In a Hilbert space setting homogenization of evolutionary equations is discussed. In order to do so, a suitable topology on material laws is introduced and several properties of that topology are shown. With those properties homogenization theorems of a large class of linear evolutionary problems of classical mathematical physics can be obtained. The results are exemplified by the equations of piezo-electro-magnetism.

Made available in DSpace on 2016-12-12T20:25:12Z (GMT). No. of bitstreams: 1 Maisa Damazio Franco.pdf: 2101632 bytes, checksum: 7f995c92c59dbfc8861058e76fa73036 (MD5) Previous issue date: 2014-12-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Due to problems such as osteoarthritis and fractures, it is observed an increasingly amount of prosthesis implant surgery, as for example, hip prosthesis. These implants must be made with biocompatible materials such as titanium, and must have mechanical properties close to the bone, which has characteristics of porous materials. The objective of this work is the design of optimum titanium microstructures, in order to minimize the difference between the tensor of elastic properties of the bone and of the prosthesis material. For this purpose, two well established tools are used: the topology optimization and the continuous homogenization method, by means of asymptotic expansion. The efficacy of the formulation is verified by designing different microstructures. / Devido aos problemas como osteoartrite e fraturas, cada vez mais tem se recorrido às cirurgias de implante de prótese, como por exemplo, os implantes de quadril. Estas próteses devem ser produzidas com materiais biocompatíveis, como por exemplo, o titânio, e devem possuir propriedades mecânicas próximas à do meio ósseo, que apresenta características de materiais porosos. O objetivo deste trabalho é o projeto otimizado de microestruturas de titânio, de modo a minimizar a diferença entre o tensor de propriedades elásticas do osso e do material da prótese. Para isso, são utilizadas duas ferramentas bem estabelecidas na literatura: a otimização topológica de meios contínuos e o método de homogeneização por expansão assintótica. A eficácia da formulação é verificada por meio do projeto de diferentes microestruturas.

L’influence des propriétés microscopiques de l’interphase entre la matrice et les fibres sur le comportement mécanique macroscopique n’est pas suffisamment connue dans le domaine des polymères renforcés par fibres courtes. Dans le cadre de cette thèse, une étude systématique des propriétés géométriques et mécaniques de l’interphase est réalisée concernant la description des effets sur la réponse viscoélastique linéaire du composite. Dans ce contexte, les résultats présentés mettent l’accent sur l’interaction entre la modélisation micromécanique et la caractérisation expérimentale. D’une part, un nouveau modèle micromécanique en deux étapes est développé pour la description d’un composite anisotrope à trois phases avec interphases. D’autre part, les paramètres du matériau utilisés pour la modélisation micromécanique sont identifiés avec des méthodes expérimentales aux échelles micro- et macroscopiques. En comparaison des résultats expérimentaux avec les propriétés effectives calculées de matériau composite, une inférence peut être faite sur les propriétés mécaniques du composite à partir de celles de l’interphase. Par conséquent, une méthode inverse est proposée offrant un accès aux propriétés inconnues de l’interphase. Enfin, la combinaison de la modélisation micromécanique et des résultats expérimentaux permet une meilleure compréhension des propriétés mécaniques de l’interphase, qui n’étaient auparavant pas accessibles au moyen de seules approches expérimentales / In order to improve the mechanical properties of short fiber composites, the fiber-matrix adhesion is decisive and depends strongly on the intersection region between the fiber and the matrix material. However, no perspicuous information about the influence or mechanical properties of the fiber-matrix interphase in short fiber reinforced thermoplastic composites is available. Thus, the present thesis aims for a systematic identification of the geometrical and mechanical impacts of an interphase on the linear-viscoelastic behavior in short glass fiber reinforced thermoplastics. Thereby, the performed investigations are focused on the interaction between micromechanical material modeling and experimental testing. On the one hand, a two-step modeling approach is developed for the realistic description of an entire three phase composite with interphase including anisotropic and linear-viscoelastic effects. On the other hand, the input of this model is provided by different experimental testing methods ranging from the micro- to the macroscale characterization of the composite and matrix material. By comparing these experimental results with the linear-viscoelastic modeling output, the impact of the interphase on the mechanical properties of the composite is accessible. Thus, it is shown that a realistic material modeling and experimental investigations are closely interlinked

