This thesis deals with the design process of a tensile test specimen geometry with the intention that the specimen will show failure in a shear band during a tensile test. The triggered shear band is linked to a characteristic length lc, which is required for a nonlocal approach to continuum damage mechanics that predicts the life expectancy of a combustion chamber independent of the FEM mesh size. To predict if a specimen will fail in the preferred manner, numerical simulations have been performed and were analysed with the newly defined failure-in-shear-band indicator. Ductile failure modes and the fracture process depend strongly on the stress state. Therefore the indicator is formulated as a function of the Lode parameter and the stress triaxiality. Several double-notched bar specimens have been designed with different notch radii and notch depths. The failure-in-shear-band indicator implies promising values for a small notch radius and larger notch depth. Tensile tests were performed on four specimens which successfully failed in a shear band. Furthermore, a first statement on the magnitude of the characteristic length of CuAgZr is given. / Detta arbete behandlar designprocessen för en dragprovstavskonfiguration framtagen för att uppvisa brott i ett skjuvband under draghållfasthetsprovning. Initiering av skjuvbandet är kopplat till en karakteristisk längd lc, som krävs för att kunna använda en icke lokal metod för att analysera kontinuerlig skademekanik oberoende av maskstorleken i den numeriska modellen. Metoden är utvecklad för att kunna uppskatta den förväntade livslängden för en förbränningskammare. För att förutsäga om ett provobjekt kommer att gå sönder på det sätt som önskashar datorsimuleringar utförts och analyserats med den nyligen definierade indikatorn för skjuvbrott. Plastisk deformation, och så småningom brott, är starkt beroende avspänningstillståndet. Indikatorn är därför formulerad som en funktion av en s.k. Lode parametern och det treaxliga spänningstillståndet. Flera provstavsgeometrier har utformats med dubbla brottanvisningar vars radie och storlek varierats. Indikatorn för skjuvbrott ger lovande värden för små radier och ett större anvisningsdjup. Draghållfasthetsprovning utfördes på fyra provkroppar som uppvisade önskat skjuvbrott. Dessutom erhölls en första indikation om storleken på den karakteristiska längden för CuAgZr.

Styrene-Butadiene Rubber (SBR) is a form of rubber compound that is widely used in the tire industry. This is due to some of their unique characteristics such as high strength, high elasticity and resilience, high abrasion resistance, ability to absorb and dissipate shocks and vibrations, low plastic deformation, high deformation at low levels of stresses, and high product life. One of the most important and often overlooked causes of SBR degradation and eventual tire failure is 'rubber aging.' It can be defined as an alteration in the mechanical, chemical, physical, or morphological properties of elastomers under the influence of various environmental factors during processing, storing and use. Some of these environmental factors are humidity, ozone, oxygen, temperature, radiation (UV rays), etc. This study focuses on the effects of two of these factors acting in tandem, oxygen and temperature. In the past, studies have been conducted to observe the effects of rubber aging on the mechanical and wear properties of rubber. Studies have also been conducted to study the reactions taking place in rubber during aging and changes in its chemical structure. These studies use different modelling techniques and experiments to quantify the effects of aging. In this study, a material aging model that can predict the hyperplastic response of styrene-butadiene rubber (SBR) was mathematically developed using an integrated testing and continuum damage model framework. Coupling between the mechanical changes of SBR to the change in the chemical properties, specifically crosslink density (CLD) was also investigated. SBR dogbone shaped samples were accelerated aged in an aging oven at various temperatures and aging periods. Subsequently, hyperelastic tests were conducted to obtain the high strain response taking the 'Mullin's effect' into consideration. These responses were calibrated to different hyperelastic material models and the Arruda-Boyce model was chosen, due to its stable behavior and optimal fit. An aging evolution function was developed based on the variation in the model coefficients. This damage model is able to predict the hyperelastic response of SBR as it ages. A user material subroutine (UMAT) was also implemented in Abaqus based on the obtained aging evolution function to predict the stress response of SBR for varied applications. Additionally, to couple the chemical variations with the hyperelastic response, the rubber structure and composition was probed using Fourier-transform infrared spectroscopy (FTIR). The degradation of additives and SBR polymer chains were analyzed microscopically to