[pt] A previsão da produção de poços tem um papel crucial na engenharia de petróleo. Logo, a modelagem do escoamento no reservatório e no poço é fundamental em diversos problemas nessa área. Na maioria esmagadora dos problemas, a equação de Darcy é a escolha para prever o comportamento do fluxo em rochas petrolíferas. O grande sucesso do uso da equação de Darcy, infelizmente, levou sua aplicação para fora do âmbito dos problemas para os quais esta se aplica. A equação clássica de Darcy apresenta limitações quando aplicadas em meios porosos altamente heterogêneos, por exemplo com cavidades conectadas por redes de fraturas, com vugs e cavernas. Ao longo dos anos, outras modelagens foram propostas e derivadas de outros pontos de vista para tratar o escoamento em meios porosos, por exemplo, através do processo de média de volume ou através de teoria de mistura. O presente trabalho utiliza as equações médias em meios porosos. O modelo desenvolvido contabiliza termos adicionais para a equação de quantidade de movimento linear que são relevantes em várias situações práticas, e envolve a solução conjunta das equações de conservação. No modelo desenvolvido neste trabalho, o escoamento no reservatório é resolvido de forma acoplada ao escoamento ao longo do poço, considerando a possibilidade de utilização de diferentes tipos de completação. As previsões dos campos de pressão e velocidade, assim como a produtividade de poços de petróleo utilizando o modelo desenvolvido são comparadas com as previsões do modelo baseado na equação de Darcy. Mostra-se que para determinadas situações, em especial em reservatórios carbonáticos, altamente heterogêneos, grandes diferenças podem ser obtidas. A previsão da produtividade de um poço a partir da equação de Darcy pode ser significativamente super-estimada. / [en] Predicting wellbore production plays a crucial role in petroleum engineering. Therefore, the modeling of the ow in reservoir and in wellbore is fundamental in several problems in this area. In the overwhelming majority problems, Darcy s equation is the choice to predict the behavior of ow in reservoirs. The great success of Darcy s equation, unfortunately, took its application out of the scope of the problems for which it applies. The classic Darcy s equation presents limitations when applied in highly heterogeneous porous media, for example with cavities connected by fracture networks, with vugs and caves. Over the years, other models have been proposed and derived from other points of view to treat ow in porous media, for example through the average volume process or through mixture theory. The present work considers the average volume process in porous media. The developed model includes additional terms for the linear momentum equation that are relevant in several practical situations, and involves the joint solution of conservation equations. In the model developed in this work, the ow in the reservoir is solved coupled to the wellbore ow, considering the possibility of using different completion types. The pressure and velocity fields predictions as well as the productivity of oil wellbores using the developed model are compared with the predictions of the model based on the Darcy s equation. It is shown that for certain situations, especially in highly heterogeneous carbonate reservoirs, large differences can be obtained. The prediction of the productivity of a wellbore from the Darcy s equation can be significantly overestimated.

This work presents a study on modeling error estimates in linear elastic structures of heterogeneous materials. The employed formulation is based on a theory of a posteriori estimation of modeling errors and uses the Finite Element Method as numerical tool. The evaluated modeling errors consist of global errors based on energy norm and local errors in quantities of interest induced by replacing the fine-scale micromechanical properties of the material by homogenized or effective properties. These effective properties are determined from different micromechanical models and considered in the surrogate physical models of the heterogeneous materials. The quantities of interest may be, for example, averaged stress or strain on chosen regions, such as surfaces of inclusions, and interfacial displacements. Several numerical examples involving structures of heterogeneous materials are analyzed and the results are presented to demonstrate the performance of the formulation in the evaluation of global and local modeling errors. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho apresenta um estudo sobre estimativas de erro de modelagem em estruturas elásticas lineares de materiais heterogêneos. A formulação empregada é baseada em uma teoria de avaliação de erro de modelagem à posteriori e utiliza o Método dos Elementos Finitos como ferramenta numérica. Os erros de modelagem avaliados consistem em erros globais, baseados em norma energia, e erros locais, em quantidades de interesse, induzidos pela substituição das propriedades micromecânicas do material em escala refinada por propriedades efetivas homogeneizadas. Estas propriedades efetivas são determinadas a partir de diferentes modelos da micromecânica e consideradas nos modelos físicos substitutos dos materiais heterogêneos. As quantidades de interesse podem ser, por exemplo, tensões médias ou deformações sobre a região escolhida, tais como superfície de inclusões e deslocamentos nas interfaces. Diversos exemplos numéricos envolvendo estruturas de materiais heterogêneos são analisados e os resultados são apresentados para demonstrar o desempenho da formulação na avaliação de erros de modelagem global e local.