Ce travail s’inscrit dans la thématique classique en mécanique de l’endommagement de milieux polycristallin. Il a pour but d’étudier et de modéliser le comportement thermique et mécanique d’un matériau énergétique. Ce matériau, dont le comportement en compression est quasi-fragile, présente en particulier un coefficient de dilatation thermique qui diminue lors de cycles de refroidissement-réchauffement.L’étude repose sur un modèle morphologique de type Johnson-Mehl avec grains non convexes et une méthode numérique à champ complet par transformée de Fourier rapide. La précision de ces méthodes en termes de réponse effective et de champs en pointe de fissure est étudiée par comparaison avec des éléments finis. Plusieurs types de microstructures sont ensuite étudiés de façon heuristique par ordre croissant de complexité.Le comportement élastique du polycristal non endommagé, calculé par méthode FFT, surestime celui observé expérimentalement. L’ajout de liant et de porosité dans le matériau n’expliquant pas le comportement mécanique expérimental, on étudie l’influence de différentes populations de fissures.Seule l’ajout de fissures intergranulaires permet de rendre compte du comportement effectif du matériau à l’état initial. La chute du coefficient de dilatation thermique est prédite par méthode FFT dans le cas de fissures dans le plan graphitique des monocristaux, dont l’existence est confirmée par des images MEB. / This work aims to study the thermal and mechanical behavior of an energetic polycrystal. This material displays a quasi-brittle behavior and its thermal dilation coefficient decreases when it undergoes cooling-heating cycles.The study relies on the use of a Johnson-Mehl tessellation model which has non-convex grains, and a full-field numerical method based on the Fourier transform. The accuracy of such methods concerning cracked media are determined by comparison with Finite Elements computations. The numerical tool is then used to investigate different microstructural assumptions, from the simplest to the most sophisticated.The first computation is that of an undammaged polycrystal, which overestimates the overall mechanical properties. The attempt to account for porosity and the presence of binder gives interesting results, but the latter are not enough to reproduce the experimental behavior.Finally, different types of microcracks are investigated and two major conclusions are drawn. First, in its initial state, the material contains intergranular cracks, that are uncorrelated to the local microstructure. Such cracks can lower the elastic moduli and leave the thermal properties unaffected. To obtain a decrease in terms of thermal dilation coefficient, one must consider families of cracks which are correlated to the local crystal orientation, especially along the weak plane of the crystal.

Le creuset est une structure majoritairement composée de matériaux réfractaires destinés à supporter de fortes sollicitations thermomécaniques, dues au contact direct de ses parois internes avec la fonte à 1500°C. L’objectif de cette thèse est de développer un modèle thermomécanique de creuset capable de localiser les zones sensibles de la structure et d’estimer les contraintes. Des blocs de carbone, des structures maçonnées (briques avec mortier) et un pisé carboné sont les principaux constituants du creuset. Afin d’identifier leur comportement, des essais de caractérisation ont été développés pour des températures atteignant les 1500°C. Un modèle de type Cam-Clay modifié est proposé pour modéliser le comportement compactant du pisé. L’influence de la température et des fortes pressions est prise en compte. Une bonne corrélation est obtenue entre les résultats expérimentaux et numériques. Les structures maçonnées, en contact direct avec la fonte, sont fortement sollicitées, ce qui peut conduire à l’ouverture des joints de mortier. La modélisation proposée pour ces structures est basée sur une approche micro-macro où les briques et le mortier sont remplacés par un matériau homogène équivalent, et ce pour différents états d’ouverture de joints. La non-linéarité du comportement est reproduite grâce à un critère d’ouverture en contrainte, qui permet le passage d’un état à un autre. Les propriétés homogénéisées sont obtenues par homogénéisation périodique en s’appuyant sur une approche énergétique. La modélisation d’un essai de la littérature permet la validation du modèle. La modélisation finale du creuset est confrontée aux résultats de l’instrumentation d’un creuset. Une bonne concordance entre ces résultats est obtenue. / The