explain the impact on the macroscopic properties. This study helps to correlate the change in crosslink density to ameliorate mechanical properties, such as strain at break, modulus, and stiffness. The effects of aging on the viscoelastic properties of SBR were also studied. Dynamic Mechanical Analysis (DMA) was used to characterize the viscoelastic response. Master curves of storage and loss modulus were generated using the time-temperature superposition principle (TTSP). The friction coefficient was estimated from the storage and loss modulus using a simplified form of the Persson equation [1]. CLD was also estimated from DMA data. Wear experiments were conducted on the Dynamic Friction Tester (DFT) for various aging conditions. The estimated friction coefficient was compared to the one from the experiments. Archard's law was used to correlate the frictional energy to the volume loss during wear experiments. Correlation between the wear and the viscoelastic properties of SBR is also studied. Finally, the lifetime of SBR for various aging temperatures is predicted using various models. [1] M. Ciavarella, "A Simplified Version of Persson's Multiscale Theory for Rubber Friction Due to Viscoelastic Losses," J. Tribol., vol. 140, no. 1, 2018, doi: 10.1115/1.4036917. / Master of Science / Elastomers or rubbers are they are generally referred to are an indispensable part of human life. They are made up of long-chain polymer units linked to one other through crosslinks. This peculiar morphology of rubbers is what gives them their unique characteristics. There are as many as 40,000 known products that use some form of rubber as the primary raw material. Apart, from this, they are also widely used in aviation and aerospace, automobiles, dampers and absorbers, civil engineering, electronics, medical, toys, clothing, sports, footwear, and so on. This is due to some of their unique characteristics such as high strength, high elasticity and resilience, high abrasion resistance, ability to absorb and dissipate shocks and vibrations, low plastic deformation, high deformation at low levels of stresses, and high product life. Over the last couple of years, it has also played a pivotal role in personal protective equipment (PPE) and masks worn by billions of people and frontline workers all over the globe. The fact that rubber is included in the EU's list of critical raw materials highlights its global importance. However, over the past several years, the rubber supply has dwindled. COVID-19 also caused disruptions in the supply chain of rubber. As the effects of COVID-19 are fading, there has been a spike in the demand for rubber; the primary reason being automotive tires! Even though substantial research is being conducted to try and replace rubber as a raw material with synthetic alternatives such as polyurethane, the excellent blend of damping, friction and wear characteristics, heat dissipation provided by natural rubber cannot be replicated by any of these laboratory compounds. Hence, at this time, there is an increased need to conserve and improve the longevity of rubber compounds. Styrene-Butadiene Rubber (SBR) is a form of a rubber compound that is widely used in the tire industry. One of the most important and often overlooked causes of SBR degradation and eventual tire failure is 'rubber aging.' It can be defined as an alteration in the mechanical, chemical, physical, or morphological properties of elastomers under the influence of various environmental factors during processing, storing and use. Some of these environmental factors are humidity, ozone, oxygen, temperature, radiation (UV rays), etc. This study focuses on the effects of two of these factors acting in tandem, oxygen and temperature. In the past, studies have been conducted to observe the effects of rubber aging on the mechanical and wear properties of rubber. Studies have also been conducted to study the reactions taking place in rubber during aging and changes in its chemical structure. These studies use different modelling techniques and experiments to quantify the effects of aging. The present study aims to model changes in the hyperelastic (large stretching) behavior of SBR using a Continuum Damage Mechanics (CDM) approach. This mathematical model is translated into ABAQUS, a finite element analysis software to study the mechanical response of components with various geometries and loading conditions. Secondly, the effects of aging on the viscoelastic behavior of SBR is studied. This helps us to estimate the cross-link density (CLD) as well as the friction coefficient of SBR as it is aged. The impact of aging on the wear and friction properties of SBR is studied experimentally. Finally, using various mechanical and chemical models the lifetime of SBR is estimated for various aging temperatures. Thus, the end goal of the study is to drive the development of new rubber compounds that will help improve the service life of rubbers and also have a positive impact on the environment.

