No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o acúmulo da degradação do concreto produzido por cargas repetidas. O modelo de dano apresenta as condições necessárias exigidas na chamada aproximação de descontinuidades fortes proposta por Simó, Oliver e Armero e, conseqüentemente, pode ser empregado na formulação de elementos finitos com descontinuidade forte incorporada. Em decorrência de sua capacidade de descrever o comportamento do meio descontínuo independentemente da posição dos contornos do elemento finito, essa classe de formulação constitui uma alternativa valiosa para remediar a forte dependência da malha observada nos modelos de fissuras distribuídas, assim como para evitar as sofisticadas técnicas de reconstrução da malha exigidas nos modelos de fissura discreta, nos quais a fissura é introduzida na interface entre elementos. O trabalho traz contribuições no sentido de proporcionar uma ferramenta alternativa para a análise de propagação de fissuras por fadiga em elementos estruturais de concreto, dentro do contexto da mecânica do dano contínuo. Verifica-se a eficiência da formulação mediante análise numérica de problemas de fadiga em elementos estruturais de concreto. / A constitutive model based on the continuum damage mechanics is proposed to describe the accumulation of the degradation produced by repeated loads in concrete materials. The proposed damage model presents the necessary conditions required in the strong discontinuity approach advocated by Simó, Oliver and Armero and, consequently, it can be used in the embedded strong discontinuity finite element approach. This class of approach has been recognized by its capability to model discontinuities independently on the element boundaries. In fracture mechanics, the embedded strong discontinuity element has been proved to be a efficient alternative to remedy the strong mesh dependence verified in smeared crack approaches, as well as to avoid the sophisticated remeshing techniques required in the discrete crack approaches, in which the crack is introduced in the element interfaces. This work provides an alternative tool for the analysis of crack propagation in concrete structures under fatigue in the context of the continuum damage mechanics. Numerical analysis of concrete elements under fatigue are performed to access the effectiveness of the proposed approach.

On étudie le comportement thermomécanique de colis de déchets vitrifiés par modélisation multi- physiques. Les colis sont réalisés avec un conteneur en acier inoxydable dans lequel est coulé un verre borosilicaté. Pour le verre, la méthode des éléments finis est employée pour les calculs thermiques, la relaxation structurale du volume massique, le comportement viscoélastique et l’endommagement. Ces lois consécutives modélisent l’influence de la sollicitation thermique initiale. La relaxation structurale du verre, issue du modèle TNM-KAHR, permet la prise en compte d’effets fondamentaux quant à la transition vitreuse, en fonction des traitements thermiques expérimentaux et simulés. Lorsque le verre dépasse localement une criticité du champ de contrainte, on procède au couplage du calcul de structure viscoélastique, pour le verre solide en relaxation,avec la mécanique de l’endommagement qui réactualise la rigidité et les contraintes en mode I et en mode II. On applique cette méthodologie complète de simulation à l’issue des adaptations nécessaires au cas de blocs de verre massifs en solidification. Ces modèles permettent alors l’obtention de surfaces de fracturation quantifiées, dans le verre, à partir de l’énergie dissipée par le modèle d’endommagement. / We study the thermomechanical behavior of vitrified waste packages by multiphysics modeling. The packages are manufactured by the cast of borosilicate glass into stainless steel canisters. The finite element method is used for the thermal computations.In the glass, the finite element analysis is also used to compute the specific volume evolution and the viscoelastic behavior, due to the structural relaxation of glass, as well as the simulation of the damage behavior. These consecutive behavior laws model theinfluence of the initial thermal response. Glass structural relaxation is computed using the TNM-KAHRmodel, which allows us to take into account fundamental phenomena of the glass transition, depending on the results of experimental and simulated thermal treatments. For the solid glass within this relaxation process, the stress may locally increase beyond critical values. The viscoelastic structure simulation is then coupled with continuum damage mechanics where stresses and stiffness are updated in mode I and mode II. We apply this simulation protocol after adopting conditions relative to the case of these manufactured bulky solidifying glass casts. The models then allow us to quantify the cracking surfaces inside the glass fromthe energy dissipated within the damagemodel.

