Neste trabalho foram desenvolvidas as funções de interpolação com regularidades C1 e C2, utilizando o Método da Partição de Unidade, referentes ao elemento quadrilateral de quatro nós. Estes elementos quadrilaterais Hermitianos de regularidade C1 e C2 foram implementados em uma plataforma própria de elementos finitos, considerando uma estratégia do tipo sub-paramétrica. De forma comparativa com os elementos Lagrangeanos de regularidade C0 e diferentes ordens polinomiais, os elementos de regularidade C1 e C2 foram aplicados na solução de: problemas clássicos de elasticidade plana infinitesimal isotrópica; aproximação das frequências naturais de vibração livre de barras e viga; pro- pagação de onda elástica em barra devido à aplicação de força impulsiva. Os resultados obtidos mostraram que foi possível se obter um maior percentual de frequências naturais aproximadas do espectro discreto, dado um certo nível de erro máximo, com os elementos de regularidade C1 e C2 em comparação com os elementos Lagrangeanos de regularidade C0 de quatro, oito, dezesseis e vinte e cinco nós. Quanto ao problema de propagação de onda elástica devido à aplicação de força impulsiva, as soluções obtidas com os elementos de regularidade C1 e C2 também apresentaram-se satisfatórias em relação à solução ana- lítica e às soluções aproximadas obtidas com os elementos Lagrangeanos de regularidade C0 de quatro e oito nós. Por outro lado, nas simulações dos problemas de elasticidade plana infinitesimal isotrópica, os elementos de regularidade C1 e C2 não apresentaram um comportamento satisfatório. Os erros relativos em normas L2 e de energia da solução aproximada foram maiores do que aqueles obtidos com o elemento Lagrangeano de regularidade C0 de oito nós, por exemplo, e as taxas de convergência em norma de energia obtidas com tais elementos foram inferiores às preditas pelo estimador de erro a priori. / In this work the shape functions with regularity C1 e C2 were developed, by means of the Partition of Unity Method, concerning to the four-node quadrilateral element. These Hermitian quadrilateral elements with regularity C1 e C2 were implemented in an own platform of finite elements, considering the subparametric strategy. Comparatively with the C 0 regularity Lagrangian elements of different polynomial order, C1 and C2 regularity elements were applied in simulations of: classical isotropic infinitesimal plane elasticity problems; approximation of natural frequencies of free vibration for bars and beam; elastic wave propagation in bar caused by forced vibration with impulsive loading applied. The results obtained showed that was possible to get a major number of natural frequencies of free vibration for the discrete spectrum, given a certain level of error, for C1 and C2 regularity elements in comparison with C 0 regularity Lagrangian elements of four, eight, sixteen and twenty-five nodes. Regarding to the elastic wave propagation problem in bar due to the application of impulsive loading, the solution obtained with C1 and C2 regularity elements also presented satisfactory results with relation to the analytical solution and those obtained with C 0 regularity Lagrangian elements with four and eight nodes. On the other hand, for isotropic infinitesimal plane elasticity problems, C1 and C2 regularity elements did not present satisfactory results. Relative errors in L2 and energy norms of approximate solution were greater than those computed for the C 0 Lagrangian element of eight nodes, for example, and convergence rates obtained with the C1 and C2 regularity elements were lower than those predicted by the a priori error estimator.