Lors de leur construction, les structures massives (ex. les enceintes de confinement des centrales nucléaires) sont soumises à des déformations dues à l’hydratation du béton. En effet, d’une part la réaction chimique du ciment avec l’eau est exothermique et thermo activée, ce qui induit des déformations de dilatation puis de contraction. D’autre part une dépression capillaire étant créée par la consommation d’eau due à l’hydratation du ciment, des déformations de contraction se produisent. Lorsqu’elles sont empêchées par la partie de la structure déjà construite, ces déformations volumiques induisent des contraintes de compression puis de traction pouvant causer une fissuration traversante augmentant alors sensiblement la perméabilité du béton. Mon travail de thèse a consisté à caractériser le comportement au jeune âge du matériau que l’on utilise (basé sur la formulation utilisée lors de la construction d’une enceinte) puis à mettre au point un essai permettant d’étudier la fissuration d’une éprouvette de béton soumise à des déformations empêchées lors de son durcissement. Ce nouvel essai est en fait une évolution de l’essai à l’anneau de retrait gêné permettant de prendre également en compte les déformations d’origine thermique. Les essais de caractérisation concernent essentiellement, d’un point de vue macroscopique, le retrait (endogène et thermique), le fluage (propre et thermique transitoire) et l’évolution des caractéristiques mécaniques (résistance à la compression, à la traction et module d’élasticité). La campagne d’essais réalisée avec ce nouveau dispositif, appelé essai à l’anneau thermique actif, et l’analyse numérique de ces essais par des simulations aux éléments finis (basées sur un modèle viscoélastique endommageable introduisant un couplage entre le fluage et l’endommagement) a permis d’évaluer ce couplage, d’identifier la diminution de résistance en traction due à une reprise de bétonnage et de quantifier l’effet des armatures sur le comportement du béton. Des mesures de transfert d’air sec à travers une éprouvette fissurée ont également été réalisées sur ce dispositif. Finalement, des simulations numériques d’ouvrages massifs ont mis en exergue l’influence des conditions de restriction du retrait sur le faciès d’endommagement et l’influence du couplage fluage fissuration sur le calcul des ouvertures de fissures. / At early-age, massive concrete structures (ex. nuclear power plant) are submitted to strains due to the hydration reaction. If they are restrained, crossing cracks can occurs. This cracking may increase significantly the concrete wall permeability. The objectives of this work was to characterize the early age concrete behavior (thermal and endogenous shrinkage, basic and thermal transient creep, mechanical characteristic evolution) as well as develop a new device to study the early age cracking of a concrete structure submitted to restrained shrinkage.The experimental campaign achieved with this new device (called thermal active ring test) and the numerical analysis of the test thanks to finite element simulations allows us to evaluate the coupling betwwen creep and damage, to identify the tensile strength decrease due to construction joints and to quantify the effect of reinforcement on the concrete behaviour. Moreover, with this device, permeability measurements have been performed on a cracked specimen. Finally, numerical simulations of massive structures highlight the influence of boundary conditions for restrained shrinkage and the influence of the coupling between creep and damage on the damage pattern.