The present work extends the Parametric Formulation of the Finite-Volume Theory to the case of heterogeneous materials with time-dependent behavior. Such a theory has already proved to be an efficient alternative to the Finite Element Method in the modeling of linear elastic heterogeneous materials. Firstly, general expressions for linear viscoelasticity are considered, determining deferred strains with a State Variables formulation. Expressions for the basic rheological models are given, extended to 3D situations and set in an adequate matrix form. Temperature dependence is modeled using the time-temperature equivalence principle. Then, the Parametric Formulation of the Finite-Volume Theory is reviewed and extended including the consideration of viscoelastic deformations. Detailed matrix expressions for the incremental solution of linear thermoviscoelastic problems are given. The numerical results are verified with several examples using analytical solutions found in the literature or determined by using the Correspondence Principle. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O presente trabalho tem por objetivo expandir a formulação numérica denominada Formulação Paramétrica da Teoria de Volumes Finitos para o caso de materiais com comportamento dependente do tempo. Tal teoria tem demonstrado ser uma eficiente alternativa ao Método dos Elementos Finitos para a modelagem de materiais heterogêneos elásticos lineares. Primeiramente, expressões gerais da viscoelasticidade linear são apresentadas, empregando-se uma formulação baseada em Variáveis de Estado para determinação das deformações dependentes do tempo. Expressões para os modelos reológicos básicos são dadas, estendidas para situações tridimensionais e estabelecidas em adequada forma matricial. A influência da temperatura sobre as propriedades viscoelásticas é modelada através de um princípio de equivalência tempo-temperatura. Em seguida, a Formulação Paramétrica da Teoria de Volumes Finitos é revisada e estendida para incluir a consideração de deformações viscoelásticas. Expressões detalhadas para a solução incremental de problemas termoviscoelásticos lineares são apresentadas. Os resultados numéricos são verificados através de vários exemplos usando soluções analíticas disponíveis na literatura ou determinadas pelo uso do Princípio da Correspondência.

L'objectif de cette thèse est d'étudier l'impact de la structure interne des matériaux isotropes granulaires sur leurs propriétés thermiques macroscopiques. Nous avons développé un code de calcul pour résoudre les transferts thermiques au sein d'un matériau hétérogène tridimensionnel. Ce code est couplé avec un algorithme de génération de structures aléatoires. Après validation expérimentale, nous avons généré des géométries granulaires dont nous avons caractérisé la structure interne, puis nous avons étudié l'impact de cette structure sur la conductivité thermique. Nous avons également développé une nouvelle méthode de mesure expérimentale de la capacité thermique surfacique d'un élément de paroi à structure interne complexe. L'originalité de cette méthode est le couplage d'un modèle analytique de la capacité thermique, indépendant des propriétés thermiques des constituants, et d'une étude expérimentale. / The objective of this thesis is to study the impact of the internal structure of isotropic granular materials on the macroscopic thermal properties. We have developed a model to solve the heat transfer problem within a heterogeneous three-dimensional material. This code is coupled with an algorithm generating random structure. After an experimental validation, we first generated granular materials and we characterized their internal structure; then we studied the impact of this structure on the thermal conductivity. We also developed a new experimental method for measuring the heat capacity area of a wall element with complex internal structure. The originality of this method is the coupling of an analytical model of heat capacity area, which is independent of the thermal properties of the constituents, and an experimental study.