Orientadores: José Roberto de França Arruda, Jean-Mathieu Mencik / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-28T14:24:53Z (GMT). No. of bitstreams: 1 Silva_PriscillaBrandao_D.pdf: 13049086 bytes, checksum: 2f821e196dd604384d15489bda2360cb (MD5) Previous issue date: 2015 / Resumo: Nesta tese de doutorado, o método dos elementos finitos ondulatórios é utilizado para cálculo da resposta harmônica de sistemas mecânicos envolvendo estruturas com periodicidade unidimensional, i.e., estruturas compostas por subestruturas idênticas arranjadas ao longo de uma direção. Tais sistemas mecânicos podem ser complexos e são comumente encontrados em aplicações de engenharia como, por exemplo, nas fuselagens de aviões. A primeira parte da tese é dedicada ao cálculo das ondas que se propagam ao longo dessas estruturas. Uma breve revisão da literatura sobre as formulações disponíveis para o problema de autovalor associado ao método dos elementos finitos ondulatórios é apresentada, assim como um estudo dos erros numéricos induzidos por estes problemas de autovalor no caso de um guia de ondas sólido. Na segunda parte desta tese, modelagens de superelementos para estruturas periódicas são propostas. Neste contexto, matrizes de rigidez dinâmica e de receptância ou flexibilidade de estruturas periódicas são expressas a partir dos modos de onda. Comparadas às matrizes de rigidez dinâmica e receptância obtidas pelo método dos elementos finitos convencional, as matrizes baseadas no método dos elementos finitos ondulatórios são calculadas de forma bastante rápida e sem perda de acuracidade. Ademais, uma estratégia eficiente de redução de ordem de modelo é apresentada. Comparada às formulações que utilizam a base completa de ondas, esta estratégia proporciona redução do tempo computacional requerido para cálculo da resposta forçada de estruturas periódicas. De fato, é mostrado que elementos espectrais numéricos de alta ordem podem ser construídos a partir do método dos elementos finitos ondulatórios. Isto constitui uma alternativa ao método dos elementos espectrais convencional, cuja utilização está limitada a estruturas simples para as quais soluções analíticas por ondas existam. A motivação por trás das formulações de matrizes de superelementos a partir do método dos elementos finitos ondulatórios está na utilização do conceito de ondas numéricas para calcular a resposta harmônica de sistemas mecânicos acoplados que envolvam estruturas com periodicidade unidimensional e junções elásticas a partir de procedimentos de montagem clássicos de elementos finitos ou técnicas de decomposição de domínio. Este assunto é tratado na terceira parte desta tese. Nesse caso, o método de Craig-Bampton é usado para expressar as matrizes de superelementos de junções por meio de modos estáticos e de interface fixa. Um critério baseado no método dos elementos finitos ondulatórios é considerado para a seleção dos modos da junção que mais contribuem para a resposta forçada do sistema. Isto também contribui para o aumento da eficiência da simulação numérica de sistemas acoplados. Finalmente, na quarta parte desta tese, o método dos elementos finitos ondulatórios é utilizado para mostrar que é possível projetar estruturas periódicas com potencial para funcionar como filtros de vibração em bandas de frequência específicas. Com o intuito de destacar a relevância dos desenvolvimentos propostos nessa tese, ensaios numéricos envolvendo guias de onda sólidos, pórticos planos e estruturas tridimensionais do tipo fuselagem aeronáutica são realizados / Abstract: In this thesis, the wave finite element (WFE) method is used for assessing the harmonic forced response of mechanical systems that involve structures with one-dimensional periodicity, i.e., structures which are made up of several identical substructures along one direction. Such mechanical systems can be quite complex and are commonly encountered in engineering applications, e.g., aircraft fuselages. The first part of the thesis is concerned with the computation of wave modes traveling along these structures. A brief literature review is presented regarding the available formulations for the WFE eigenproblem, which need to be solved for expressing the wave modes, as well as a study of the numerical errors induced by these eigenproblems in the case of a solid waveguide. In the second part of the thesis, the WFE-based superelement modeling of periodic structures is proposed. In this context, the dynamic stiffness matrices and receptance matrices of periodic structures are expressed in terms of wave modes. Compared to the conventional FE-based dynamic stiffness and receptance matrices, the WFE-based matrices can be computed in a very fast way without loss of accuracy. In addition, an accurate strategy for WFE-based model order reduction is presented. It provides significant computational time savings for the forced response analysis of periodic structures compared to WFE-based superelement modeling, which makes use of the full wave basis. Indeed, it is shown that higher-order numerical spectral elements can be built by means of the WFE method. This is an alternative to the conventional spectral element method, which is limited to simple structures for which closed-form wave solutions exist. The motivation behind the formulation of WFE-based superelement matrices is the use of the concept of numerical wave modes to assess the forced response of coupled mechanical systems that involve structures with one-dimensional periodicity and coupling elastic junctions through classic finite element assembly procedures or domain decomposition techniques. This issue is addressed in the third part of this thesis. In this case, the Craig-Bampton method is used to express superelement matrices of coupling junctions by means of static and fixed-interface modes. A WFE-based criterion is considered to select among junction modes those that contribute most to the system forced response. This also contributes to enhancing the efficiency of the numerical simulation of coupled systems. Finally, in the fourth part of this thesis, the WFE method is used to show the potential of designing periodic structures which work as vibration filters within specific frequency bands. In order to highlight the relevance of the developments proposed in this thesis, numerical experiments which involve solid waveguides, two-dimensional frame structures, and three-dimensional aircraft fuselage-like structures are carried out / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutora em Engenharia Mecânica / 2010/17317-9 / FAPESP