A Mecânica do Dano Contínuo (MDC) teve importante desenvolvimento desde os trabalhos iniciais de Kachanov e Rabotnov sendo uma ferramenta prática para considerar processos de danificação em materiais e estruturas em nível de contínuo macroscópico. Neste trabalho, apresenta-se uma aplicação da teoria do dano anisotrópico baseada em teorias desenvolvidas a partir dos trabalhos de Murakami. Nas formulações apresentadas, o tensor de dano de quarta ordem M (que relaciona tensões aplicadas e tensões efetivas) é determinado com base no tensor Ω (densidade de área tridimensional devida ao dano) que, por sua vez, pode ser determinado com base em dados experimentais. São propostas três formulações teóricas que são transformadas em formulações incrementais e incorporadas em um programa computacional de elementos finitos (para placas e cascas laminadas em material compósito) que considera efeitos geométricos não-lineares. A primeira e segunda formulação são casos particulares da terceira formulação que é um modelo termodinâmico tridimensional. As forças termodinâmicas associadas à evolução do tensor de dano são deduzidas a partir da expressão da dissipação intrínseca. Um critério fenomenológico para o dano é proposto. Em consistência com a positividade da dissipação intrínseca é adotada uma regra de normalidade para a evolução da força termodinâmica. Também é proposta, baseada em dados experimentais, uma lei para o encruamento associada ao processo de dano. Os modelos são validados comparando resultados numéricos a soluções analíticas ou a resultados experimentais. A formulação viscoelástica é definida do dano elástico e por componentes viscoelásticas representadas no formato de variáveis de estado e, posteriormente, validadas através de resultados experimentais. / The Continuum Damage Mechanics (CDM) had important development since the initial works of Kachanov and Rabotnov and constitutes now a practical tool to account for macroscopic damage in materials and structures. In this work, an application of an anisotropic damage theory based in Murakami theory is presented. In the formulations presented here, the fourth order damage tensor M (that relates Cauchy stress and effective stress) is determined on the basis of the tensor Ω (damaged three-dimensional area density) that, can be determined through experimental data. The three theoretical formulations presented here are transformed into incremental formulations and implemented in a finite element program (for plates and shell structures in composite material) taking account of geometrically non-linear effects. The first and second formulations are particular cases of the third formularization that is a tridimensional model for continuous damage formulated. The thermodynamic force associated with the evolution of the damage tensor is deduced from the expression of the intrinsic dissipation. A phenomenological criterion for damage yielding is proposed. In consistence with the positivity of the intrinsic dissipation, a normality rule is adopted for the evolution of the thermodynamic force. In addition, a hardening law associated with the damage process is identified from available experiment results. The models are validated by comparison with closed-form solutions or with experiment results. The viscoelastic formulation is defined through damage elastic and viscous components and set in a state variables format and then validated by comparison with experimental creep tests.

Friction Spot Welding (FSpW) é um processo de solda ponto por fricção, que opera na fase sólida do material e permite unir duas ou mais chapas de metal sobrepostas. Além de ser bastante usado para soldar materiais leves, ele também é aplicável a qualquer material que apresente boa plasticidade. Neste trabalho são analisados dois materiais: AA Alclad 2024-T351 e AA 2024-T351, diferindo entre si no uso, ou não, da camada de proteção contra a corrosão (Alclad). As uniões são feitas sob os mesmos parâmetros do processo, previamente estudados para o material com Alclad. Dois parâmetros são utilizados: um dito ótimo, capaz de produzir soldas com bom desempenho mecânico e reprodutibilidade e um segundo, dito insuficiente, por produzir soldas de baixo desempenho mecânico e baixa reprodutibilidade. Pretende-se, com este trabalho, avaliar os efeitos que a camada Alclad pode acarretar nas juntas soldadas, em seu desempenho mecânico, no modo de fratura, na microestrutura e na geometria da junta. Os resultados apresentam uma grande influência do Alclad, tendo em vista que durante o processo o recobrimento migra das superfícies das chapas para o centro da solda. Assim, uma interface deste material, que possui baixa resistência mecânica, é criada, influenciando negativamente o desempenho da junta e alterando o modo de fratura. O principal escopo desta dissertação é realizar uma análise da fratura do ensaio de cisalhamento, com o uso do método de elementos finitos. Portanto, fazse necessário estudar e desenvolver um modelo numérico capaz de representar a nucleação, coalescimento, formação de uma ou mais trincas e a consequente propagação até a fratura do corpo. Para a realização da análise utilizou-se o modelo numérico de fratura Johnson-Cook (JC), o qual expressa a tensão equivalente como uma função da deformação plástica, da taxa de deformação e da temperatura. Realizou-se, ainda, um estudo acerca das teorias do Continuum Damage Mechanics (CDM), bem como se fez necessário obter novos parâmetros para o modelo, que descrevessem o fenômeno e o material. Nesse sentido, serão realizadas duas análises, sendo