We develop a dual-purpose damage model (DPDM) that can simultaneously model intralayer damage (ply failure) and interlayer damage (delamination) as an alternative to conventional practices that models ply failure by continuum damage mechanics (CDM) and delamination by cohesive elements. From purely computational point of view, if successful, the proposed approach will significantly reduce computational cost by eliminating the need for having double nodes at ply interfaces. At the core, DPDM is based on the regularized continuum damage mechanics approach with vectorial representation of damage and ellipsoidal damage surface. Shear correction factors are introduced to match the mixed mode fracture toughness of an analytical cohesive zone model. A predictor-corrector local-nonlocal regularization scheme, which treats intralayer portion of damage as nonlocal and interlayer damage as local, is developed and verified. Two variants of the DPDM are studied: a single- and two- scale DPDM. For the two-scale DPDM, reduced-order-homogenization (ROH) framework is employed with matrix phase modeled by the DPDM while the inclusion phase modeled by the CDM. The proposed DPDM is verified on several multi-layer laminates with various ply orientations including double-cantilever beam (DCB), end-notch-flexure (ENF), mixed-mode-bending (MMB), and three-point-bending (TPB). The simulation is executed in the platform of FOOF (Finite element solver based on Object-Oriented Fortran). The objective of FOOF is to develop a new architecture of the nonlinear multiphysics finite element code in object oriented Fortran environment. The salient features of FOOF are reusability, extensibility, and performance. Computational efficiency stems from the intrinsic optimization of numerical computing intrinsic to Fortran, while reusability and extensibility is inherited from the support of object-oriented programming style in Fortran 2003 and its later versions. The shortcomings of the object oriented style in Fortran 2003 (in comparison to C++) are alleviated by introducing the class hierarchy and by utilizing a multilevel programming style.

Este trabalho busca avaliar a ductilidade de ligas metálicas utilizando como ferramenta a teoria da mecânica do dano proposta por Kachanov e desenvolvida por Lemaitre, a qual é apresentada desde as hipóteses básicas até as equações que modelam a deterioração de um material em regime de fratura dúctil. Como o enfoque do trabalho é a predição de trincas em processos de conformação mecânica, em especial estampagem de chapas, o mecanismo de formação destes defeitos é revisado, buscando na literatura o entendimento de como os parâmetros microestruturais influenciam na fratura dúctil. Ensaios de tração foram efetuados em corpos de prova retirados de chapas de aço SAE 1050 em duas condições microestruturais, cementita esferoidizada em matriz ferrítica e ferritaperlita, e em duas direções em relação à laminação da chapa original, paralelo e transversal. A evolução do dano foi medida de maneira indireta por meio da variação do módulo elástico e as propriedades mecânicas necessárias para utilização do modelo de Lemaitre foram calculadas. Por meio de difração de raios X, efetuamos o estudo da evolução da textura cristalográfica, apresentado na forma de figuras de distribuição de orientação e análise da intensidade das principais fibras encontradas em aços laminados a quente. Não foi observada influência significativa do tipo de microestrutura e da direção de deformação na evolução da textura. Por fim, o modelo de evolução de dano de Lemaitre foi transformado em um algoritmo numérico e implementado no código comercial Abaqus, em sua versão explícita, por meio do uso da subrotina VUMAT. Resultados foram obtidos e comparados com os experimentos, validando a aplicação do modelo. A evolução do dano para o aço SAE 1050 também foi comparada com resultados para outros aços ao manganês encontrados na literatura. Relações empíricas entre o teor de carbono e parâmetros como a deformação limite para início do dano, resistência à evolução do dano e dano máximo suportado foram desenvolvidas e apresentadas, com o intuito de funcionar como guias gerais para cálculo sem a necessidade de uma bateria de ensaios dedicados, facilitando a utilização da teoria da mecânica do dano em condições