O início da construção de estruturas para reserva de água no mundo é conhecido há milhares de anos, e, desde então, as barragens são consideradas alternativas viáveis não apenas para reserva de água para consumo, mas também para as finalidades de geração de energia hidrelétrica, contenção de rejeitos, entre outras. Entretanto, mesmo com os contínuos avanços nas técnicas construtivas e na fiscalização da segurança destas estruturas, a possibilidade de rompimento de barragens é uma realidade constante. Nesta perspectiva, o presente texto objetiva analisar os aspectos hidráulicos de metodologias simplificadas para estimativa de parâmetros de inundação proveniente do rompimento de barragens, a saber, as vazões e respectivas profundidades atingidas no vale a jusante, em um evento de rompimento hipotético. Para tal, analisaram-se os resultados de três metodologias simplificadas existentes, aplicadas em três barragens estudo de caso, com características estruturais e geometria do vale a jusante distintas. Os resultados das metodologias simplificadas foram comparados com os estudos de Dam Break das três barragens estudo de caso, obtidos com o uso do software HEC-RAS unidimensional e cedidos por empreendedores. O presente texto também sugere uma nova equação empírica para previsão da vazão máxima resultante do rompimento de barragens por galgamento, e propõe uma nova metodologia simplificada para análise preliminar de rompimento de barragens, com base nos métodos analisados e nas respectivas conclusões obtidas. Os resultados indicam que o uso de metodologias simplificadas na análise preliminar de rompimento de barragens é uma alternativa viável em vales cuja declividade do talvegue é acentuada e cujas características geométricas são aproximadamente constantes. Identificou-se que pequenas alterações no coeficiente de rugosidade do terreno e na declividade da linha de energia refletiram em diferenças nos resultados de profundidades e larguras máximas de 20%, em média. A proposta de nova equação empírica para previsão de vazão máxima na seção da barragem baseou-se na análise de 39 casos reais envolvendo ruptura de barragens por galgamento e resultou em um coeficiente de determinação (R²) de 0,79. Quando comparada com as principais equações semelhantes indicadas na bibliografia, a equação proposta obteve vazões máximas próximas ou superiores às dos demais pesquisadores analisados sempre que a altura da barragem foi inferior a 30 m. Evidencia-se a importância na estimativa cautelosa da vazão máxima na seção da barragem, uma vez que essa reflete em diferenças significativas nas vazões e respectivas profundidades alcançadas ao longo do vale a jusante da estrutura. Nos casos analisados, diferentes vazões máximas na seção da barragem refletiram em distinções de até 50%, em média, nas profundidades e larguras máximas a jusante. A nova metodologia proposta para definição de características de inundação provenientes do rompimento de barragens pode contribuir em estudos preliminares para tal, especialmente aos empreendedores que possuem número expressivo de barragens. Nesses casos, a metodologia poderá nortear a prioridade a ser dada em estudos detalhados de Dam Break. / For thousands of years, water reservoir structures have been built worldwide. Since then, dams have been considered viable alternatives not only for reserving water for consumption but also for the purposes of hydroelectric power generation and sediment retention, among others. Despite the continuous advances in the construction techniques and in the safety inspection of these structures, the possibility of breaking of dams remains a constant reality. Hence, this paper aims to analyze the hydraulic aspects of simplified methodologies for estimating flood parameters on dam ruptures, namely, the flows and respective depths reached in the downstream valley in a hypothetical breach event. Results of three existing simplified methodologies were studied applied in three dams with different structural characteristics and downstream valley geometry. The results of simplified methodologies were compared with dam break studies of three study case dams, obtained with one-dimensional HEC-RAS and provided by entrepreneurs. The present paper suggests also a new empirical equation for predicting the maximum flow resulting from the overtopping dam failure and proposes a new simplified methodology for preliminary analysis of dam rupture, based on the analyzed methods and respective obtained conclusions. The results indicate that the use of simplified methodologies in the preliminary dam break analysis is a viable alternative in valleys with high thalweg declivities and close to constant geometric characteristics. It was identified that small changes in the coefficient of rough terrain and in the energy line slope reflected in differences in the results of depths and maximum widths of 20%, on average. The proposed new empirical equation for maximum flow prediction in the dam section was based on the analysis of 39 actual cases involving overtopping dam failure and resulted in a coefficient of determination (R²) of 0.79. When compared to similar main equations indicated in the bibliography, the proposed equation obtained maximum flows near or higher than those of other researchers analyzed whenever the height of the dam did not exceed 30 m. The importance of a cautious estimation of the maximum flow rate in the dam section is to be highlighted, since it results in significant variations of flow and respective depths along the valley and downstream of the structure. Different maximum flows were found in the dam section, which reflected in distinctions of up to 50%, in average, in the maximum depths and widths downstream. The new proposed methodology for defining dam break characteristics caused by dam rupture may contribute to preliminary studies, especially to entrepreneurs who own a significant number of dams. In these cases, the methodology may guide the priority to be given in detailed studies of dam break.