que a primeira considera o efeito da camada de Alclad e, a segunda, considera uma solda livre de defeitos. Espera-se identificar os locais em que trinca é nucleada e analisar a resposta da junta, passo a passo, durante a propagação da trinca, até a fratura completa do corpo. E, por fim, avaliar a interferência no modelo numérico da presença da camada contra a corrosão Alclad. / Friction Spot Welding (FSpW) is a friction spot weld process, it operates in the solid-state of the material and allows joining two or more sheets in overlap configuration. It is used to join light weight materials, also is suitable to any material that shows good ductility. In this work two different materials are analyzed AA Alclad 2024-T351 e AA 2024-T351, between them the use, or not, of the corrosion protection layer Alclad. The welds are made under the same process parameters previously studied to the material with Alclad. Two parameters are utilized: the first one is the optimum parameter capable to produce welds with good mechanical performance and reproducibility, and another one inadequate because it produces joins with poor mechanical response and reproducibility. It is intended with this work, to evaluate the effects that the Alclad layer can cause in the welds, in its mechanical performance, fracture mode, microstructure and geometry of the join. The results showed a considerable influence of the Alclad, considering that during the process, it migrates from the sheet surface to the center of the weld. Thus, an interface of this material, that has a very low hardness, is created, influencing negatively the performance of the weld and changing the fracture mode. The aim of this dissertation is to perform an analysis of the fracture from the lap shear test, using the finite element method. Therefore, becomes necessary study and develop a numerical model capable to represent the nucleation, coalescence, formation of one or more cracks and, the consequent propagation until the fracture of the body. To perform the analysis it was used the numerical model of fracture called Johnson-Cook (JC), which expresses the equivalent stress as a function of the plastic deformation, the strain rate and the temperature. It was also made a study about the Continuum Damage Mechanics (CDM) theories, and it was necessary to obtain new parameters for the model, that describe the phenomenon and the material. In this sense, it will be performed two analyses, and the first considers the Alclad layer and, the second, considers a weld without defects. It is expected to identify the places where the crack nucleated, and analyze the behavior of the weld, step by step, during the crack propagation, until the complete fracture of the component. And, finally, evaluate the interference in the numerical model of the presence of the protection corrosion layer Alclad.

Dans cette thèse, des considérations fondamentales de modélisation des phénomènes de rupture sont abordées pour des systèmes discrets endommageables. Le but est d’établir, en commençant par des problèmes structuraux simples, un pont entre la Mécanique de l’Endommagement Discret (MED) et celle de la Mécanique de l’Endommagement Continu (MEC) non local. Il est actuellement admis que la MEC doit être considérée dans un cadre non local afin d’obtenir des résultats cohérents, notamment lors de la modélisation numérique de phénomènes de radoucissement basés sur des lois d’endommagement. Nous appuyons cette non-localité sur l’échelle de la microstructure du matériau. A l’aide d’une procédure de continualisation et l’utilisation de l’approximant de Padé, nous avons pu obtenir l’expression analytique de l’approximation continue non-locale offrant une représentation très fidèle du comportement du problème discret dans tout le processus d’endommagement. Nous étudions les systèmes de la chaîne axiale discrète en traction, de la poutre console discrète en flexion ainsi que de la membrane microstructurée sous pression uniforme. Le système discret est tout d’abord résolu puis les équations discrètes sont continualisées pour obtenir un modèle non local continu. Pour chacun de ces problèmes une attention toute particulière est portée aux conditions aux limites du problème continualisé, dont l’importance est illustrée tout au long de ce manuscrit. / In this thesis, some fundamental considerations of the modeling of failure are addressed for discrete damage systems. The goal is to establish, starting with simple structural problems, a bridge between the Discrete Damage Mechanics (DDM) and that of the non-local Continuum Damage Mechanics (CDM). It is currently accepted that DDM systems must be considered in a non-local framework to obtain consistent results, especially during numerical modeling of softening phenomena based on damage laws. We support this non- locality on the scale of the microstructure of the material. Using a continualisation procedure and with the use of the Padé approximant, we were able to obtain the analytic expression of the non-local continuous approximation offering an accurate simulation of the discrete problem for the whole damage process. We study the systems of the discrete axial chain under traction, the discrete bending beam and the microstructured membrane under uniform pressure. The discrete system is first solved, then the discrete equations are continualised to obtain a non-local continuum model. For each of these problems, careful attention is paid to the boundary conditions of the continual problem, the importance of which is illustrated throughout this manuscript.

