For over forty years, researchers have attempted to refine the Fourier heat equation to model heat transfer in engineering materials. The equation cannot accurately predict temperatures in some applications, such as during transients in microscale (< 10^-12 s) situations. However, even in situations where the time duration is relatively large, the Fourier heat equation might fail to predict observed non-Fourier behavior. Therefore, non-Fourier models must be created for certain engineering applications, in which accurate temperature modeling is necessary for design purposes. In this thesis, we use the Fourier heat equation to create a general non-Fourier, but diffusive, equation that governs the matrix temperature in a composite material. The composite is composed of a matrix with embedded particles. We let the composite materials be governed by Fourier's law and let the heat transfer between the matrix and particles be governed by contact conductance. After we make certain assumptions, we derive a general integro-differential equation governing the matrix temperature. We then non-dimensionalize the general equation and show that our model reduces to that used by other researchers under a special limit of a non-dimensional parameter. We formulate an initial-boundary-value problem in order to study the behavior of the general matrix temperature equation. We show that the thermalization time governs the transition of the general equation from its small-time limit to its large-time limit, which are both Fourier heat equations. We also conclude that our general model cannot accurately describe temperature changes in an experimental sand composite. / Master of Science

In this thesis, we propose some innovative developments for the implementation of mean-field homogenization schemes adapted to the prediction of the behavior of elasto-plastic and elasto-viscoplastic composites. For elasto-plastic materials, the local constitutive laws written in a rate form are linearized incrementally over several time-steps so that homogenization schemes developed in the context of linear elasticity can apply over each time interval. Since the original implementation gave too stiff predictions, we propose different stiffness reductions for the matrix tangent operator and study theoretically and numerically the influence on the final macroscopic prediction. Definition of the per phase reference state in also studied and linked to the fields heterogeneity effect. Predictions thus obtained are confronted with those of a secant (or total) formulation of the constitutive laws. For elasto-viscoplastic composites, we use the affine formulation which reduces the constitutive laws to fictitious linear thermo-elastic relations in the Laplace domain where the homogenization can apply. Our main contribution is a full treatment of internal variables in the linearization procedure. This enables to deal with realistic constitutive behaviors and general loading histories. We illustrate the influence of viscous effects under various loading conditions and study the accuracy of the method with respect to the loading rate. For both classes of composites, numerous predictions obtained by mean-field homogenization schemes are confronted against those of three-dimensional finite element simulations and experimental results. For a wide range of materials and loading conditions, a good agreement at the macroscopic level between our predictions and the reference results is observed.

The application of heterogeneous materials has become common in modern product design such as composites and porous media. Computational design tools for such materials, with higher complexity than the traditional homogeneous ones, will be a critical component in the realization of the heterogeneity systematically. It is foreseen that computer-aided design (CAD) systems will include computer-aided materials design modules in future so that the design of functional materials and structures can be integrated for optimal product design. The traditional CAD systems model three-dimensional (3D) geometry at macro-scales with boundary representation (B-Rep), whereas computer-aided materials design is concerned with the specification of material composition at scales ranging from nano-, meso-, to micro-. Thus, multi-scale CAD systems are desirable for the integration of product and materials information. The existing B-Rep based modeling scheme needs to be extended to incorporate heterogeneous material compositions. The new modeling scheme should also support seamless zoom-in and zoom-out operations in multi-scale CAD systems. Recently, a multi-scale model, dual-Rep, was proposed to represent geometry and material property distribution implicitly. The core part of dual-Rep is a new basis function called surfacelet. Surfacelet is able to represent boundary information more efficiently than the traditional wavelets, while keeping a unified form with wavelets so that the role exchange of boundary and internal structures during zooming operations is enabled. A surfacelet transform is able to represent microstructure distributions in 3D images with surfacelet coefficients. In this dissertation, three enabling techniques for surfacelet-based heterogeneous materials modeling are developed. First, a method of inverse surfacelet transform is developed such that the original images can be reconstructed from the surfacelet coefficients. The surface integrals of voxel (i.e., volumetric pixel) values are obtained from the surfacelet coefficients using the one-dimensional inverse wavelet transform. The images are then reconstructed by solving linear equations from discretized surface integrals. The prior knowledge of material properties and distributions is applied to solve the under-constrained problems. Second, composite surfacelets with the combinations of different types of primitive surfacelets are created to increase the flexibility of the surfacelet transform with potentially fewer surfacelets and improved reconstruction accuracy. Third, a multi-scale materials modeling method is proposed to support interactive design and visualization of material microstructures at multiple levels of details. It has the capability to support seamless zoom-in and zoom-out. This method provides a feature-based design approach based on the surfacelet basis.