La connaissance de la turbulence atmosphérique en visée horizontale permet de mieux appréhender la physique des flux de chaleur à l’interface sol-atmosphère. Elle permet également, en visée verticale, d’améliorer les performances des futurs systèmes d’optique adaptative grand-champ pour l’observation astronomique. Le profil de Cn² caractérise localement la force de la turbulence. La méthode CO-SLIDAR, développée par l’ONERA, permet de réaliser des profils de Cn² le long de la ligne de visée du télescope à partir des pentes et de scintillations mesurées par un Analyseur de Shack-Hartmann sur source double. Cette méthode a été validée en visée verticale mais n’avait pas encore montré son efficacité en visée horizontale. Les deux expériences à Lannemezan et à Châtillon-Meudon ont vu la mise en place d'un nouveau profilomètre Shack-Hartmann Infrarouge : le SCINDAR. Elles ont été réalisées sur des surfaces respectivement hétérogène et homogène par morceaux, et elles participent à la validation de la méthode pour des applications agronomiques et écologiques. Mon étude consiste à améliorer le traitement du signal du profilomètre SCINDAR et à valider la méthode CO-SLIDAR pour des mesures de la turbulence atmosphérique proche du sol. Cette méthode a été adaptée en utilisant un formalisme de propagation en onde sphérique. L'étude a permis d'identifier et prendre en compte des sources d'erreur dans le traitement : à savoir la vibration de la machine à froid de l'analyseur de front d'onde cryogénique du SCINDAR et l'étendue des sources dans les fonctions de poids du modèle direct posé pour le traitement des données. Mon étude se consacre à l’amélioration du traitement des données du SCINDAR et à la validation expérimentale des profils de Cn² obtenus avec des mesures de Cn² acquises par des scintillomètres. J'ai construit tout d'abord une base de données de pentes et scintillations de qualité vérifiée. Pour l'inversion des données, j'ai choisi la régularisation L1L2 qui est adaptée pour des mesures de Cn² proches du sol. La méthode de réglage des hyperparamètres de cette régularisation est non-supervisée. Elle permet d’augmenter la fiabilité et la précision de l’estimation du profil de Cn² de façon pragmatique à l'aide des erreurs relatives sur les paramètres turbulents macroscopiques. Le profilomètre SCINDAR avec la méthode CO-SLIDAR ainsi améliorée produit finalement des profils de Cn² d'excellente qualité. Ces profils sont comparés avec succès aux mesures des scintillomètres. L’ensemble de ces travaux constitue l'adaptation de la méthode CO-SLIDAR pour des mesures de la turbulence proche du sol. / The knowledge of atmospheric turbulence in horizontal aim allows to better understand the physics of the heat fluxes at the ground-atmosphere interface. It also allows, in vertical aim, to improve the performance of future wide-field adaptive optics systems for astronomical observation. The profile of Cn²locally characterizes the force of turbulence. The CO-SLIDAR method, developed by ONERA, allows profiles of Cn² along the line of sight of the telescope, from the slopes and scintillations of a double source measured by Shack-Hartmann analyzer. This method was validated in vertical aim but had not yet shown its effectiveness in horizontal aim. The two experiments in Lannemezan and Châtillon-Meudon introduced a new Shack-Hartmann Infrared profilometer: the SCINDAR. They were carried out on heterogeneous and piecewise homogeneous surfaces respectively, and they participate in the validation of the method for agronomic and ecological applications. My study consists of improving SCINDAR profilometer signal processing and validating the CO-SLIDAR method for near-ground atmospheric turbulence measurements. This method has been adapted using a spherical wave propagation formalism. The study identified and took into account sources of error in processing: the cold machine vibration of the SCINDAR cryogenic wavefront analyzer and the extent of the sources in the weight functions of the direct model set for data processing. My study focuses on improvement of the SCINDAR data