to homogenize, macroscopic constitutive models either do not present sufficient robustness or miss on important phenomena. One of the limitations to the resolution of this issue is the lack of experimental data. Indeed, because of the complexity of the experiments to set up, few results on alternate cyclic tests on concrete are available in the literature.A virtual testing approach has therefore been established on a microscopic model of the material, able to provide results needed to the formulation and the calibration of a macroscopic model. In the microscopic model, the material is considered as structure itself, it is developed so as to only necessitate a reduced amount of results from controlled experimental tests, in order to be used. The microscopic model, a lattice discrete element model, has been developed on the basis of an existing lattice model and extended to the simulation of multi-axial and cyclic loadings. The microscopic model has then been validated as a virtual testing tool and used to establish equations of the macroscopic model, on the basis of damage and plasticity theories. The consistency of the proposed constitutive relation, embedding progressive unilateral effect, has been achieved using non-linear elasticity. The macroscopic model has finally been calibrated, entirely with the microscopic model, and employed to simulate the response of a reinforced concrete wall under alternate shear loading. This simulation has served to showcase the numerical robustness of the proposed model, as well as the significant contribution of the uni-axial alternate behavior of concrete to the structural damping of such structures.

In this thesis, a program for fracture test in civil engineering has been optimized. The simulation is used for a validation of the fracture characteristics for blocks of construct material used for historic buildings reconstructure. This thesis illustrates the possibilities of an effective usage of the processor’s potential without the loss of the output quality. The individual parts of the simulation are analyzed and this thesis proposes for the critical sections some possible optimizations such as vectorization or parallel processing. The techniques used in this thesis may be used on similar computing problems and help shorten the required runtime. The prototype of the simulation was able to process the simulation in 7.7 hours. Optimized version is capable to process the same simulation in 2.1 hours on one core or 21 minutes on eight cores. The parallel optimized version is 21 times faster than the prototype.

[pt] A previsão do comportamento de materiais quase-frágeis desde o início de sua degradação até o aparecimento de fraturas pode ser apoiada pelo o uso da mecânica do dano contínuo. Efeitos térmicos, além de mecânicos, podem apresentar contribuição significativa na resposta do material e da estrutura. Nesse sentido, o acoplamento entre os distintos ramos da física descrevem a livre conversão da energia em suas diversas formas. O presente trabalho trata do acoplamento térmico em problemas de dano em materiais quase frágeis, em que são abordados o modelo de dano isótropico e os critério de danificação, bem como leis de evolução do dano térmico e mecânico. Além disso, aspectos inerentes à termodinâmica e transferência de calor são explicitados. O efeito térmico na análise estrutural inicia-se com uma investigação sobre os requisitos para que variações de temperatura produzam tensões térmicas e prossegue com um estudo do efeito no material, que reduz as propriedades de módulo de elasticidade, resistência à tração e à compressão além da energia de fratura. No entanto, a modelagem em elementos finitos da degradação da rigidez da estrutura devido ao processo de dano apresenta problemas de dependência da malha, que requerem o uso de técnicas de regularização da solução. Esse tópico é também abordado no trabalho. Exemplos numéricos demonstram os efeitos do acoplamento termomecânico na previsão da integridade de estruturas de materias quase-frágeis. / [en] Predicting the behavior of almost brittle materials in face of material degradation up to fracture is a topic that can be addressed with the use of continuous damage mechanics. Thermal effects, in addition to mechanical ones, may contribute significantly to the structural and material response. In this sense, the coupling between the different branches of physics takes into account the free conversion of energy in its various forms. The present work is about the thermal-mechanical coupling in in quasi-brittle materials, in which the isotropic damage model and the damage criteria are addressed, as well as the laws of evolution of thermal and mechanical damage. In addition, aspects inherent to thermodynamics and heat transfer are explained. The thermal effect in the structural analysis begins with an investigation of the requirements for temperature variations to produce thermal stresses and follows with a study of the effect of temperature on the material, which affects the elasticity module, the tensile and compression strength, in addition to the fracture energy. However, finite element modeling of stiffness degradation due to the damage process leads to problems of dependence on the mesh, which requires the use of regularization techniques, as addressed in this work. Numerical examples demonstrate the effects of thermo-mechanical coupling in the assessment of structure integrity.