industriais. / The aim of the present work is to evaluate the ductility of metallic alloys employing the theory of damage mechanics as suggested by Kachanov and developed by Lemaitre, which is presented since its basic hypothesis until the equation that model the material deterioration under a regime of ductile fracture. As the focus of the work is the fracture prediction during mechanical working processes (mainly sheet metal stamping), the mechanism of formation of these defects is revised, based upon literature data, aiming at the understanding of how the material microstructural parameters influence ductile fracture. Tensile tests have been performed on samples obtained from SAE 1050 steel sheets for two microstructural conditions namely spheroidized cementite and regular ferrite-perlite for two rolling directions (rolling and transverse directions). In those tests, damage evolution has been measured indirectly through the materials variation in the Young modulus with strain, obtaining the mechanical properties, needed to be used in the calculation of Lemaitres model. Through X-ray diffraction measurements, the crystallographic texture evolution, presented in the form of orientation distribution functions and the associated fiber intensities observed for both microstructural conditions, has been evaluated. No major influence has been observed in this texture evolution, for the tested conditions. Finally, the Lemaitre damage evolution model has been transformed into a numerical algorithm and implemented in the Abaqus commercial code, in its explicit form, through the VUMAT sub-routine. Results have been obtained and compared with the experimental values, validating the suggested model. Damage evolution for the SAE 1050 steel has been also compared with results from literature for other C-Mn steels. Empirical relationships between C level and damage parameters such as limit strain for damage initiation, resistance to damage evolution and maximum allowable damage, have been developed and presented, envisaging their application as general guidelines, without requiring a sequence of dedicated tests, making easier the usage of damage mechanics under industrial conditions.

<div>Despite the advances of analytical and numerical methods for composite materials, it is still challenging to predict the onset and evolution of their different failure mechanisms. Because most failure mechanisms are irreversible processes in thermodynamics, it is beneficial to model them within a unified thermodynamic framework. Noting the advantages of so-called generalized standard models (GSMs) in this regard, the objective of this work is to formulate constitutive models for several main failure mechanisms: brittle fracture, interlaminar delamination, and fatigue behavior for both continuum damage and delamination, in a generalized standard manner.</div><div><br></div><div>For brittle fracture, the numerical difficulties caused by damage and strain localization in traditional finite element analysis will be addressed and overcome. A nonlocal damage model utilizing an integral-type regularization technique will be derived based on a recently developed ``local'' continuum damage model. The objective is to make this model not only rigorously handle brittle fracture, but also incorporate common damage behavior such as damage anisotropy, distinct tensile and compressive damage behavior, and damage deactivation. A fully explicit integration scheme for the present model will be developed and implemented.</div><div><br></div><div>For fatigue continuum damage, a viscodamage model, which can handle frequently observed brittle damage phenomena, is developed to produce stress-dependent fatigue damage evolution. The governing equation for damage evolution is derived using an incremental method. A class of closed-form incremental constitutive relations is derived. </div><div><br></div><div>For interlaminar delamination, a cohesive zone model (CZM) will be proposed. Focus is placed on making the associated cohesive elements capable of displaying experimental critical energy release rate--mode mixture ratio relationships. To achieve this goal, each cohesive element is idealized as a deformable string exhibiting path dependent damage behavior. A damage model having a path dependence function will be developed, which will be constructed such that each cohesive element can exhibit designated, possibly sophisticated mixed-mode behavior. The rate form of the cohesive law will be subsequently derived.