processing and experimental validation profiles Cn² obtained with Cn² measurements acquired by scintillometers. I first built a database of slopes and scintillations of verified quality. For the inversion of the data, I chose the L1L2 regularization which is suitable for near-ground Cn² measurements. The method of setting the hyperparameters of this regularization is unsupervised. It makes it possible to increase the reliability and the accuracy of the Cn² profile estimation in a pragmatic way using the relative errors of the macroscopic turbulent parameters. The SCINDAR profilometer with the improved CO-SLIDAR method finally produces Cn² profiles of excellent quality. These profiles are successfully compared to scintillometer measurements. All of this work constitues the adaptation of the CO-SLIDAR method for measurements of near-ground turbulence.

Shape memory alloys (SMAs) exhibit the ability to absorb large dynamic loads and, therefore, are excellent candidates for structural components where impact loading is expected. Compared to the large amount of research on the shape memory effect and/or pseudoelasticity of polycrystalline SMAs under quasi-static loading conditions, studies on dynamic loading are limited. Experimental research shows an apparent difference between the quasi-static and high strain rate deformation of SMAs. Research reveals that the martensitic phase transformation is strain rate sensitive. The mechanism for the martensitic phase transformation in SMAs during high strain rate deformation is still unclear. Many of the existing high strain rate models assume that the latent heat generated during deformation contributes to the change in the stress-strain behavior during dynamic loading, which is insufficient to explain the large stress observed during phase transformation under high strain rate deformation. Meanwhile, the relationship between the phase front velocity and strain rate has been studied. In this dissertation, a new resistance to phase transformation during high strain rate deformation is discussed and the relationship between the driving force for phase transformation and phase front velocity is established. With consideration of the newly defined resistance to phase transformation, a new model for phase transformation of SMAs during high strain rate deformation is presented and validated based on experimental results from an austenitic NiTi SMA. Stress, strain, and martensitic volume fraction distribution during high strain rate deformation are simulated using finite element analysis software ABAQUS/standard. For the first time, this dissertation presents a theoretical study of the microscopic band structure during high strain rate compressive deformation. The microscopic transformation band is generated by the phase front and leads to minor fluctuations in sample deformation. The strain rate effect on phase transformation is studied using the model. Both the starting stress for transformation and the slope of the stress-strain curve during phase transformation increase with increasing strain rate.

Infrasound is undetectable by the human ear and excessive exposure may be a substantial health risk. Low frequency sound propagates through walls with minimal attenuation, making it difficult to avoid. This study interprets the results from both analytical calculations and simulations of pressure waves propagating through a wall in one dimension. The wall is thin compared to the wavelength; the model implements properties of three materials commonly used in walls. The results indicate that the geometry of the wall, most importantly the small ratio between wall width and wavelength, is the prime reason for the low levels of attenuation observed in transmitted amplitudes of low frequency sounds, and that damping is negligible for infrasound. Furthermore, a one-dimensional homogeneous wall model gives rise to periodicity in the transmitted amplitude, which is not observed in experiments. Future studies should prioritize the introduction of at least one more dimension to the model, to allow for variable angles of incidence.

