Ce travail consiste à développer un logiciel métier basé sur la modélisation thermomécanique linéaire de l'échangeur tout en intégrant les techniques d'homogénéisation. Une méthodologie de modélisation de l'échangeur constitué par un empilement de différentes ondes et tôles brasées, est donc adoptée. Cette méthodologie suppose que le comportement global de chaque couche d'ondes et tôles, est encadré par deux comportements limites déterminés par des approches mécanique périodique (HMP) et cinématique périodique (HCP). Ces deux approches sont mises en œuvre pour l’application numérique tout en étudiant le chargement interne global dû à la température et à la pression. Un outil d'homogénéisation (HomPass) est ensuite développé afin de déterminer automatiquement les comportements équivalents à chaque onde et tôle brasées. Cela contribue au développement de l'outil métier final (SiTEME) dédié à l'étude thermomécanique globale de l'échangeur. / This work consists of developing a software tool based on the linear thermomechanical modeling of the heat exchanger using homogenization techniques. A methodology for modeling the heat exchanger constituted by stacking of different brazed fins and sheets is adopted. This methodology assumes that the global behavior of every layer of fins and sheets is found between two behavior limits determined by periodic mechanical approach (HMP) and periodic kinematical approach (HCP). These techniques are implemented for numerical application while studying global loading due to the temperature and pressure internal loads. A homogenization tool (HomPass) is then developed in order to calculate automatically equivalent behaviors to each layer of brazed fins and sheets. That contributes to the development of the final software tool (SiTEME) dedicated to the global thermomechanical study of the heat exchanger.

Les composites élastomères sont actuellement utilisés dans de nombreuses applications commerciales et ont montré de grandes promesses pour l'utilisation dans les nouvelles technologies. Cela soulève la pratique, ainsi que théorique nécessaire pour comprendre le lien entre la microstructure sous-jacente de composites en élastomère et de leurs propriétés mécaniques et physiques, et comment celui-ci peut être améliorée avec des changements dans l'ancienne. Dans ce contexte, l'objectif principal de cette thèse est le développement d'une analyse, le cadre homogénéisation non linéaire pour déterminer la réponse globale des composites élastomères soumis à des déformations finies. Les comptes-cadre pour l'évolution de la microstructure sous-jacente, ce qui entraîne des changements dans la géométrie finie induite par la charge appliquée. Ce point est essentiel que l'évolution de la microstructure peut avoir un assouplissement significatif géométrique (ou raidissage) effet sur la réponse globale du matériau, qui, à son tour, peut conduire à l'élaboration éventuelle d'instabilités macroscopiques. Le concept principal derrière la méthode d'homogénéisation non linéaire proposé est la construction de principes variationnels appropriés en utilisant l'idée d'un "portail composite linéaire», qui a finalement permettre la conversion des estimations disponibles homogénéisation linéaire dans les estimations analytiques pour la grande déformation de réponse global de l' non linéaire des composites en élastomère. Cette thèse comprend des applications de la théorie proposée pour les différentes classes des élastomères renforcés et poreux aléatoire et des microstructures périodiques. Une analyse complète du comportement efficace, l'évolution de la microstructure et le développement d'instabilités macroscopiques est prévu pour toutes ces applications.

