Dans ce travail de thèse, nous nous sommes intéressés à la modélisation et la simulation de la propagation d'ondes ultrasonores dans l'os cortical. Plus précisément, nous avons étudié et analysé la technique dite des ultrasons quantitatifs (Quantitative Ultrasound, QUS) pour l'évaluation de la qualité du tissu osseux. Il s'agit d'une technique émergente dont l'application aux tissus osseux suscite un intérêt particulier dans la communauté scientifique. Le tissu osseux étant un tissu vivant, il est sujet au vieillissement et à divers pathologies parmi lesquelles on peut citer ostéoporose, ostéomalacie, ostéoporomalacie, ou encore, la maladie dite de Paget. Pour accompagner les soins à prodiguer au tissu osseux, une surveillance de sa qualité s'avère indispensable. Dans ce contexte, les méthodes ultrasonores sont réputées être intéressantes, de par leurs caractères non-invasif, peu coûteux, portable et non-ionisant. Cependant, utiliser des ultrasons dans le cadre de la caractérisation du tissu osseux, suppose une compréhension profonde des différents phénomènes physiques mis en jeu lors de leur propagation. Dans cette optique, notre travail est développé dans la thématique de la modélisation dédiée à la propagation des ondes ultrasonores dans des guides d'ondes multidimensionnels, hétérogènes, anisotropes, et composés de matériaux dont l'hétérogénéité peut être qualifiée d'aléatoire. Une des originalités de cette thèse concerne l'étude des coefficients de réflexion et de transmission et des courbes de dispersion en présence d'incertitudes dues aux propriétés matérielles. Dans une première partie, nous étudions les phénomènes de réflexion/transmission via un modèle tri-couches bidimensionnels prenant en compte les tissus mous et l'hétérogénéité aléatoire du tissu osseux. Nous avons pu analyser l'impact de ces caractéristiques sur les coefficients de réflexion et de transmission. Un gradient de propriétés matérielles de l'os est introduit, et son impact sur les coefficients d'intérêt est examiné. L'aspect modal des ondes est exploré, en étudiant la dispersion des ondes de Lamb. Les résultats obtenus dans une configuration géométrique bidimensionnelle ont permis de discuter l'influence des divers paramètres, en terme de propriétés mécaniques et/ou géométriques, sur la propagation des ondes ultrasonores dans le tissu cortical. Dans une deuxième partie, le modèle est étendu pour une configuration géométrique cylindrique. La discussion est menée afin d'analyser l'influence de la géométrie tridimensionnelle de l'os sur les phénomènes de propagation / In this thesis, we are interested in the modeling and simulation of the propagation of ultrasonic waves in the cortical bone. Precisely, we have studied and analyzed the Quantitative Ultrasound (QUS) technique for the evaluation of the quality of bone tissue. It is an emerging technique those the application to bone tissue arouses particular interest in the scientific community. Since bone tissue is a living tissue, it is subject to aging and various pathologies, such osteoporosis, osteomalacia, osteoporomalacia, or the so-called Paget disease. To assist in therapeutic follow-up of the bone, monitoring of quality of bone tissue is essential. In this context, methods based on QUS technique are deemed to be interesting, due of their non-invasive, inexpensive, portable and non-ionizing characteristics. However, use the ultrasound in the context of characterization of bone tissue, requires a deep understanding of the different physical phenomena involved in their propagation. In this perspective, our work is developed in the modeling theme dedicated to the propagation of ultrasonic waves in multidimensional, heterogeneous, anisotropic waveguides, constituted of materials whose heterogeneity can be qualified as random. One of the originalities of this thesis concerns the study of the reflection and transmission coefficients and the dispersion curves in the presence of uncertainties in the material properties. In a first part, we study the reflection/transmission phenomena via a two-dimensional tri-layer model taking into account the soft tissues and the random heterogeneity of the bone tissue. We analyzed the impact of these characteristics on the reflection and transmission coefficients. A gradient of material properties is introduced, and its effect on the coefficients of interest is examined. The modal aspect of the waves is explored, by studying the dispersion of Lamb waves. The results obtained in a two-dimensional geometrical configuration made it possible to discuss the influence of the various parameters, in terms of mechanical and/or geometric properties, on the propagation of the ultrasonic waves in the cortical tissue. In a second part, the proposed model is extended for a cylindrical geometric configuration. The discussion is carried out in order to analyze the influence of the three-dimensional geometry of the bone on the phenomena of propagation