La recherche de nouveaux matériaux a permis de nouveaux développements au cours de ces dernières décennies. Ce sont entre autres les diélectriques artificiels ou encore les métamatériaux. Cependant, si ces matériaux restent passifs, malgré tous les développements possibles, les performances des antennes, ou autres structures électromagnétiques qui découlent d’eux seront toujours confrontés aux mêmes limitations fondamentales. En intégrant des circuits actifs dans ces matériaux, par exemple des résistances négatives, des capacités négatives et des inductances négatives, il est possible de dépasser ces limitations ainsi les propriétés synthétisables et les applications d’ingénierie pourront être significativement élargies. En effet, cela permettrait de créer des matériaux et des dispositifs dont les propriétés ne seront pas possibles autrement et surpasseraient celles des matériaux existant dans la nature. Cette thèse a été l’occasion dans un premier temps d’utiliser les circuits non-Foster qui sont des circuits à rétroaction actif, pour l’adaptation d’une antenne électriquement petite à basses fréquence. Ceci a permis de mettre en évidence ses avantages par rapport à une adaptation passive plus conventionnelle.Ensuite, des capacités négatives ainsi que des inductances négatives et positives ont été conçues. Leur fonctionnement totalement différent des composants passifs a été mis en exergue. Ce qui nous a conduit à les appliquer sur des structures périodiques. Cela a donné des résultats intéressants comme la propagation supraluminique sur une ligne de transmission des ondes. Et en les appliquant à la cellule unitaire d’une surface de métamatériaux qui est aussi une structure périodique, sa taille est réduite pour une plus grande compacité des antennes à cavités conçues pour les basses fréquences où la longueur d’onde est très grande. / The search of new materials has enabled new developments in recent decades. Among these are artificial or dielectric metamaterials. However, if these materials are passive, despite all the possible developments, the antennas performances or other structures resulting from them will still face the same fundamental limitations. By adding active circuits in these materials, such as negative resistors, negatives capacitors and negative inductors, it is possible to overcome these limitations and the synthesized properties and engineering applications can be significantly expanded. Indeed, this would create materials and devices with properties which can allow us to obtain behavior nonexistent in nature. This open the way to new applications. In this thesis, we explore the opportunity at first to use non-Foster circuits that are active feedback circuit, in the matching network of an electrically small antenna for low frequency operation. This helped to highlight its advantages over more conventional passive matching. Then, negative capacitors and negative and positive inductors were fabricated. Their totally different behaviors with passive components were also highlighted. This led us to apply them on periodic structures. Interesting results were obtained as superluminal wave propagation on a transmission line. And by applying to the unit cell of a metamaterial surface which is also a periodic structure, the size is reduced to a more compact cavity antennas designed for low frequency where the wavelength is very large.

Les objectifs de cette thèse sont la modélisation mathématique et la simulation numérique de l’élastographie impulsionnelle basée sur la force de radiation acoustique (FRA) dans un tissu mou précontraint, et en particulier le myocarde. La première partie du manuscript concerne la modélisation mathématique de la FRA, la propagation d’ondes de cisaillement qui en résulte et la caractérisation de la vitesse des ondes de cisaillement pour une loi de comportement générale du tissu myocardique. Nous montrons aussi des applications pour l’estimation de l’orientation des fibres cardiaques dans le myocarde et l’évaluation de “pathologies synthétiques ”. Une des contributions principales de ce travail est le développement d’un modèle mathématique original de la FRA. En particulier, à partir d’un modèle biomécanique tridimensionnel du coeur, nous obtenons, à travers une approche asymptotique, les équations qui régissent les champs de pression et de cisaillement induits par la FRA. De plus, nous calculons une expression analytique du terme source responsable de la génération des ondes de cisaillement à partir d’une impulsion acoustique en pression. Dans la deuxième partie de la thèse, nous proposons des outils numériques efficaces pour une simulation numérique réaliste d’une expérience d’élastographie impulsionnelle dans un tissu quasi-incompressible, précontraint et fibré. La discrétisation en espace se base sur des éléments finis spectraux d’ordre élevé. Pour la discrétisation en temps, nous proposons une nouvelle méthode adaptée à l’élasticité incompressible. En particulier, seuls les termes correspondant à des vitesses infinies, associés à la contrainte d’incompressibilité, sont