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

We use Darcy's law and conservation of mass to model the flow of a fluid through a porous medium. It is a second order elliptic system with a heterogeneous coefficient. We consider the equations written in mixed form. In the heterogeneous case, we define a new multiscale mortar space that incorporates purely local information from homogenization theory to better approximate the solution along the interfaces with just a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient of period epsilon, we prove that the new method achieves both optimal order error estimates in the discretization parameters and good approximation when epsilon is small. Moreover, we present numerical examples to assess its performance when the coefficient is not obviously locally periodic. We show that the new mortar method works well, and better than polynomial mortar spaces. On the other hand, we also propose to use multiscale mortars as a coarse component to construct a two-level preconditioner for the saddle point linear system arising from the fine scale discretization of the mixed finite element system. The two-level preconditioners are constructed based on the interfaces. We propose a framework to define the interpolation operators for the face based two-level preconditioners for different combination of coarse and fine scale mortar spaces for matching and nonmatching grids. In this dissertation, we show that for quasi-homogeneous problems and matching grids, the condition number of the preconditioned interface operator is bounded by (log(H/h))², which is the same as the traditional two-level preconditioners, for quasi-homogeneous problems. We show several numerical examples to demonstrate that for the strongly heterogeneous porous media, it is often desirable and even necessary to use a higher dimensional coarse mortar space to construct the coarse preconditioner to achieve convergence. We apply our ideas to study slightly compressible single phase and two-phase flow in a porous medium. We find that for the nonlinear single phase problem, the two-level preconditioners could be successfully applied to the symmetrized linear system. For the two-phase problem, using the fine scale, instead of multiscale, velocity solutions from the flow problem can greatly benefit the transport problem. / text

In this thesis we investigate numerical methods for the homogenization of materials the structures of which, at fine scales, are characterized by random heterogenities. Under appropriate hypotheses, the effective properties of such materials are given by closed formulas. However, in practice the computation of these properties is a difficult task because it involves solving partial differential equations with stochastic coefficients that are additionally posed on the whole space. In this work, we address this difficulty in two different ways. The standard discretization techniques lead to random approximate effective properties. In Part I, we aim at reducing their variance, using a well-known variance reduction technique that has already been used successfully in other domains. The works of Part II focus on the case when the material can be seen as a small random perturbation of a periodic material. We then show both numerically and theoretically that, in this case, computing the effective properties is much less costly than in the general case

La théorie d'homogénéisation élastodynamique des matériaux hétérogènes initiée par J.R. Willis il y a environ une trentaine d'années a récemment reçu une très grande attention. D'après cette théorie qui est mathématiquement exacte, la loi constitutive homogénéisée est non locale en espace et en temps ; le tenseur des contraintes dépend non seulement du tenseur des déformations mais aussi de la vitesse ; la quantité du mouvement dépend à la fois de la vitesse et du tenseur des déformations, faisant apparaître en général une masse anisotrope. Ces propriétés constitutives effectives, qui pourraient être surprenantes d'un point de vue mécanique classique, se révèlent en fait très utiles pour la conception de métamatériaux acoustiques et de capes acoustiques. Ce travail de thèse consiste essentiellement à proposer et développer deux méthodes numériques efficaces pour déterminer les propriétés élastodynamiques effectives des matériaux périodiquement hétérogènes. La première méthode relève de la méthode des éléments finis alors que la deuxième méthode est basée sur la transformée de Fourier rapide. Ces deux méthodes sont d'abord élaborées pour une microstructure périodique 3D quelconque et ensuite implantées pour une microstructure périodique 2D quelconque. Les avantages et les inconvénients de chacune de ces deux méthodes sont comparés et discutés. A l'aide des méthodes numériques élaborées, la théorie de Willis est appliquée au calcul élastodynamique sur un milieu infini hétérogène et celui homogénéisé. Les différents cas d'homogénéisabilité