Diversos materiais de interesse tecnológico podem ser considerados como materiais heterogêneos, onde sua natureza aleatória deve ser considerada para representar corretamente o comportamento não-linear. A avaliação quantitativa do dano em materiais sujeitos a estados de tensão ou deformação tem grande importância devido ao caráter crítico desse fenômeno, que pode crescer de forma abrupta e resultar em uma falha catastrófica da estrutura. Em estudos anteriores, Carpinteri e seus colaboradores apresentaram diferentes aspectos relacionados à caracterização do dano em materiais heterogêneos. Três desses aspectos são discutidos neste trabalho: (i) a proposta do número de fragilidade como medida da fragilidade da estrutura em análise; (ii) a evolução da dimensão fractal em que o processo de dano é desenvolvido; (iii) e os índices globais obtidos pela análise de Emissão Acústica (EA). Neste trabalho, uma versão do método dos elementos discretos formado por barras é utilizada para explorar esses aspectos. Espécimes de material quase-frágil são simulados e, quando possível, os resultados numéricos são comparados com resultados experimentais. Além disso, a discussão dos resultados obtidos é realizada visando compreender o comportamento desse tipo de material, como por exemplo, o fato de que estruturas com diferentes dimensões, porém com o mesmo número de fragilidade, têm comportamentos similares. Ademais, o método numérico empregado é apresentado como uma ferramenta viável para complementar a informação obtida em ensaios experimentais na avaliação do processo de dano. Pelo sinal de EA obtido através do método numérico empregado, obtiveram-se parâmetros para a classificação do tipo de falha e para o cálculo do tensor momento, onde comparando os resultados obtidos pelo modelo numérico e pela EA se observam comportamentos coerentes. / Several materials with technological interest can be considered as heterogeneous materials, where their random nature must be accounted to correctly represent the nonlinear behavior. The quantitative evaluation of damage in materials subjected to stress or strain states have great importance due to the critical nature of this phenomenon, which abruptly can rise to catastrophic failure. In previous studies, Carpinteri and his coworkers have presented different aspects of the damage process characterization in heterogeneous materials. Three of these aspects are discussed in this work: (i) the brittleness number proposal to measure the brittleness level of the analyzed structure, (ii) the relationship of the fractal dimension in which the damage process is developed, (iii) and the global indexes obtained by the Acoustic Emission (AE) analysis. In the present work, a version of discrete element method formed by bars is used to explore these concepts. A set of quasi-brittle material specimen is simulated and, when possible, the numerical results are compared with experimental ones. Moreover, a discussion of the obtained results is carried out aiming to understand the behavior of this kind of material, for instance, the fact that structures with different dimensions, but with the same brittleness number, have similar behavior. In addition, the numerical method is presented as a viable tool to complement information from experimental test on the damage process. From the AE signal obtained by the numerical method, parameters to classify the type of crack and for calculating the moment tensor were obtained, where consistent behaviors are observed by comparing the results of the numerical model and the AE.

Diversos materiais de interesse tecnológico podem ser considerados como materiais heterogêneos, onde sua natureza aleatória deve ser considerada para representar corretamente o comportamento não-linear. A avaliação quantitativa do dano em materiais sujeitos a estados de tensão ou deformação tem grande importância devido ao caráter crítico desse fenômeno, que pode crescer de forma abrupta e resultar em uma falha catastrófica da estrutura. Em estudos anteriores, Carpinteri e seus colaboradores apresentaram diferentes aspectos relacionados à caracterização do dano em materiais heterogêneos. Três desses aspectos são discutidos neste trabalho: (i) a proposta do número de fragilidade como medida da fragilidade da estrutura em análise; (ii) a evolução da dimensão fractal em que o processo de dano é desenvolvido; (iii) e os índices globais obtidos pela análise de Emissão Acústica (EA). Neste trabalho, uma versão do método dos elementos discretos formado por barras é utilizada para explorar esses aspectos. Espécimes de material quase-frágil são simulados e, quando possível, os resultados numéricos são comparados com resultados experimentais. Além disso, a discussão dos resultados obtidos é realizada visando compreender o comportamento desse tipo de material, como por exemplo, o fato de que estruturas com diferentes dimensões, porém com o mesmo número de fragilidade, têm comportamentos similares. Ademais, o método numérico empregado é apresentado como uma ferramenta viável para complementar a informação obtida em ensaios experimentais na avaliação do processo de dano. Pelo sinal de EA obtido através do método numérico empregado, obtiveram-se parâmetros para a classificação do tipo de falha e para o cálculo do tensor momento, onde comparando os resultados obtidos pelo modelo numérico e pela EA se observam comportamentos coerentes. / Several materials with technological interest can be considered as heterogeneous materials, where their random nature must be accounted to correctly represent the nonlinear behavior. The quantitative evaluation of damage in materials subjected to stress or strain states have great importance due to the critical nature of this phenomenon, which abruptly can rise to catastrophic failure. In previous studies, Carpinteri and his coworkers have presented different aspects of the damage process characterization in heterogeneous materials. Three of these aspects are discussed in this work: (i) the brittleness number proposal to measure the brittleness level of the analyzed structure, (ii) the relationship of the fractal dimension in which the damage process is developed, (iii) and the global indexes obtained by the Acoustic Emission (AE) analysis. In the present work, a version of discrete element method formed by bars is used to explore these concepts. A set of quasi-brittle material specimen is simulated and, when possible, the numerical results are compared with experimental ones. Moreover, a discussion of the obtained results is carried out aiming to understand the behavior of this kind of material, for instance, the fact that structures with different dimensions, but with the same brittleness number, have similar behavior. In addition, the numerical method is presented as a viable tool to complement information from experimental test on the damage process. From the AE signal obtained by the numerical method, parameters to classify the type of crack and for calculating the moment tensor were obtained, where consistent behaviors are observed by comparing the results of the numerical model and the AE.