Les applications tribologiques des matériaux cellulaires en présence de liquide nécessitent une connaissance de leurs modes d’endommagement, mais elles restent peu connues à l’heure actuelle. L’étude, la compréhension et la modélisation du comportement d’un matériau composite cellulaire nécessitent une approche pluridisciplinaire due au caractère hétérogène du matériau qui reste difficilement caractérisable. Ce matériau peut être analysé suivant 3 axes bien distincts : les propriétés rhéologiques (analyses sous état de déformation complexe en compression et en cisaillement avec des rhéomètres adaptés), la morphologie des alvéoles (analyses 3D optiques et tomographiques), les propriétés tribologiques (analyse en frottement de l'interface et des particules d'usure). L’intérêt majeur de notre approche est d'aborder simultanément ces 3 axes et de comprendre leurs interactions respectives. La tomographie aux rayons X, suivie d’un traitement mathématique assisté par ordinateur, complété par l'analyse des particules d'usure a permis d'identifier les morphologies responsables des fonctions spécifiques du matériau cellulaire. Un tribo-abrasimètre innovant avec des surfaces abrasives modèles a mis en évidence l’importance des cinématiques dans l’endommagement du matériau. Des méthodes de caractérisation ont été mises au point afin de quantifier la dégradation tribologique du matériau permettant également de mesurer l’impact du vieillissement (chimique, thermique et mécanique). / Tribological applications of cellular materials in the presence of liquid require acknowledge of their modes of damage, but they remain little known at present. The study, understanding and modeling the behavior of a composite cell requires a multidisciplinary approach due to the heterogeneity of the material that is difficult to characterize. This material can be analyzed along three distinct axes: the rheological properties (analysis in complex state of deformation in compression and shear with adapted rheometer), the morphology of the cells (3D optical tomographic analysis), the tribological properties (analysis in interface friction and wear particles). The major advantage of our approach is to simultaneously address these three areas and to understand their interactions. The X-ray tomography, followed by computer-assisted mathematical treatment, supplemented by the analysis of wear particles identified morphologies responsible for specific functions of cellular material. A tribo-abrasimeter with innovative models abrasive surfaces highlighted the importance of kinematics in the damage of the material. Characterization methods have been developed to quantify the tribological degradation of the material can also measure the impact of aging(chemical, thermal and mechanical).

[pt] O objetivo da pesquisa é investigar a proposta de ciclos no contexto da prática em relação ao atendimento à eterogeneidade referente ao desempenho dos alunos. Utilizou- se como referencial Ball e Bowe (ciclos de política) e autores nacionais que têm pesquisado a escola em ciclos no Brasil como Sá Barreto, Gomes, Mainardes e outros. Investigou-se o cotidiano de uma escola do Município de Casimiro de Abreu no Estado do Rio de Janeiro considerada referência. A análise baseou-se em observação da sala de aula de um professor, entrevistas semi- estruturadas e documentos. A prática investigada aponta possibilidades de atendimento efetivo da heterogeneidade na escola em ciclos. Os dados revelaram a importância do planejamento de atividades diferenciadas, do agrupamento de alunos baseado em diferentes níveis, das estratégias didáticas com ênfase em arte e música, da avaliação diagnóstica e do apoio pedagógico. / [en] The objective of this research is to investigate the cycles proposal, into the context of practice, regarding the heterogeneity that refered to the performance of the students. As theoretical references, Ball and Bowe (the policy cycle approach) were used and also national authors, who have researched the cycles` school in Brazil, such as Sá Barreto, Gomes, and Mainardes, among others. We investigated the day life of a school in the city of Casimiro de Abreu, State of Rio de Janeiro, considered a reference school. The analysis was based on the observation of a teacher in class, interviews and documents. The researched practice showed possibilities of effective attending to the heterogeneity of the students in the cycles` school. Data revealed the importance of planning different activities, grouping students based on different levels, using didactic strategies with emphasis in art and music, using diagnostic evaluation and pedagogical support.