</div><div><br></div><div>Finally, a CZM for interlaminar fatigue, capable of handling brittle damage behavior, is developed to produce realistic interlaminar crack propagation under high-cycle fatigue. An implicit integration scheme, which can handle complex separation paths and mixed-mode delamination, is developed. Many numerical examples will be utilized to clearly demonstrate the capabilities of the proposed nonlocal damage model, continuum fatigue damage model, and CZMs for quasi-static and fatigue delamination.</div>

Abstract not available

Made available in DSpace on 2016-12-12T20:25:11Z (GMT). No. of bitstreams: 1 Thiago Andre Carniel.pdf: 5594070 bytes, checksum: 5e24f59f581ec79c2edb07d9afdd502e (MD5) Previous issue date: 2013-07-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work presents the development of a numerical formulation for the transient analysis of spatial truss structures considering geometrical and material nonlinearities. The equilibrium problem is formulated using the Principle of the Virtual Power in a current Lagrangian description. The displacement and velocity fields are discretized employing the Finite Element Method and the nonlinear equilibrium equations are solved by the full Newton- Raphson procedure. In order to obtain quadratic convergence, the algorithmic tangent matrix expression is developed and presented. Next, the transient problem is formulated and solved using the Newmark integration algorithm. The material model adopted is viscoelastic-viscoplastic coupled to Lemaitre s damage. The viscoelastic behavior is represented by the generalized Kelvin-Voigt rheological model and the viscoplastic contribution is introduced via Perzyna s equation. The evolution laws of the material model are integrated numerically using the implicit Euler scheme, resulting in the corresponding return mapping. The algorithmic tangent modulus for this material model is derived and validated by means of numerical differentiation using the complex variable approach. The constitutive parameters for the model are obtained by minimization of the difference between experimental and numerical curves, aiming at polymeric materials. Since non-uniqueness is expected for the minimization problem, the gradient free Particle Swarm Optimization method (PSO) is adopted for its solution. Finally, the results obtained and some particularities of the proposed model are discussed. / Este trabalho tem por objetivo desenvolver uma formulação numérica para a análise transiente de estruturas treliçadas tridimensionais considerando não linearidade geométrica e material. O problema de equilíbrio é apresentado através do Princípio das Potências Virtuais segundo uma formulação Lagrangeana Corrente. O campo de deslocamentos e velocidades é discretizado através do Método dos Elementos Finitos. As equações não lineares de equilíbrio são resolvidas pelo método de Newton-Raphson, sendo apresentado o desenvolvimento da matriz de rigidez tangente consistente. Posteriormente, o problema transiente é formulado, sendo as equações do movimento solucionadas pelo método de integração implícito de Newmark. O modelo constitutivo proposto é viscoelástico-viscoplástico acoplado com o modelo de dano de Lemaitre. A formulação viscoelástica é representada pelo modelo generalizado de Kelvin-Voigt e a contribuição viscoplástica é dada pela equação de Perzyna. As leis de evolução do modelo material são integradas numericamente através do algoritmo implícito de Euler, resultando no algoritmo de retorno. Para obter a taxa de convergência quadrática do método iterativo de Newton-Raphson durante o equilíbrio estrutural, é apresentado o cálculo analítico do módulo tangente algoritmo consistente, o qual é validado através do método da derivada complexa. Os parâmetros materiais são encontrados através do ajuste entre as curvas experimental e teórica, visando a aplicação para materiais poliméricos. Para o ajuste das curvas utilizou-se o método de Otimização por Nuvem de Partículas Particle Swarm Optimization (PSO). Ao final é realizada uma discussão dos resultados encontrados e comentado as particularidades do modelo proposto.