La prévision du comportement mécanique macroscopique de matériaux hétérogènes à partir des propriétés de leurs constituants est possible pour diverses classes de comportement (élastique, viscoélastique, etc) et ce, grâce à la théorie de l'homogénéisation. Néanmoins l'extension de cette théorie pour des matériaux possédant un comportement viscoélastique non linéaire (ou élasto-viscoplastique) reste une question ouverte à laquelle nous nous attaquons dans ce travail afin de prédire le comportement macroscopique des combustibles oxydes mixtes uranium-plutonium (MOX) utilisés dans les réacteurs nucléaires à eau sous pression (REP) français. Dans cette optique des solutions analytiques et purement nunériques ont été obtenues et le modèle retenu est utilisé pour simuler le comportement des combustibles / The prediction of the macroscopic mechanical behavior of heterogeneous materials from the properties of their constituents is possible for various classes of behavior (elastic, viscoelastic, etc.) thanks to the theory of homogenization. Nevertheless, the extension of this theory for materials with a non-linear (or elasto-viscoplastic) viscoelastic behavior remains an open question that we are tackling in this work in order to predict the macroscopic behavior of uranium-plutonium (MOX) mixed oxide fuels used in french pressurized water reactors (PWRs). From this perspective analytical and purely numerical solutions have been obtained and the model adopted is used to simulate the behavior of fuels.

[pt] Esta dissertação teve como objetivo verificar se grandes acionistas – blockholders, não pertencentes ao bloco de controle, em um cenário de baixa proteção ao investidor e alta concentração de capital, como o brasileiro, atuam como um mecanismo de governança corporativa, reduzindo os custos de agência devido ao monitoramento dos gestores/controladores. A base de dados compreendeu as empresas não financeiras de capital aberto no Brasil, pelo período de 2010 até 2019, totalizando 1.091 empresas-ano. Foi utilizada regressão por efeitos fixos para dados em painel, e, como análise de robustez, o Propensity Score Matching, tendo como resultado um impacto negativo no Q de Tobin para as empresas que possuem blockholder em sua estrutura. Tal resultado apesar de divergir da literatura internacional, encontra eco em outros trabalhos realizados no cenário brasileiro, e justifica-se pela alta concentração acionária das empresas, pois blockholders não representariam ameaça real aos controladores, que geralmente possui mais que 50 por cento do capital votante, pela baixa qualidade das leis de proteção aos investidores e a fatores culturais, que incentivam a passividade dos acionistas brasileiros. A existência de blockholders neste cenário demonstra uma diluição do capital acionário e do fluxo de caixa que aumenta os incentivos que os gestores/controladores possuem para expropriar a empresa. Com relação a heterogeneidade dos blockholders, verificou-se que empresas com blockholders do tipo familiar apresentam Q de Tobin inferior aos demais tipos. Este resultado é explicado pois os blockholders do tipo familiar teriam maior propensão a formação de alianças com o controlador para expropirar valor dos demais acionistas minoritários. / [en] This dissertation aimed to verify whether large shareholders - blockholders, not belonging to the control block, in a scenario of low investor protection and high concentration of capital, such as the Brazilian, act as a corporate governance mechanism, reducing agency costs due to the monitoring of managers / controllers. The database comprised non-financial publicly traded companies in Brazil, from 2010 to 2019, totaling 1,091 company-years. Fixed effects regression was used for panel data, and, as a robustness analysis, the Propensity Score Matching, resulting in a negative impact on Tobin s Q for companies that have blockholders in their structure. This result, despite diverging from the international literature, is echoed in other works carried out in the Brazilian scenario, and is justified by the high shareholding concentration of the companies, as blockholders would not represent a real threat to controller s, which generally has more than 50 percent voting capital, due to the low quality of investor protection laws and cultural factors, which encourage the passivity of Brazilian shareholders. The existence of blockholders in this scenario demonstrates a dilution of share capital and cash flow that increases the incentives that managers / controllers have to expropriate the company. Regarding the heterogeneity of the blockholders, it was found that companies with family-type blockholders have Tobin s Q lower than the other types. This result is explained by the fact that family-type blockholders would be more likely to form alliances with the controlling shareholder to expropriate other minority shareholders.