blast furnace hearth is mainly composed of refractory materials to support strong thermo-mechanical loads. Indeed, there is a direct contact between its internal walls and the molten pig iron at 1500°C. The objective of this thesis is to develop a thermo-mechanical model able to locate the sensitive areas and to estimate the stress fields. Carbon blocks, masonries (bricks and mortars) and a carbon ramming mix are the main constituents of the hearth. In order to identify their behaviours, characterization tests have been developed for temperatures up to 1500°C. A modified Cam-Clay model is proposed in order to reproduce the hardening behaviour of the ramming mix. The influences of temperature and pressure are taken into account. Experimental and numerical results are in good agreement. Masonries, submitted to high temperature gradients are highly stressed, which can lead to the opening of the mortar joints. The proposed masonry modelling is based on a micro-macro approach where bricks and mortars are replaced by an equivalent homogenous material for different joint states. The non-linearity of the behaviour is reproduced thanks to a stress criterion, allowing the transition from one state to another. Homogenized properties are obtained by periodic homogenization with an energetic approach. The modeling of a shear test available in the literature allows the validation of this model. The final modelling of a hearth is compared with in-situ instrumentation results. A good agreement is reached between these results.

No presente trabalho, é apresentado um modelo numérico para análise tridimensional de túneis escavados em maciços rochosos reforçados por tirantes aderidos ao longo de todo o seu comprimento. O método numérico utilizado é o método dos elementos finitos. A abordagem usada na modelagem da interação maciço/tirante é o método de homogeneização de meios periódicos. Essa abordagem substitui o meio compósito constituído de rocha e tirantes por um meio homogeneizado equivalente, dispensando a tarefa de discretizar cada tirante separadamente. O comportamento do maciço é considerado elastoplástico perfeito, caracterizado pelo critério de Drucker-Prager, com regra de fluxo associada. O revestimento é considerado elástico, enquanto os tirantes são tratados como inclusões lineares em tração/compressão com lei de comportamento elastoplástica. Com esse modelo foi implementado um código, tridimensional, que simula o processo de escavação pelo método da ativação/desativação de elementos. Esse código é capaz de levar em conta diferentes situações de profundidade, geometria e estado inicial de tensões. Com a finalidade de avaliar o desempenho da abordagem de homogeneização, foi implementado um segundo código, que modela a interação maciço/tirante por meio do método incorporado. Esse método, muito usado em análises de concreto armado, tem em comum com o método de homogeneização a capacidade de lidar com diferentes configurações de reforços utilizando a mesma malha base. Ao final, os dois códigos são utilizados em modelagens de um caso real, o túnel experimental Kielder (Inglaterra), para o qual se dispõe de dados medidos in situ. A comparação destes dados com os resultados das duas modelagens mostra uma aproximação muito boa. / A numerical model for three-dimensional analysis of tunnels excavated in reinforced rock mass by fully grouted bolts is presented in this work. The numeric method utilized is the finite element method and the approach used in the modeling of the interaction mass/bolt is the homogenization of periodic media method. This approach replaces the composite medium formed by rock and bolts by a homogenized equivalent medium eliminating the task of discretizing each bolt separately. The rockmass behavior is considered elastoplastic perfect caracterized by the Drucker-Prager criterion with associated flow rule. The lining is elastic, while the bolts are treated as linear inclusions in tension / compression with elastoplastic behavior law. A three-dimensional code was implemented with this model that simulates the excavation process by means of the activation-deactivation method. This code is able to consider different situations of depth, geometry and initial state of stress. In order to evaluate the performance of the homogenization approach, a second code was implemented to model the interaction rockmass/bolts by means of the embedded method. This method, widely used in analysis of reinforced concrete, has in common with the approach of the homogenization the capacity to deal with different configurations of reinforcements with the same base mesh. Finally, the two codes are used to model a real case, the Kielder experimental tunnel (England), for which in situ measured data are available. The comparison of these data with the results of the two modeling shows a very good approximation.