et de non-homogénéisabilité sont discutés / The elastodynamic homogenization theory of heterogeneous materials initiated by J.R. Willis about thirty years ago has recently received considerable attention. According to this theory which is mathematically exact, the homogenized constitutive law is non-local in space and time; the stress tensor depends not only on the strain tensor but also on the velocity; the linear momentum depends on both the velocity and the strain tensor, making appear an anisotropic mass tensor in general. These effective constitutive properties, which may be surprising from a classical mechanical point of view, turn out in fact to be very useful for the design of acoustic metamaterials and acoustic cloaks. The present work is essentially to propose and develop two efficient numerical methods for determining the effective elastodynamic properties of periodically heterogeneous materials. The first method belongs to the finite element method while the second method is based on the fast Fourier transform. These two methods are first developed for any 3D periodic microstructure and then implanted for any 2D periodic microstructure. The advantages and disadvantages of each of these two methods are compared and discussed. Using the elaborated numerical methods, the Willis theory is applied to the elastodynamic computation over the infinite heterogeneous medium and the homogenized one. The various cases of homogeneisability and non-homogeneisability are discussed

Ce travail est dédié au calcul des propriétés de transfert thermique et de transport dans les milieux hétérogènes périodiques. Les résultats sont établis dans le cadre d'homogénéisation périodique pour lequel les propriétés macroscopiques sont obtenues par la résolution de problèmes élémentaires pour la cellule irréductible. Plusieurs contributions sont ainsi apportées, visant à établir de nouvelles estimations par des approches analytiques ou en développant des méthodes numériques adaptées. Ainsi dans une première partie, on s'intéresse à la modélisation des propriétés non linéaires de filtration dans les milieux poreux. A l'échelle microscopique l'écoulement est régi par l'équation de Navier-Stokes. En développant la solution en série, on obtient par homogénéisation, une loi de filtration polynomiale. Tous les coefficients constitutifs de cette loi sont alors obtenus en résolvant en cascade des problèmes élémentaires sur la cellule à l'aide de schémas itératifs utilisant sur la transformée de Fourier rapide. On propose ensuite de nouvelles expressions analytiques pour les propriétés de conductivité thermique de composites périodiques renforcés par des inclusions sphériques. On résout l'équation intégrale de Lippmann-Schwinger par des développements en série de Neumann et en choisissant une polarisation constante dans les inclusions. Des expressions analytiques sont alors obtenues pour diverses configurations spatiales : réseaux cubiques et répartitions aléatoires isotropes. Dans la dernière partie de ce travail, on détermine les propriétés de transfert thermique par conduction et convection dans les milieux poreux saturés par un fluide. A nouveau, on propose des schémas de résolution basés sur la transformée de Fourier rapide pour le calcul du tenseur de diffusivité de milieux poreux / In this work, we determine the macroscopic properties of thermal transfer and mass transport in periodic heterogeneous materials. All the results are established in the framework of periodic homogenization, for which, the macroscopic properties are deduced by solving elementary problems for the irreducible cell. Various contributions are provided, leading to the derivation of new closed-form expressions for the effective properties or by developing numerical tools. In the first part, we determine the nonlinear filtration properties of porous media. At the microscopic scale, the fluid flow obeys to the Navier-Stokes equation. By expanding the solution into power series, we obtain, after homogenization, a polynomial type macroscopic filtration law. All the constitutive coefficients of are determined by solving a hierarchy of cell problems by means of a numerical approach based on the Fast Fourier Transform algorithm. The problem of conductivity of periodic composites reinforced by spherical inclusions is thereafter considered by an analytic approach. We solve the Lippmann-Schwinger integral equation using Neumann series and a constant polarization in the inclusion. Closed-form estimate of the macroscopic conductivity are then obtain for different spatial configurations: cubic lattice and isotropic distribution of inclusions. In the last part, we determine the thermal transfer properties by conduction and convection of porous media fulfilled by a viscous fluid. Again, numerical tools based on FFT are considered to solve the unit cell problems and to compute the diffusivity tensor