This study focuses on developing explicit analytical and numerical process models for mechanical micro-machining of heterogeneous materials. These models are used to select suitable process parameters for preparing and micro-machining of these advanced materials. The material system studied in this research is Magnesium Metal Matrix Composites (Mg-MMCs) reinforced with nano-sized and micro-sized silicon carbide (SiC) particles. This research is motivated by increasing demands of miniaturized components with high mechanical performance in various industries. Mg-MMCs become one of the best candidates due to its light weight, high strength, and high creep/wear resistance. However, the improved strength and abrasive nature of the reinforcements bring great challenges for the subsequent micro-machining process. Systematic experimental investigations on the machinability of Mg-MMCs reinforced with SiC nano-particles have been conducted. The nanocomposites containing 5 Vol.%, 10 Vol.% and 15 Vol.% reinforcements, as well as pure magnesium, are studied by using the Design of Experiment (DOE) method. Cutting forces, surface morphology and surface roughness are characterized to understand the machinability of the four materials. Based on response surface methodology (RSM) design, experimental models and related contour plots have been developed to build a connection between different materials properties and cutting parameters. Those models can be used to predict the cutting force, the surface roughness, and then optimize the machining process. An analytical cutting force model has been developed to predict cutting forces of MgMMCs reinforced with nano-sized SiC particles in the micro-milling process. This model is iv different from previous ones by encompassing the behaviors of reinforcement nanoparticles in three cutting scenarios, i.e., shearing, ploughing and elastic recovery. By using the enhanced yield strength in the cutting force model, three major strengthening factors are incorporated, including load-bearing effect, enhanced dislocation density strengthening effect and Orowan strengthening effect. In this way, the particle size and volume fraction, as significant factors affecting the cutting forces, are explicitly considered. In order to validate the model, various cutting conditions using different size end mills (100 µm and 1 mm dia.) have been conducted on Mg-MMCs with volume fraction from 0 (pure magnesium) to 15 Vol.%. The simulated cutting forces show a good agreement with the experimental data. The proposed model can predict the major force amplitude variations and force profile changes as functions of the nanoparticles’ volume fraction. Next, a systematic evaluation of six ductile fracture models has been conducted to identify the most suitable fracture criterion for micro-scale cutting simulations. The evaluated fracture models include constant fracture strain, Johnson-Cook, Johnson-Cook coupling criterion, Wilkins, modified Cockcroft-Latham, and Bao-Wierzbicki fracture criterion. By means of a user material subroutine (VUMAT), these fracture models are implemented into a Finite Element (FE) orthogonal cutting model in ABAQUS/Explicit platform. The local parameters (stress, strain, fracture factor, velocity fields) and global variables (chip morphology, cutting forces, temperature, shear angle, and machined surface integrity) are evaluated. Results indicate that by coupling with the damage evolution, the capability of Johnson-Cook and Bao-Wierzbicki can be further extended to predict accurate chip morphology. Bao-Wierzbiki-based coupling model provides the best simulation results in this study. v The micro-cutting performance of MMCs materials has also been studied by using FE modeling method. A 2-D FE micro-cutting model has been constructed. Firstly, homogenized material properties are employed to evaluate the effect of particles’ volume fraction. Secondly, micro-structures of the two-phase material are modeled in FE cutting models. The effects of the existing micro-sized and nano-sized ceramic particles on micro-cutting performance are carefully evaluated in two case studies. Results show that by using the homogenized material properties based on Johnson-Cook plasticity and fracture model with damage evolution, the micro-cutting performance of nano-reinforced Mg-MMCs can be predicted. Crack generation for SiC particle reinforced MMCs is different from their homogeneous counterparts; the effect of micro-sized particles is different from the one of nano-sized particles. In summary, through this research, a better understanding of the unique cutting mechanism for particle reinforced heterogeneous materials has been obtained. The effect of reinforcements on micro-cutting performance is obtained, which will help material engineers tailor suitable material properties for special mechanical design, associated manufacturing method and application needs. Moreover, the proposed analytical and numerical models provide a guideline to optimize process parameters for preparing and micro-machining of heterogeneous MMCs materials. This will eventually facilitate the automation of MMCs’ machining process and realize high-efficiency, high-quality, and low-cost manufacturing of composite materials.