Dans les générateurs de vapeur des centrales nucléaires à eau pressurisée, les tuyauteries sont soumises à des chargements thermique et mécanique, qui sont variables et divisés en deux régimes différents : la fatigue oligocyclique et la fatigue gigacyclique. Les aciers au carbone – manganèse, type A42, A48 et Tu48 (normes françaises) sont souvent utilisés dans de telles applications. Les propriétés du matériau manifestent certains caractères spéciaux en mécanique et métallurgie comme le vieillissement dynamique conduisant à une augmentation de la valeur de la contrainte maximale et une diminution de la ductilité à la température 200 ℃. Le comportement en fatigue oligocyclique et gigacyclique sont étudiés à température ambiante et 200 ℃. Des essais de fatigue cumulée ont été mis en oeuvre pour étudier l’effet du cumul de dommage combinant des cycles de fatigue oligocyclique suivis de cycles en fatigue gigacyclique. Tous les résultats sont analysés en utilisant la mécanique de l’endommagement des milieux continus et l’analyse microfractographique. Les cycles d’hystérésis en fatigue oligocyclique sont dus à la déformation plastique de durcissement cinématique, ils peuvent être décrits par sous le modèle d’Armstrong – Frederick ; le durcissement isotrope est utile pour prédire l’évolution de l’amplitude de contrainte. Mais avec l’augmentation de la déformation plastique accumulée, le dommage ne peut être négligé. Le modèle de Chaboche d’endommagement par fatigue est utilisé pour décrire l’évolution des dommages oligocyclique et il est étendu au régime gigacyclique. Un modèle de fatigue cumulée des dommages a été développé à partir du modèle de Chaboche et appliqué à l’estimation des dommages de fatigue pour décrire le comportement de l’évolution de la contrainte en fonction du nombre de cycles. En fatigue oligocyclique à la température de 200 ℃, l’acier A48 est sensible au phénomène de vieillissement dynamique et il apparaît un durcissement secondaire, qui peut être prédit par la théorie des dislocations et est simulé dans la thése. L’analyse des surfaces de rupture est effectuée par fractographie au Microscope Electronique à Balayage pour les essais en oligocyclique, gigacyclique et cumul. En fatigue oligocylique, la fissure est initiée en surface. En fatigue gigacyclique, certaines fissures sont initiées sur des inclusions situées à l’intérieur d’éprouvettes. / In steam generators of nuclear power plants, typical pipes components are subjected to thermal and mechanical loading which are variable and divided into two different regimes: low cycle fatigue and gigacycle fatigue. Carbon-manganese steels A42, A48 and Tu48 steels (French standards) are often used in such applications. The material properties manifest some special characters in mechanics and metallurgy such as Dynamic Strain Aging, increasing UTS values in 200℃ temperature domain. The LCF and VHCF behaviors are investigated respectively by test method at room temperature and 200℃. The cumulative fatigue tests are implemented through referencing the load as prior LCF following gigacycle fatigue from the steam generator pipes thermal loads in order to obtain the performance of material under accumulated fatigue damage. All the test results are analyzed by using plastic mechanics, continuums damage mechanics and microscopic analysis. Hysteresis loops are due to plastic deformation in LCF which is the effect of kinematic hardening and they can be described by Armstrong – Frederick form models; the isotropy hardening is used to predict the evolution of stress amplitude in LCF. But with rising of accumulated plastic deformation, the damage can not be neglected. The Chaboche fatigue damage model is applied to describe the damage evolution of LCF and extended to VHCF regime. The cumulative fatigue damage model is extended from Chaboche model and applies to the estimation cumulative fatigue damage. The constitutive relationship and isotropy rule are coupled with fatigue damage model that can describe the whole fatigue behavior. In 200℃ for LCF, A48 is sensitive to dynamic strain aging and its secondary hardening behavior is important which can be predicted by dislocation theory and is simulated in the paper. The fractographic analysis is performed by SEM for LCF, VHCF and cumulative fatigue tests. The LCF crack is initiated in surface. Some of cracks of VHCF are given birth from the inclusions located at interior of sample.