traités implicitement, à travers la resolution d’un problème de Poisson à chaque pas de temps de l’algorithme. En outre, nous proposons une nouvelle méthode d’ordre élevé et efficace pour la résolution d’un problème de Poisson, qui se base sur la transformée de Fourier discrète. / This PhD thesis concerns the mathematical modelling and numerical simulation of impulsive Acoustic Radiation Force (ARF)-driven Shear Wave Elastography (SWE) imaging in a prestressed soft tissue, with a specific reference to the cardiac setting. The first part of the manuscript deals with the mathematical modelling of the ARF, the resulting shear wave propagation, and the characterisation of the shear wave velocity in a general constitutive law for the myocardial tissue. We also show some applications to the extraction of fibre orientation in the myocardium and the detection of “synthetic pathologies”. One of the main contributions of this work is the derivation of an original mathematical model of the ARF. In more detail, starting from an accurate biomechanical model of the heart, and based on asymptotic analysis, we infer the governing equation of the pressure and the shear wave field remotely induced by the ARF, and we compute an analytical expression of the source term responsible for the generation of shear waves from an acoustic pressure pulse. In the second part of the PhD thesis, we propose efficient numerical tools for a realistic numerical simulation of an SWE experiment in a nearly-incompressible, pre-stressed, fibered soft tissue. The spatial discretisation is based on high-order Spectral Finite Elements (HO-SEM). Concerning the time discretisation, we propose a novel method adapted to incompressible elasticity. In particular, only the terms travelling at infinite velocity, associated with the incompressibility constraint, are treated implicitly by solving a scalar Poisson problem at each time step of the algorithm. Furthermore, we provide a novel matrix-free, high-order, fast method to solve the Poisson problem, based on the use of the Discrete Fourier Transform.

Une forte concurrence avec d'autres moyens de transport a poussé l’industrie ferroviaire à se réinventer et rechercher des performances toujours plus élevées. De nos jours, l’obtention de vitesses chaque fois plus élevées exige le développement de modèles numériques précis pour concevoir et prédire le comportement des voies ferrées sous les contraintes mécaniques imposées par le passage du convoi. Dans cette thèse, nous avons concentré l'étude sur la couche de ballast. Ce composant présente un comportement mécanique complexe, lié à la nature granulaire de ses composants, il peut être solide, liquide ou gazeux.Ce comportement dépend de l'état de contrainte et de l'historique de déformation du milieu.Deux classes de modèles numériques sont couramment utilisées pour prédire le comportement de ces systèmes : (1) les approches discrètes et (2) les approches continues. Pour ces premières, chaque grain du ballast est représenté par un corps rigide et interagit avec ses voisins parle biais de forces de contact non linéaires en utilisant, par exemple, la méthode de dynamique non régulière des contacts. En raison des limites de calcul, ce type de méthode ne peut résoudre que quelques mètres de longueur de ballast. Le couplage avec le sol sous la couche de ballast et avec les traverses reste également un problème non résolu dans la littérature. Pour les approches continues, le ballast est remplacé par un milieu continu homogénéisé, de façon à permettre l’utilisation de la méthode par éléments finis classique (EF). Cependant, ces modèles sont normalement utilisés avec des paramètres mécaniques homogènes, de sorte qu'ils ne représentent pas complètement l'hétérogénéité des déformations et des contraintes dans la couche de ballast.Nous étudions dans cette thèse une approche alternative, utilisant un modèle de continuum hétérogène stochastique, qui peut être résolu avec une méthode par éléments finis tout en conservant dans une large mesure l'hétérogénéité des champs de contrainte et de déformation.L'objectif de ce modèle continu est de représenter statistiquement l'hétérogénéité du champ de contraintes dans un modèle de milieu continu ainsi que dans un modèle granulaire discret. Pour ce faire, les propriétés mécaniques sont représentées à l'aide de champs aléatoires. La présente thèse est divisée en trois parties: (1) la construction du modèle et l'identification des paramètres du matériau continuum (densité marginale de premier ordre, moyenne, variance, modèle de corrélation) ;(2) la propagation des ondes dans une voie ferrée ballastée et (3) l’exploration préliminaire de deux ensembles de données expérimentales. La première partie définit le modèle du continuum à fluctuations aléatoires et identifie les paramètres de notre modèle de continuum sur de petits échantillons cylindriques de ballast discret. Des modèles continus équivalents aux échantillons discrets sont générés et résolus en utilisant la méthode EF, et le champ stochastique utilisé pour fournir