This research work has contributed in various ways to help develop a better understanding of textile composites and materials with complex microstructures in general. An instrumental part of this work was the development of an object-oriented framework that made it convenient to perform multiscale/multiphysics analyses of advanced materials with complex microstructures such as textile composites. In addition to the studies conducted in this work, this framework lays the groundwork for continued research of these materials. This framework enabled a detailed multiscale stress analysis of a woven DCB specimen that revealed the effect of the complex microstructure on the stress and strain energy release rate distribution along the crack front. In addition to implementing an oxidation model, the framework was also used to implement strategies that expedited the simulation of oxidation in textile composites so that it would take only a few hours. The simulation showed that the tow architecture played a significant role in the oxidation behavior in textile composites. Finally, a coupled diffusion/oxidation and damage progression analysis was implemented that was used to study the mechanical behavior of textile composites under mechanical loading as well as oxidation. A parametric study was performed to determine the effect of material properties and the number of plies in the laminate on its mechanical behavior. The analyses indicated a significant effect of the tow architecture and other parameters on the damage progression in the laminates.

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

A Mecânica do Dano Contínuo (MDC) teve importante desenvolvimento desde os trabalhos iniciais de Kachanov e Rabotnov sendo uma ferramenta prática para considerar processos de danificação em materiais e estruturas em nível de contínuo macroscópico. Neste trabalho, apresenta-se uma aplicação da teoria do dano anisotrópico baseada em teorias desenvolvidas a partir dos trabalhos de Murakami. Nas formulações apresentadas, o tensor de dano de quarta ordem M (que relaciona tensões aplicadas e tensões efetivas) é determinado com base no tensor Ω (densidade de área tridimensional devida ao dano) que, por sua vez, pode ser determinado com base em dados experimentais. São propostas três formulações teóricas que são transformadas em formulações incrementais e incorporadas em um programa computacional de elementos finitos (para placas e cascas laminadas em material compósito) que considera efeitos geométricos não-lineares. A primeira e segunda formulação são casos particulares da terceira formulação que é um modelo termodinâmico tridimensional. As forças termodinâmicas associadas à evolução do tensor de dano são deduzidas a partir da expressão da dissipação intrínseca. Um critério fenomenológico para o dano é proposto. Em consistência com a positividade da dissipação intrínseca é adotada uma regra de normalidade para a evolução da força termodinâmica. Também é proposta, baseada em dados experimentais, uma lei para o encruamento associada ao processo de dano. Os modelos são validados comparando resultados numéricos a soluções analíticas ou a resultados experimentais. A formulação viscoelástica é definida do dano elástico e por componentes viscoelásticas representadas no formato de variáveis de estado e, posteriormente, validadas através de resultados experimentais. / The Continuum Damage Mechanics (CDM) had important development since the initial works of Kachanov and Rabotnov and constitutes now a practical tool to account for macroscopic damage in materials and structures. In this work, an application of an anisotropic damage theory based in Murakami theory is presented. In the formulations presented here, the fourth order damage tensor M (that relates Cauchy stress and effective stress) is determined on the basis of the tensor Ω (damaged three-dimensional area density) that, can be determined through experimental data. The three theoretical formulations presented here are transformed into incremental formulations and implemented in a finite element program (for plates and shell structures in composite material) taking account of geometrically non-linear effects. The first and second formulations are particular cases of the third formularization that is a tridimensional model for continuous damage formulated. The thermodynamic force associated with the evolution of the damage tensor is deduced from the expression of the intrinsic dissipation. A phenomenological criterion for damage yielding is proposed. In consistence with the positivity of the intrinsic dissipation, a normality rule is adopted for the evolution of the thermodynamic force. In addition, a hardening law associated with the damage process is identified from available experiment results. The models are validated by comparison with closed-form solutions or with experiment results. The viscoelastic formulation is defined through damage elastic and viscous components and set in a state variables format and then validated by comparison with experimental creep tests.