In the present work, the Parametric Finite-Volume Theory is expanded by using the inclusion of homogenization processes on mechanical and thermal properties of periodically elastic and viscoelastic composites, with interphase effects. This work introduces models for evaluation of thermal conductivity, coefficient of thermal expansion, elastic and viscoelastic constitutive tensors with unit cell concept applied and periodical boundary conditions in state of generalized plane strain. The current interphase model between inclusion and matrix are considered thin and replaced by equivalent imperfect interfaces. The materials of the interphase are admitted to have lower thermal and mechanical properties. The formulation of the thermal and mechanic homogenization models is based on the traditional strategy of temperature and displacement field expansion in macroscopic and fluctuating components. The effective coefficients of thermal expansion are analytically evaluated using the effective elastic properties and coefficient of thermal expansion of the constitutive phases. Procedures on viscoelastic homogenization are based on Generalized Maxwell model, which allows the assessment of the effective relaxation tensors, providing the effective creep tensors using the Correspondence Principle. The viscoelastic model applied is incremental in time and uses the internal variables formulation. The created models are applied on the solution of many case studies, involving different kinds of composite materials (including size-dependent effects), volume fraction, unit cell geometry and interphase properties influence on the behavior of effective mechanical and thermal properties. The results are compared to analytical and FEM solutions to calculate the method’s efficiency. / No presente trabalho, a versão paramétrica da teoria dos volumes finitos (TVF) é expandida pela incorporação de processos de homogeneização de propriedades térmicas e mecânicas de compósitos periódicos elásticos e viscoelásticos, incluindo efeitos de interfase. O trabalho apresenta modelos para avaliação de condutividade térmica, coeficiente de dilatação térmica, tensores constitutivos elástico e viscoelástico efetivos, considerando o conceito de célula unitária, com condição de contorno periódica em estado plano de deformações generalizado. As interfases existentes entre as inclusões e a matriz são consideradas finas e substituídas por interfaces imperfeitas equivalentes. Os materiais que constituem tais interfases são admitidos com propriedades térmicas e mecânicas inferiores àquelas dos outros constituintes. Os modelos de homogeneização térmica e mecânica são formulados com base na tradicional estratégia de expansão dos campos de temperatura e deslocamentos, respectivamente, em parcelas macroscópica e flutuante. Os coeficientes de dilatação térmica efetivos são avaliados analiticamente em função das propriedades efetivas elásticas e dos coeficientes de dilatação térmica das fases constituintes. Os procedimentos de homogeneização viscoelástico tem como base o modelo de Maxwell generalizado e permitem a determinação dos tensores de relaxação efetivos, a partir dos quais são obtidos os tensores de fluência efetivos através do Princípio da Correspondência. O modelo viscoelástico utilizado é do tipo incremental e utiliza o conceito de variáveis internas. Por fim, os modelos são aplicados na solução de exemplos envolvendo diferentes tipos de materiais compósitos, os quais incluem investigação de efeitos de tamanho, fração volumétrica, geometria da célula unitária, influência das propriedades da interfase sobre as propriedades efetivas térmicas e mecânicas. Os resultados de tais exemplos são comparados com soluções analíticas e com o método dos elementos finitos, demonstrando desempenho dos modelos apresentados.

As invasões biológicas são consideradas a segunda maior causa de perda de biodiversidade, pois podem causar diversos impactos ecológicos. Recentemente foi chamado à atenção um novo mecanismo pelo qual espécies invasoras podem afetar as nativas: através da interferência no nicho acústico. O mascaramento dos sinais a partir de fontes de ruídos pode afetar diretamente a fisiologia reprodutiva ou o consumo de energia. A vocalização está diretamente ligada com a seleção sexual em anfíbios, aves, insetos e muitos mamíferos, de maneira que a presença de novas fontes sonoras no ambiente pode afetar a aptidão das espécies. Uma das piores invasoras do mundo, a rã-touro Lithobates catesbeianus, nativa dos EUA, Canadá e México, está distribuída em mais de 40 países, e em pelo menos 130 municípios brasileiros. A rã-touro possui uma vocalização de amplo espectro de frequências, diferente do que é encontrado nas espécies nativas brasileiras. Seus cantos têm frequência dominante baixa, grande propagação e pouca degradação e atenuação no ambiente. A presença do canto da espécie pode causar alteração nos parâmetros dos cantos de uma espécie nativa da Mata Atlântica brasileira. Entretanto, não é