Les propriétés effectives mécaniques et physiques des matériaux hétérogènes dépendent d'une part de leurs constituants, mais peuvent également être fortement modifiées par leur répartition géométrique à l'échelle de la microstructure. L'optimisation topologique a pour but de définir la répartition optimale de matière dans une structure en vue de maximiser un ou plusieurs objectifs tels que les propriétés mécaniques sous des contraintes telles que la masse de matière. Récemment, les développements rapides de l'impression 3D ou d'autres techniques de fabrication additive ont rendu possible la fabrication de matériaux avec des microstructures "à la demande", ouvrant de nouvelles perspectives inédites pour la conception de matériaux. Dans ce contexte, les objectifs de cette thèse sont de développer des outils de modélisation et de simulation numériques pour concevoir des matériaux et des structures hétérogènes ayant des propriétés optimisées basés sur l'optimisation topologique. Plus précisément, nous nous intéressons aux points suivants. Premièrement, nous proposons des contributions à l'optimisation topologique à une seule échelle. Nous présentons tout d'abord une nouvelle méthode d'optimisation topologique avec évolution pour la conception de structures continues par description lisse de bords. Nous introduisons également deux techniques d'homogénéisation topologique pour la conception de microstructures possédant des propriétés effectives extrêmes et des « méta propriétés » (coefficient de Poisson négatif).Dans une seconde partie, des techniques multi échelle basées sur l'optimisation topologique sont développées. Nous proposons d'une part une approche concourante de structures hétérogènes dont les microstructures peuvent posséder plus de deux matériaux. Nous développons ensuite une approche d'optimisation topologique dans un cadre d'homogénéisation pour des échelles faiblement séparées, induisant des effets de gradient. Enfin dans une troisième partie, nous développons l'optimisation topologique pour maximiser la résistance à la fracture de structures ou de matériaux hétérogènes. La méthode de champs de phase pour la fracture est combinée à la méthode BESO pour concevoir des microstructures permettant d'augmenter fortement la résistance à la rupture. La technique prend en compte l'initiation, la propagation et la rupture complète de la structure / Mechanical and physical properties of complex heterogeneous materials are determined on one hand by the composition of their constituents, but can on the other hand be drastically modified by their microstructural geometrical shape. Topology optimization aims at defining the optimal structural or material geometry with regards to specific objectives under mechanical constraints like equilibrium and boundary conditions. Recently, the development of 3D printing techniques and other additive manufacturing processes have made possible to manufacture directly the designed materials from a numerical file, opening routes for totally new designs. The main objectives of this thesis are to develop modeling and numerical tools to design new materials using topology optimization. More specifically, the following aspects are investigated. First, topology optimization in mono-scale structures is developed. We primarily present a new evolutionary topology optimization method for design of continuum structures with smoothed boundary representation and high robustness. In addition, we propose two topology optimization frameworks in design of material microstructures for extreme effective elastic modulus or negative Poisson's ratio. Next, multiscale topology optimization of heterogeneous materials is investigated. We firstly present a concurrent topological design framework of 2D and 3D macroscopic structures and the underlying three or more phases material microstructures. Then, multiscale topology optimization procedures are conducted not only for heterogeneous materials but also for mesoscopic structures in the context of non-separated scales. A filter-based nonlocal homogenization framework is adopted to take into account strain gradient. Finally, we investigate the use of topology optimization in the context of fracture resistance of heterogeneous structures and materials. We propose a first attempt for the extension of the phase field method to viscoelastic materials. In addition, Phase field methods for fracture able to take into account initiation, propagation and interactions of complex both matrix and interfacial micro cracks networks are adopted to optimally design the microstructures to improve the fracture resistance