les propriétés mécaniques. Un processus d'optimisation est utilisé pour trouver une variance normalisée pour le matériau hétérogène stochastique. La deuxième partie de ce travail se concentre sur la résolution des équations dynamiques sur un modèle à grande échelle d'une voie ferrée ballastée utilisant la méthode des éléments spectraux. L'influence de l'hétérogénéité est mise en évidence et étudiée. En conséquence,des courbes de dispersion sont obtenues. Enfin, la troisième partie présente deux jeux de données distincts de mesures expérimentales sur le matériau de ballast : (1) une boîte de ballast ; (2) un passage de train dans un segment de voie ferrée ballastée.Les courbes de mobilité ont été extraites de l'expérience sur les ballasts. Un problème inverse a été résolu afin d'estimer la vitesse de l'onde homogénéisée et la vitesse de l'onde locale dans le milieu. Les passages de trains enregistrés pour l'analyse de la vibration à moyenne fréquences. / The stronger competition with other means of transportation has increased the demand for performance in the railway industry. One way to achieve higher performance is using accurate numerical models to design/predict railways tracks behaviour. Two classes of numerical models are commonly used to predict the behaviour of these systems: (i) discrete approaches and (ii) continuum approaches. In the former, each grain of the ballast is represented by a rigid body and interacts with its neighbours through nonlinear contact forces using, for example, the nonsmooth contact dynamics method. Due to computational limits, this kind of method can only solve a few meters-length of ballast. The coupling with the soil under the ballast layer and with the sleepers also remains an open problem. In continuum approaches, the ballast is replaced by a homogenized continuum and the classical Finite Element (FE) Method (or similar) is used. However, they are normally used with homogeneous mechanical parameters, so that they do not represent fully the heterogeneity of the strains and stresses within the ballast layer. We investigate in this thesis an alternative approach using a stochastic heterogeneous continuum model, that can be solved with a FElike method while retaining to a large degree the heterogeneity of the stress and strain fields. The objective of this continuous model is to represent statistically the heterogeneity of the stress field in a continuum model as well as in a discrete granular model. To do this, the mechanical properties are represented using random fields. The present thesis is divided into three parts: (1) the construction of the model and the identification of the parameters of the continuum material (first-order marginal density, mean, variance, correlation model, and correlation length); (2) wave propagation in a ballasted railway track. (3) preliminary exploration of two experimental datasets. The first part sets the randomly-fluctuating continuum model and identifies the parameters of our continuum model on small cylindrical samples of discrete ballast. Continuum models equivalent to the discrete samples are generated and solved using the FE method, and the stochastic field used as mechanical properties. An optimization process is used to find a normalized variance for the stochastic heterogeneous material. The second part of this work concentrates on the solution of the dynamical equations on a large-scale model of a ballasted railway track using the Spectral Element Method. The influence of the heterogeneity is highlighted and studied. As a result, dispersion curves are obtained. Finally, the third part presents two distinct datasets of experimental measurements on ballast material: (1) a ballast box; (2) a train passage in a segment of ballasted railway track. Mobility curves were extracted from the ballast box experiment. An inverse problem was solved in order to estimate the homogenized wave velocity and local wave velocity in the medium. The trains pass-by recorded for the analysis of the vibration at medium frequencies.

For optical propagation through the turbulent atmosphere, the angle of arrival (AOA) cross-correlation function obtained from two spatially separated light sources carries information regarding the transverse wind velocity averaged along the propagation path. Two methods for the retrieval of the beam transverse horizontal wind velocity, v_t, based on the estimation of the time delay to the peak and the slope at zero lag of the AOA cross-correlation function, are presented. Data collected over a two week long experimental campaign conducted at the Boulder Atmospheric Observatory (BAO) site near Erie, CO was analyzed. The RMS difference between 10 s estimates of v_t retrieved optically, and 10 s averages of the transverse horizontal wind velocity measured by an ultrasonic anemometer, was found to be 14 cm/s for the time-delay-to- peak method and 20 cm/s for the slope-at-zero-lag method, for a 2 h period beginning 0345 MDT on 16 June, 2010, during which the transverse horizontal wind velocity varied between -1 m/s and 2 m/s.