sabido se outras espécies também podem ser afetadas e se a introdução da rã-touro é capaz de afetar o comportamento acústico das comunidades nativas. Neste estudo, nós avaliamos os efeitos da invasão de L. catesbeianus sobre o nicho acústico das espécies nativas, usando duas perspectivas, no nível de indivíduos e de comunidades. No Capítulo I nós avaliamos se o estímulo acústico da rã-touro pode alterar parâmetros temporais e espectrais dos cantos de espécies nativas com e sem sobreposição espectral com a espécie invasora. Nós testamos a hipótese de que espécies com sobreposição de frequências com a invasora apresentam mudanças maiores nos parâmetros de vocalização do que espécies que estejam fora desse espectro. Para isso realizamos um experimento em campo, introduzindo a vocalização da espécie em área onde não existe registro da sua ocorrência. Nós utilizamos mais dois estímulos, um ruído branco e uma vocalização de uma espécie nativa, Rhinella icterica. Todas as espécies testadas foram expostas aos três estímulos, onde comparamos com a sua atividade de vocalização espontânea. Nossos resultados mostram efeito de todos os tipos de ruídos nos cantos, mas todas as espécies responderam com mudanças maiores nos parâmetros para os dois anuros do que para o ruído. É provável que esse resultado esteja relacionado ao fato de que ambas as espécies de anuros utilizados nos experimentos tenham a frequência dominante baixa. Entretanto, os resultados reforçam que a introdução de novos sons no ambiente tem potencial de modificar os cantos. No Capítulo II, nós testamos se existe diferença na diversidade funcional acústica em ambientes com e sem a presença de L. catesbeianus em áreas invadidas da Mata Atlântica no sul do Brasil. Nós testamos a hipótese de que poças com a presença dos machos de rã-touro em atividade de vocalização e poças sem a presença dos mesmos apresentam distintos padrões de diversidade funcional acústica e composição funcional acústica mais homogênea. Para isso, nós utilizamos dados coletados em 15 pares de poças invadidas e não invadidas na Mata Atlântica no sul do Brasil e realizamos análises de diversidade e composição funcional utilizando atributos acústicos. Nossos resultados mostram que a composição funcional foi mais homogênea nas poças invadidas do que nas poças não invadidas. Nessas poças, há uma seleção de frequências, onde predominantemente as espécies com frequências dominantes mais altas vocalizam. Ou seja, as espécies que não possuem sobreposição de frequência dominante com a rã-touro. Este estudo é um dos primeiros a testar efeitos da invasão do nicho acústico sobre as comunidades nativas. Ambientes nativos podem ser vulneráveis à introdução de espécies generalistas que produzem sinais de baixa frequência e grande amplitude. Assim, a eficiência de propagação dos sinais confere à rã-touro vantagem adaptativa na comunicação e reprodução, favorecendo o processo de estabelecimento e dispersão em detrimento das espécies nativas. / Biological Invasions are considered the second leading cause of biodiversity loss, because they may cause many ecological impacts. Recently, was called attention to a new mechanism by which invasive species can affect native species: through interference in the acoustic niche. The masking of signals from noise sources can directly affect reproductive physiology or energy consumption. Vocalization is directly connected with the sexual selection in amphibians, birds, insects, and many mammals, so that the presence of new sound sources in the environment can affect the fitness of the species. One of the worst invasive species of the world, the bullfrog Lithobates catesbeianus, native from USA, Canada and Mexico, is distributed in over 40 countries around the world and, at least, 130 Brazilian municipalities. The bullfrog has a wide spectrum of frequencies vocalization, different from what is founded in Brazilian native species. Their calls have low dominant frequency, large propagation and little degradation and attenuation in the environment. The presence of the species’ call can cause changes in the parameters of the native species’ calls from Brazilian Atlantic Forest. However, it is not known if other species may also be affected and the introduction of bullfrogs can affect the acoustic behavior of the native communities. In this study, we evaluated the effects of L. catesbeianus invasion on the acoustic niche of native species, using two perspectives at the level of individuals and communities. In Chapter I we evaluate how the acoustic stimulus of bullfrogs can change temporal and spectral parameters of the native species’ calls with and without spectral overlap with invasive species. We tested the hypothesis that species with overlapping frequencies with the invading show greater change in vocalization parameters than species outside this spectrum. To make this we conducted a field experiment, introducing the vocalization of the invasion species in