O concreto reforçado com fibras de aço (CRFA) é um material compósito formado por uma matriz cimentícia e por uma certa quantidade de fibras aleatoriamente dispersas. Buscou-se neste estudo “construir” um modelo constitutivo capaz de representar o comportamento do CRFA e cuja formulação está fundamentada na Teoria da Homogeneização, no Método dos Elementos Finitos (MEF), como também em observações experimentais disponíveis na literatura. Na primeira etapa do trabalho foram desenvolvidos estudos visando a análise do comportamento elástico e viscoelástico do CRFA. Inicialmente, o comportamento elástico linear foi investigado através da aplicação do esquema de homogeneização de Mori-Tanaka, o qual é baseado nos resultados estabelecidos por Eshelby (1957). A precisão dos resultados obtidos pela abordagem analítica foi verificada pela comparação com a solução via MEF, bem como com os resultados experimentais disponíveis. As estimativas micromecânicas das propriedades elásticas efetivas se mostraram coerentes àquelas obtidas através de análise numérica de um volume elementar representativo (VER) do material, modelado como um meio heterogêneo, como também, aos dados experimentais. Posteriormente, a formulação do comportamento viscoelástico sem envelhecimento foi obtida fazendo-se uso da resposta em elasticidade e do Princípio da Correspondência Elástica-Viscoelástica. Os resultados obtidos foram comparados aos dados experimentais e a modelos analíticos disponíveis. Na segunda etapa do trabalho, as propriedades de resistência do CRFA foram investigadas empregando-se a abordagem estática da análise limite combinada à teoria da homogeneização. O critério de resistência macroscópico para o CRFA foi teoricamente obtido a partir do conhecimento da resistência dos seus constituintes, ou seja, da matriz de concreto e das fibras. Adotando-se o critério de ruptura de Drucker-Prager para a matriz de concreto e considerando-se distribuição espacial isotrópica das fibras através de um modelo aproximado, um critério aproximado para a estimativa das propriedades de resistência homogeneizadas foi formulado. A formulação do critério foi complementada através da consideração de um critério de cut-off em tração e das propriedades limitadas de resistência da interface. Os resultados analíticos foram comparados a resultados experimentais e àqueles obtidos na resolução numérica do problema de análise limite formulado sobre o VER do CRFA, através de uma ferramenta numérica baseada no MEF no contexto da plasticidade. A comparação permitiu avaliar a influência da anisotropia do modelo aproximado empregado, como também da geometria real das fibras sobre a resistência do compósito. / Steel fiber reinforced concrete (SFRC) is a composite material formed by a cement matrix and a certain amount of randomly dispersed fibers. The main objective of the present work is the formulation of a comprehensive constitutive model for SFRC behavior that relies upon homogenization theory, finite element method (FEM) and taking advantage of experimental data available in the literature as well. The first part of the work is devoted to the assessment of elastic and viscoelastic behavior of SFRC. The study starts with the analysis of linear elastic behavior by implementation of a Mori-Tanaka homogenization scheme, which is based on the Eshelby equivalent inclusion approach. It was found that the micromechanical predictions for the overall stiffness proved to be considerably close to the experimental data, as well as to the finite element solutions obtained from numerical analysis of a representative elementary volume (REV) of SFRC (modeled as a randomly heterogeneous medium). Subsequently, the formulation of the nonaging viscoelastic behavior is carried out by making use of results from Elasticity and the Elastic-Viscoelastic Correspondence Principle. The results are compared to available experimental data and analytical models. The second part of the work focuses on the assessment of macroscopic strength properties of fiber reinforced concrete (FRC). Combining the static approach of limit analysis and the homogenization theory, the macroscopic strength criterion for SFRC was theoretically obtained from the knowledge of the strength properties of the individual constituents (concrete matrix and fibers). Adopting a Drucker-Prager failure condition for the concrete matrix and adopting a simplified geometrical model for fiber orientations and length, an approximate criterion was formulated for the overall strength properties. This formulation was complemented by considering a tensile cut-off condition for the concrete and limited strength properties for the interface. The analytical results were compared to experimental data and also to results obtained from a numeric resolution of the problem of limit analysis stated on the REV the material by means of a specifically devised Finite Element numerical tool in the plasticity context. The comparison allowed investigating the influence of the anisotropy of the employed approximate model, as well as the real fiber morphology on the composite strength properties.