A Mecânica do Dano Contínuo (MDC) teve importante desenvolvimento desde os trabalhos iniciais de Kachanov e Rabotnov sendo uma ferramenta prática para considerar processos de danificação em materiais e estruturas em nível de contínuo macroscópico. Neste trabalho, apresenta-se uma aplicação da teoria do dano anisotrópico baseada em teorias desenvolvidas a partir dos trabalhos de Murakami. Nas formulações apresentadas, o tensor de dano de quarta ordem M (que relaciona tensões aplicadas e tensões efetivas) é determinado com base no tensor Ω (densidade de área tridimensional devida ao dano) que, por sua vez, pode ser determinado com base em dados experimentais. São propostas três formulações teóricas que são transformadas em formulações incrementais e incorporadas em um programa computacional de elementos finitos (para placas e cascas laminadas em material compósito) que considera efeitos geométricos não-lineares. A primeira e segunda formulação são casos particulares da terceira formulação que é um modelo termodinâmico tridimensional. As forças termodinâmicas associadas à evolução do tensor de dano são deduzidas a partir da expressão da dissipação intrínseca. Um critério fenomenológico para o dano é proposto. Em consistência com a positividade da dissipação intrínseca é adotada uma regra de normalidade para a evolução da força termodinâmica. Também é proposta, baseada em dados experimentais, uma lei para o encruamento associada ao processo de dano. Os modelos são validados comparando resultados numéricos a soluções analíticas ou a resultados experimentais. A formulação viscoelástica é definida do dano elástico e por componentes viscoelásticas representadas no formato de variáveis de estado e, posteriormente, validadas através de resultados experimentais. / The Continuum Damage Mechanics (CDM) had important development since the initial works of Kachanov and Rabotnov and constitutes now a practical tool to account for macroscopic damage in materials and structures. In this work, an application of an anisotropic damage theory based in Murakami theory is presented. In the formulations presented here, the fourth order damage tensor M (that relates Cauchy stress and effective stress) is determined on the basis of the tensor Ω (damaged three-dimensional area density) that, can be determined through experimental data. The three theoretical formulations presented here are transformed into incremental formulations and implemented in a finite element program (for plates and shell structures in composite material) taking account of geometrically non-linear effects. The first and second formulations are particular cases of the third formularization that is a tridimensional model for continuous damage formulated. The thermodynamic force associated with the evolution of the damage tensor is deduced from the expression of the intrinsic dissipation. A phenomenological criterion for damage yielding is proposed. In consistence with the positivity of the intrinsic dissipation, a normality rule is adopted for the evolution of the thermodynamic force. In addition, a hardening law associated with the damage process is identified from available experiment results. The models are validated by comparison with closed-form solutions or with experiment results. The viscoelastic formulation is defined through damage elastic and viscous components and set in a state variables format and then validated by comparison with experimental creep tests.