Le développement de méthodes d’identification de paramètres de lois de comportement de matériaux est devenu primordial pour avoir accès à la connaissance complète du comportement. En effet, les méthodes de mesure optiques, comme la Corrélation d’Images Numériques, permettent d’obtenir les quantités cinématiques de la relation de comportement sous forme de champs de vecteurs. En revanche, les contraintes ne sont généralement pas mesurables et il est nécessaire d’identifier les paramètres de la loi de comportement du matériau considéré pour y avoir accès. Plusieurs méthodes ont vu le jour et permettent de répondre à cette problématique mais la plupart d’entre elles supposent une homogénéité du matériau. Ce mémoire traite de l’application de certaines de ces méthodes, notamment la méthode de l’écart à l’équilibre (MEQ) et la méthode de recalage de modèle éléments finis (MREF), dans des matériaux hétérogènes à microstructure complexe où les propriétés mécaniques évoluent spatialement dans le volume. L’objectif est d’identifier ces propriétés mécaniques locales qui régissent la cinématique mesurée de tels matériaux dans le cadre de l’élasticité linéaire isotrope. Dans un premier temps, les deux méthodes citées sont décrites, implémentées et comparées sur des cas simulés en 2D. La MREF est préférée à la MEQ car plus robuste vis-à-vis des incertitudes de mesure. Basée sur un formalisme itératif, une parallélisation de l’algorithme a été opérée pour diminuer le coût en temps de la méthode. Des expérimentations dans le plan sur des éprouvettes en polyuréthane où les hétérogénéités sont maîtrisées ont permis de valider la méthode. Enfin, deux applications en 3D sur un matériau en mousse polyuréthane et un composite à base de fibres de bois démontrent l’intérêt d’une telle méthode pour l’identification de propriétés mécaniques locales. La mise en évidence d’une relation entre les propriétés locales identifiées et les propriétés locales de la microstructure de ces matériaux est effectuée. / The development of identification methods of material constitutive equation parameters has become fundamental to completely know the mechanical behavior. Indeed, optical methods, such as Digital Image Correlation, allows to get kinematics quantities of the constitutive equation as vectors fields. But, stresses are usually not available experimentally and one has to identify constitutive equation parameters to compute them. Several methods have been developed and answer to that problematic but most of them suppose the materials as homogeneous. This memoir is about the application of some of these methods, such as the equilibrium gap method (EGM) and the finite element model updating method (FEMU), in the case of heterogeneous materials with complex structures where mechanical properties vary spatially in the volume. The objective is to identify these local mechanical properties which rule the measured kinematics of such materials considering the isotropic linear elasticity. Firstly, both methods are detailed, implemented and compared on 2D simulated cases. The FEMU method is preferred because it is more robust in the presence of noisy data. Based on an iterative process, a parallelisation of the algorithm is achieved in order to reduce the cost of the method. In-plane experiments on polyurethane samples where heterogeneities are controlled have validated the method. Finally, two 3D applications on a polyurethane foam material and a wood-based fibrous composite have demonstrated the interest of this approach to identify local mechanical properties. The highlighting of a relationship between identified local properties and microstructural properties of these materials is made.