Uma maneira de analisar a estabilidade de túneis escavados em maciços rochosos fraturados é a baseada na teoria da análise limite utilizando um critério de resistência macroscópico desenvolvido a partir da teoria de homogeneização. Este trabalho primeiramente descreve o comportamento mecânico dos constituintes do maciço rochoso fraturado e os métodos usuais de análise. Posteriormente é descrita a teoria da análise limite e da homogeneização em análise limite, utilizando estas teorias é apresentado o critério de resistência macroscópico para maciços rochosos fraturados em estado plano de deformações desenvolvido por Fréard (2000) e desenvolvido um critério de resistência macroscópico para maciços rochosos fraturados para o caso tridimensional. A partir destes critérios aplicaram-se mecanismos de ruptura para se encontrar limites superiores da função de estabilidade. Assim permitindo a análise da previsibilidade do colapso do túnel estação Pinheiros do metrô de São Paulo o qual os resultados apresentavam a possibilidade de prever o colapso. / One way of analyze the stability of tunnels excavated at fractured rock masses is based on the theory of yield design using a macroscopic strength criterion developed from the theory of homogenization. This dissertation first describes the mechanical behavior of the fractured rock mass constituents and the usual methods of analysis. Later is described the yield design theory and the theory of homogenization applied to the yield design using these theories is presented macroscopic strength criterion for fractured rock masses in a state plan developed by Fréard (2000) and developed a macroscopic strength criterion for rock masses fractured to the three-dimensional case. Based on these criteria were applied failure mechanisms to meet the upper bounding of the stability function. So it’s possible to analyze the predictability of the collapse of the tunnel-station Pinheiros of the Sao Paulo subway which the results showed the possibility of predicting the collapse.

Les méthodes d'homogénéisation numériques permettent de lever les limitations associées aux approches analytiques ou semi-analytiques pour prédire le comportement des matériaux hétérogènes dont les phases sont décrites par un comportement non linéaire, en particulier pour des morphologies de géométries complexes, ou des comportements dépendant de l'histoire, ou en grandes déformations. Dans ce travail, plusieurs contributions aux méthodes d'homogénéisation numériques pour traiter les problèmes non linéaires sont proposées. Dans une première partie, nous introduisons une méthode permettant de réaliser l'homogénéisation des matériaux dont les phases sont élastoplastiques parfaites. La technique est une extension de la méthode Non Uniform Transformation Field Analysis (NTFA) dans laquelle un algorithme de type prédiction-correction est introduit pour actualiser les variables internes. Dans une seconde partie, une méthode pour réaliser l'homogénéisation des composites non linéaires élastiques en petites et grandes déformations est proposée. Celle-ci se base sur la construction de potentiels associés au comportement effectif sous forme d'une base de données composée de valeurs discrètes interpolées à partir de valeurs discrètes obtenus par calculs éléments finis réalisés sur un Volume Élémentaire Représentatif (VER). Un schéma original d'interpolation est introduit, utilisant la notion de réseaux de neurones artificiels pour limiter le nombre de valeurs pré-calculées et choisir les points aléatoirement dans l'espace du chargement et des paramètres. Il est possible d'introduire des paramètres associés à la microstructure dans le comportement tels que la fraction volumique ou des paramètres de comportement des phases, en vue de possible optimisation de la réponse associée des structures non linéaires / Computational homogenization methods allow circumventing issues associated to analytical or semi-analytical approaches, for predicting the effective behavior of heterogeneous materials whose phase are described by a nonlinear behavior, more precisely when microstructures have complex morphologies or a history-depedendent behavior, or when considering finite strains. In this work, several contributions to computational homogenization methods for modeling nonlinear heterogeneous