an area where there is no record of their occurrence. We used two stimuli, a white noise and calling of a native species, Rhinella icterica. All species tested were exposed to the three stimuli, which compared with its spontaneous vocalization activity. Our results show the effect of all kinds of noise at the calls, but all the species responded with large changes in the parameters for the two frogs than for noise. It is probable that this result is related to the fact that both species of frogs used in the experiments have low dominant frequency. However, the results reinforce the introduction of new sounds in the environment has the potential to modify the native calls. In Chapter II, we tested if exist differences in the acoustic functional diversity in environment with and without the presence of L. catesbeianus in invaded areas of the Atlantic Forest in southern Brazil. We tested the hypothesis that the ponds with presence of bullfrog males in vocalization activity and ponds without their presence have distinct patterns of acoustic functional diversity and acoustic functional composition more homogeneous. For this, we used data collected from 15 pairs of ponds invaded and not invaded by bullfrog in the Atlantic Forest in southern Brazil and realized analysis of diversity and functional composition using acoustic traits. Our results show that the functional composition was more homogeneous in ponds invaded than in ponds not invaded. In these ponds, there is a selection of frequencies, where predominantly the species that vocalize at highest frequencies are calling, that don´t have dominant frequency overlap with the bullfrog. This study is one of the first to test effects of acoustic niche invasion on native communities. Native environments may be vulnerable to the introduction of generalist species that produces low frequency and large amplitude signals. Therefore, signal propagation efficiency gives the bullfrog adaptive advantage in communication and reproduction, favoring the process of establishment and dispersion at the expense of native species.

Un modèle micromécanique est proposé pour une collection de zones cohésives insérées entre toutes les mailles d'une discrétisation de type éléments finis cohésifs-volumiques. Le principe de l'approche consiste à introduire un composite équivalent 'matrice-inclusions' comme une représentation de la discrétisation cohésive-volumique. Le modèle obtenu à l'aide de techniques d'homogénéisation (schéma de Hashin Shtrikman et approche de P. Ponte Castañeda) permet de décrire le comportement macroscopique élastique, fragile et ductile.Il est valable quel que soit le taux de triaxialité appliqué et la forme de la loi cohésive retenue, et permet de relier d'une façon explicite les propriétés macroscopiques du matériau aux différents paramètres cohésifs ainsi qu'à la densité de maillage.Un premier résultat est l'établissement d'un critère pratique permettant de définir les raideurs cohésives au regard de la souplesse additionnelle inhérente à l'utilisation des modèles de zones cohésives intrinsèques. L'extension du modèle au cas de la rupture fragile et ductile, permet d'obtenir d'autres critères pratiques pour calibrer les autres paramètres cohésifs (contrainte cohésive maximale, ouverture critique, énergie de fissuration, ...). L'utilisation couplée des critères obtenus permet une calibration inverse des paramètres de la loi cohésive en fonction des propriétés macroscopiques du matériau et de la taille de maillage. De fait il est possible de prédire un comportement homogène global indépendamment de la taille du maillage. / In this study a micromechanical model is proposed for a collection of cohesive zone models embedded between two each elements of a standard cohesive-volumetric finite element method. An equivalent 'matrix-inclusions' composite is proposed as a representation of the cohesive-volumetric discretization. The overall behaviour is obtained using homogenization approaches (Hashin Shtrikman scheme and the P. Ponte Castañeda approach). The derived model deals with elastic, brittle and ductile materials. It is available whatever the triaxiality loading rate and the shape of the cohesive law, and leads to direct relationships between the overall material properties and the local cohesive parameters and the mesh density.First, rigorous bounds on the normal and tangential cohesive stiffnesses are obtained leading to a suitable control of the inherent artificial elastic loss induced by intrinsic cohesive models. Second, theoretical criteria on damageable and ductile cohesive parameters are established (cohesive peak stress, critical separation, cohesive failure energy, ...). These criteria allow a practical calibration of the cohesive zone parameters as function of the overall material properties and the mesh length.The main interest of such calibration is its promising capacity to lead to a mesh-insensitive overall response in surface damage.