abstract: A new critical plane-energy model is proposed in this thesis for multiaxial fatigue life prediction of homogeneous and heterogeneous materials. Brief review of existing methods, especially on the critical plane-based and energy-based methods, are given first. Special focus is on one critical plane approach which has been shown to work for both brittle and ductile metals. The key idea is to automatically change the critical plane orientation with respect to different materials and stress states. One potential drawback of the developed model is that it needs an empirical calibration parameter for non-proportional multiaxial loadings since only the strain terms are used and the out-of-phase hardening cannot be considered. The energy-based model using the critical plane concept is proposed with help of the Mroz-Garud hardening rule to explicitly include the effect of non-proportional hardening under fatigue cyclic loadings. Thus, the empirical calibration for non-proportional loading is not needed since the out-of-phase hardening is naturally included in the stress calculation. The model predictions are compared with experimental data from open literature and it is shown the proposed model can work for both proportional and non-proportional loadings without the empirical calibration. Next, the model is extended for the fatigue analysis of heterogeneous materials integrating with finite element method. Fatigue crack initiation of representative volume of heterogeneous materials is analyzed using the developed critical plane-energy model and special focus is on the microstructure effect on the multiaxial fatigue life predictions. Several conclusions and future work is drawn based on the proposed study. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2016

Les propriétés du béton constituant les enceintes de confinement des centrales électronucléaires évoluent sous les effets de mécanismes de vieillissement résultant notamment de transferts couplés de chaleur et de masse au sein du matériau. Ces phénomènes peuvent être modélisés par des équations de transports moyennées : lois de Fick pour le transport d’espèces en solution et lois de Fourier pour la description de la diffusion thermique. Dans cette étude, les développements concernent la diffusion de la thermique dans un milieu hétérogène fissuré représentant un matériau cimentaire dégradé chimiquement. Le problème thermo-mécanique est traité à l'aide d'une approche multi-corps reliés par des lois d’interactions enrichies (zones cohésives). La diffusion thermique est écrite dans le formalisme cohésif-volumique en prenant en compte le couplage entre un état d'endommagement local de la zone cohésive et une conductivité homogénéisée. Afin d'optimiser les coûts de calculs, une étude est menée sur la dimension d'un volume élémentaire représentatif (VER). Pour cela, la méthode d'eigenerosion est étendue à la fissuration de milieux hétérogènes puis appliquée aux milieux cimentaires. La propagation de fissures sous chargement thermique est ensuite analysée dans des VERs de béton dégradés représentatifs des enceintes de confinement des centrales nucléaires après plusieurs années. Le vieillissement est modélisé par un taux de pré-dégradation initial entre le mortier et les granulats. Le développement de multi-fissures est relié au taux de pré-dégradation et la formation "d'écrans" à la diffusion de la thermique est mise en avant. / During their confinement in a nuclear power plant, the mechanical properties of the constitutive materials of concrete change as a result of ageing. This is due to the transportation of chemical species at the microscopic level of the media. Firstly, this can be modelled with average equations. The Fick laws represent the evolution of chemical diffusion and the Fourier laws, the transportation of heat at a mesoscopic level. In this research, we will consider thermal evolution on a fractured media.This thermomechanical problem is solved with a staggered method. The mechanical contribution used an approach based on multi-bodies system linked with cohesive zone models. The thermal problem is based on the approximation of the heat transfer equation at the cohesive interface. This approach has been implemented and validated. The description of the heat trough the interface is composed with the definition of an homogenised conductivity and the local damage parameter. In order to optimize the computational cost with a good agreement of the crack propagation, a criterion is proposed for sizing a representative elementary volume (REV). The eigenerosion method is used, validated and extended to heterogeneous media. Two studies are carried out on the morphological properties on a cementious media. As a result of those studies, a minimal size for a REV is defined.Crack spread under thermal loads are investigated on a media representing the concrete of the containment of a nuclear power station. The ageing effect are taken into account as an initial damage between the mortar and the aggregates. These parameters are expressed in terms of rate of initial damage. A study is proposed for different values of this rate. As assumed, the development of multi-cracks is linked with the rate of initial damage and the creation of thermal border is proposed.