materials are proposed. In a first part, we introduce a method for homogenizing meterials whose phases are perfectly elastoplastic. The technique extends the Non Uniform Transformation Field Analysis (NTFA) method by développing a return-mapping algorithm to update macroscopic internal variables. In a second part, a method is introduced for the homogenization of nonlinear composites whose phases are nonlinearly elastic, at both small and finite strains. The approach is based on the construction of potentials associated to the effective behavior in the form of a database whose discrete values are computed through Finite Element Computations realized on a Representative Volume Element (RVE). An original interpolation scheme is introduced, which is based on artificial Neural Networks to reduce the number of computed values which can be distributed randomly in the parameter space. It is then possible to introduce parameters associated to the microstructure in the constitutive law, such as volume fraction or constitutive parameters of local phases, for optimization of the related non linear structure response

Alguns decênios atrás, o advento da nanotecnologia abriu perspectivas inovadoras permitindo alcançar novos alvos. Na área farmacêutica, as nanopartículas abriram alternativas ineditas de acesso para tratar órgãos e tecidos. Dentre as diversas nanopartículas existentes, este trabalho assentou sobre as nanopartículas lípidicas sólidas porque elas permitem a utilização de substâncias naturais, que representam um interesse cada vez maior devido às suas potencialidades diversificadas e comprovadas. Assim, foram escolhidos o óleo de copaíba e a alantoína devido às suas propriedades farmacológicas. Da mesma maneira que existem vários tipos de nanopartículas, existem várias técnicas para produzi-las. Neste estudo, o método por homogeneização à alta pressão foi selecionado devido às diversas vantagens. Para validar essas opções tecnológicas e caracterizar as nanopartículas, análises morfológicas, físico-químicas e térmicas foram realizadas. O segundo propósito desta pesquisa foi a avaliação do potencial antifúngico das nanopartículas contra fungos leveduriformes e filamentosos multirresistentes, devido às diversas propriedades microbiológicas do óleo de copaíba. Consequentemente, diversos ensaios micológicos foram feitos a fim de determinar onde e como essas nanopartículas agiram sobre esses fungos. Os resultados mostraram que a produção de nanopartículas lípidicas sólidas homogêneas e estáveis físico-quimicamente foi possível. Além disso, essas nanopartículas, compostas por substâncias naturais, demonstraram atividade antifúngica contra fungos multiresistentes, fato que não ocorreu com as matérias-primas isoladas. A nanotecnologia foi fundamental e levou a desenvolver suspensões antifúngicas. / Some decades ago, the advent of nanotechnology has opened new perspectives allowing reaching new targets. In the pharmaceutical area, nanoparticles have opened new ways for treating organs and tissues. Among the various existing nanoparticles, this work was based on solid lipid nanoparticles because they permitted the use of natural substances which represent a growing interest due to their diverse and proven strengths. So, copaiba oil and allantoin were chosen. Just as there are several types of nanoparticles, there are several techniques to produce them. In this study, the method of high pressure homogenization was selected because of several advantages. To validate these technological options and characterize nanoparticles, morphological, physico-chemical and thermal analysis were performed. The second purpose of this research was to evaluate the antifungal potential of nanoparticles against multiresistant yeasts and filamentous fungi due to various microbiological properties of copaiba oil. Consequently, many mycological tests were performed to determine where and how these nanoparticles acted on these fungi. The results showed the production of homogeneous and physico-chemically stable solid lipid nanoparticles is possible and, moreover, these nanoparticles produced with natural substances demonstrated their antifungal activity against multiresistant fungi, which did not happen with isolated raw materials. The nanotechnology was fundamental and led to develop antifungal suspensions.