Este trabalho apresenta um novo modelo numérico para simulação de juntas de argamassa em estruturas de alvenaria no plano via método dos elementos finitos. Neste modelo, blocos de alvenaria e juntas de argamassa são representados separadamente. Elementos finitos com alta razão de aspecto são utilizados para representar as juntas de argamassa e são inseridos na malha de elementos finitos através de uma técnica de fragmentação de malha. A principal vantagem desta técnica consiste na utilização de modelos constitutivos contínuos para representar regiões descontínuas, uma vez que seu campo de deformações quando a altura do elemento de interface tende a zero é semelhante ao apresentado pela abordagem de aproximação contínua de descontinuidades fortes. Um modelo constitutivo contínuo baseado na mecânica do dano foi desenvolvido para representar o comportamento dos elementos de interface. Este modelo consegue representar a abertura e fechamento de fraturas, bem como o efeito de atrito em função da tensão de confinamento nas interfaces. Como o objetivo deste trabalho consiste na simulação da formação e propagação de fraturas ao longo das juntas de argamassa, comportamento elástico linear foi atribuindo aos elementos triangulares de três nós utilizados na discretização dos blocos de alvenaria. Vários exemplos numéricos são apresentados. Inicialmente, testes básicos são realizados para demonstrar as principais características do modelo quando submetido a carregamentos de tração, compressão e cisalhamento. Posteriormente, estruturas de alvenaria submetidas a carregamentos estáticos são analisadas e os resultados comparados com as respostas experimentais a fim de validar o modelo proposto. A técnica proposta se mostrou bastante promissora para simulação da formação e propagação de fratura em juntas de argamassa de estruturas de alvenaria. / This work presents a novel numerical model to simulate the failure process in masonry structures subjected to static loads via finite element method. Brick and mortar joints are modeled separately with their own constitutive equations. Interface finite element with high aspect ratio are used to simulate the mortar interface and inserted by the mesh fragmentation technique. The main advantage of this strategy is supported by the fact that, as the aspect ratio of a standard low-order solid finite element increases, the element strains also increase, approaching the same kinematics as the Continuum Strong Discontinuity Approach. A constitutive model was developed, based on the continuum damage mechanics, in order to represent the behavior of the interface finite elements. This model is able to simulate the creation and propagation of cracks, as well as, the frictional effects in dependence on stress confinement on the interfaces. Furthermore, as the objective of this work aims to simulate the failure in the mortar joints, the brick elements are assumed as linear elastic material. Three node standard triangular finite element are used to represent the bricks. Several numerical models are carried out. Initially, basics tests are show in order to demonstrate the main characteristics of the proposed model subjected to tensile, compression and shear loads. Subsequently, masonry structures are subjected to static loads are analyzed and the results compared with the experimental responses in order to validate the proposed model. This technique proved to be very promising for the simulation of failure onset and propagation in mortar joints of masonry structures.

No presente trabalho desenvolve-se um modelo constitutivo baseado na mecânica do dano contínuo para representar o acúmulo da degradação do concreto produzido por cargas repetidas. O modelo de dano apresenta as condições necessárias exigidas na chamada aproximação de descontinuidades fortes proposta por Simó, Oliver e Armero e, conseqüentemente, pode ser empregado na formulação de elementos finitos com descontinuidade forte incorporada. Em decorrência de sua capacidade de descrever o comportamento do meio descontínuo independentemente da posição dos contornos do elemento finito, essa classe de formulação constitui uma alternativa valiosa para remediar a forte dependência da malha observada nos modelos de fissuras distribuídas, assim como para evitar as sofisticadas técnicas de reconstrução da malha exigidas nos modelos de fissura discreta, nos quais a fissura é introduzida na interface entre elementos. O trabalho traz contribuições no sentido de proporcionar uma ferramenta alternativa para a análise de propagação de fissuras por fadiga em elementos estruturais de concreto, dentro do contexto da mecânica do dano contínuo. Verifica-se a eficiência da formulação mediante análise numérica de problemas de fadiga em elementos estruturais de concreto. / A constitutive model based on the continuum damage mechanics is proposed to describe the accumulation of the degradation produced by repeated loads in concrete materials. The proposed damage model presents the necessary conditions required in the strong discontinuity approach advocated by Simó, Oliver and Armero and, consequently, it can be used in the embedded strong discontinuity finite element approach. This class of approach has been recognized by its capability to model discontinuities independently on the element boundaries. In fracture mechanics, the embedded strong discontinuity element has been proved to be a efficient alternative to remedy the strong mesh dependence verified in smeared crack approaches, as well as to avoid the sophisticated remeshing techniques required in the discrete crack approaches, in which the crack is introduced in the element interfaces. This work provides an alternative tool for the analysis of crack propagation in concrete structures under fatigue in the context of the continuum damage mechanics. Numerical analysis of concrete elements under fatigue are performed to access the effectiveness of the proposed approach.