[pt] Este trabalho estuda o impacto das tranferências condicionais de renda do Bolsa Família sobre a quantidade de empregados formais no nível do município. Encontramos um efeito altamente heterogêneo no nível municipal. Trabalhos anteriores sobre o tema consideraram apenas o efeito médio do programa. Mostramos evidências de que o efeito do programa pode chegar a cinco vezes seu valor médio em municípios com menos renda, o que corresponde a um aumento em 1 porcento de empregados formais para um aumento em 10 porcento na quantidade de beneficiários. Para tal, combinamos dados administrativos de participação no programa com dados sobre o universo de empregos formais. Isso nos permite evitar a questão do erro de medida na variável de tratamento. Testes de robustez indicam que o efeito permanece significante após controlarmos por variáveis associadas à saúde, educação, choques climáticos e fatores financeiros e políticos. / [en] In this paper we study the impact of Bolsa Família s CCTs on the number of formal jobs at the municipality level. We find a highly heterogeneous effect across municipalities. Previous works on this topic considered only the effect on the average municipality. We show evidence that the program s effect can be five times higher on the poorest municipalities, corresponding to 1 percent increase in formal jobs for a 10 percent increase in the number of beneficiaries. To accomplish so, we combine administrative data on the program enrollment with data on the universe of formal jobs. This allows us to overcome the problem of measurement error in the treatment variable. Robustness checks indicate that the effect remains significant after controlling for health, educational, climatic shocks, financial and political factors.

La diffusion de l’hydrogène dans les métaux est un paramètre clef pour la compréhension des mécanismes de base de la fragilisation par l’hydrogène. Néanmoins, le rôle des joints de grains dans le processus de diffusion de cet élément reste à éclaircir. Avec une approche numérique, nous avons étudié les effets d’un réseau hétérogène de joints de grains sur la diffusivité macroscopique de l’hydrogène. Pour cela, des essais de perméation ont été simulés par la méthode des éléments finis, en modélisant le matériau comme un composite formé d’une phase intra-associée aux grains et deux phases intergranulaires, avec des propriétés de diffusion différentes. Nous avons montré, en caractérisant la topologie et la connectivité du réseau des joints de grains, qu’il existe des fortes corrélations entre les paramètres de connectivité et le coefficient de diffusion effectif. Il a été démontré également que ces corrélations sont plus importantes dans les matériaux nanocristallins. De plus, en utilisant une approche d’homogénéisation, il a été mis en évidence que le coefficient de diffusion effectif est contrôlé par le caractère percolant du réseau des joints de grains, sans pour autant avoir le même seuil de percolation que ces derniers. Une seconde étude, utilisant des microstructures de nickel obtenues par cartographies EBSD, a permis d’évaluer l’écart entre la connectivité des modèles simplifiés et les structures réelles. Cette étude a permis également de confronter les coefficients de diffusion effectifs obtenus par la simulation à des données de la littérature. En parallèle, une étude expérimentale a été conduite sur le nickel pour analyser l’influence des joints de grains sur la distribution locale de l’hydrogène. Les résultats ont montré des corrélations importantes entre la nature du joint de grains et le profil de concentration de l’hydrogène autour de ce joint, qui ne peuvent pas être expliquées uniquement par le processus de diffusion. / The diffusion of hydrogen in metals is a key factor for understanding the basic mechanisms of hydrogen embrittlement. However, the contribution of grain boundaries to the hydrogen diffusion is not well established. In this this work, we first investigated the effects of a heterogeneous grain boundary networks on the effective diffusivity in polycrystalline materials, using finite elements modeling. To do so, hydrogen diffusion through heterogeneous materials, modeled by a ternary continuum composite media, was simulated. We showed, by characterizing the grain-boundary connectivity, that there are strong correlations between the grain-boundary connectivity parameters and the effective diffusivity. It was found also that these correlations are more significant for nanocrystalline materials. Moreover, by using a homogenization method, it was evidenced that the percolation behavior of the effective diffusivity is controlled by the grain-boundary network evolution, without exhibiting the same percolation threshold than the latter. A second approach, using EBSD-based microstructures, was conducted to evaluate the effect of microstructural constraints on the grain boundary connectivity and to compare the effective diffusivity numerically obtained with experimental data on polycrystalline nickel from literature. In parallel, experimental analyses were performed to analyze the effects of the grain boundaries on the local hydrogen concentration. This highlighted the significant impact of grain-boundary character on the hydrogen distribution around grain boundaries, which can not be explained by the only diffusion process.