La détection, la localisation et le suivi de l’évolution de défauts dans les milieux périodiques et les guides d’ondes est un enjeu majeur dans le domaine du Contrôle Non Destructif (CND). La propagation d’ondes dans ce genre de milieux est complexe, par exemple lorsque la vitesse dépend de la fréquence (dispersion) ou de la direction de propagation (anisotropie). La signature du défaut peut également être « noyée » dans le champ acoustique renvoyé par la structure (réverbération ou diffusion multiple). C’est pour répondre à ces enjeux de taille que l’Optimisation Topologique (OT) a été adaptée aux problèmes de diffraction des ondes acoustiques par des défauts infinitésimaux afin d’obtenir des images de réflectivité des milieux inspectés. La méthode peut être appliquée à toutes sortes de milieux, quelle que soit leur complexité, à condition d’être capable de simuler correctement (sur un milieu de référence) la propagation des ondes de l’expérience physique. En s’inspirant de l’OT, les travaux de cette thèse proposent de mettre en oeuvre des méthodes d’imagerie qualitatives adaptées aux spécificités des Cristaux Phononiques (CP) et des guides d’ondes. Dans un premier temps, nous nous attachons à la description du formalisme mathématique de l’Optimisation Topologique et de la Full Waveform Inversion (FWI). Bien que ces méthodes ne cherchent pas à résoudre les mêmes problèmes inverses, nous mettons en évidence leurs points communs. Dans un deuxième temps, nous appliquons l’Imagerie Topologique (IT) à l’inspection en réflexion des milieux faiblement hétérogènes. Dans un troisième temps, nous nous inspirons de l’IT pour définir une nouvelle variante de celle-ci nommée Imagerie Topologique Hybride (ITH). Nous appliquons ces méthodes pour l’inspection en réflexion des CP crées par des tiges d’acier immergées dans l’eau. Nous comparons les performances de ces méthodes en fonction du type de défaut dans le CP. Les simulations numériques correspondantes à certains cas d’étude sont appuyées par des essais expérimentaux concluants. Dans un quatrième temps, nous adaptons l’IT à une configuration d’inspection en transmission afin de mette en oeuvre une méthode de Structural Health Monitoring (SHM) des guides d’ondes. A ce propos, nous avons mis au point une nouvelle méthode d’imagerie mieux adaptée que l’IT aux configurations d’inspection en transmission. / The detection, localization and monitoring of the evolution of defects in periodic media and waveguides is a major issue in the field of Non-Destructive Testing (NDT). Wave propagation in such media is complex, for example when the velocity depends on the frequency (dispersion) or direction of propagation (anisotropy). The signature of the defect can also be "embedded" in the acoustic field reflected by the structure (reverberation or multiple diffusion). It is to answer these stakes of the size that the Topological Optimization (TO) has been adapted to the problems of diffraction of the acoustic waves by infinitesimal defects in order to obtain reflectivity images of the inspected media. The method can be applied to all kinds of media, regardless of their complexity, provided an exact simulation of the wave propagation in a reference medium (without defects) is performed. Inspired by the TO, the work of this thesis proposes to implement qualitative imaging methods adapted to the specificities of Phononic Crystals (PC) and waveguides. First, we focus on the description of the mathematical formalism of Topological Optimization and Full-Waveform Inversion (FWI). Although these methods do not try to solve the same inverse problems, we highlight their similarities. In a second step, we apply Topological Imaging (TI) to the inspection in pulse-echo configuration of weakly heterogeneous media. Thirdly, we draw inspiration from TI to define a new variant of this method called Hybrid Topological Imaging (HTI).We apply these methods for the pulse-echo configuration inspection of PCs created by steel rods immersed in water.We compare the performance of these methods according to the kind of defects in the PC. Numerical simulations for some case studies are supported by conclusive experimental trials. In a fourth step, we adapt the TI to a pitch-catch configuration in order to implement a new method of Structural Health Monitoring (SHM) of waveguides. In this regard, we have developed a new imaging method that is better suited than TI to pitch-catch configurations.

[pt] Ondas ultrassônicas guiadas de cisalhamento horizontal (do inglês, shear horizontal SH) são comumente usadas para avaliação não destrutiva de placas e tubos. Em dutos de aço, uma camada de revestimento é frequentemente aplicada à superfície externa dos mesmos para evitar a corrosão. O material do revestimento apresenta impedância acústica consideravelmente menor que a do material principal dos dutos, a saber aço; todavia, sua presença pode alterar significativamente as características de propagação dos modos de onda SH guiada, haja vista que se trata de um problema de propagação em guia de onda multicamadas. Devido às propriedades viscoelásticas do material do revestimento, comumente utilizado, os modos de onda guiada que conhecidamente se propagam de maneira adequada em um duto cru, podem se tornar uma escolha inadequada em um duto revestido devido à alta atenuação, impossibilitando inspeções corriqueiras. Nesta dissertação, investiga-se quais modos SH são mais adequados para uma inspeção circunferencial de um tubo revestido de interesse, a saber, um duto de aço de espessura de 6.35 mm com revestimento de polietileno de espessuras variáveis. Um modelo semi-analítico foi utilizado para calcular as curvas de dispersão e atenuação e um modelo numérico de elementos finitos foi explorado para investigar os modos de propagação em um guia de onda revestidos e sob a presença de defeitos. Resultados mostram que, no regime de espessura de alta frequência, o modo quasi-SH0 no comprimento de onda 10 mm é a escolha mais adequada para uma primeira avaliação, sem conhecimento prévio do espécime. No entanto, com o conhecimento das características do espécimen avaliado, pode-se selecionar outros modos que possam ter menor atenuação. Conclui-se que, uma seleção cuidadosa do modo de operação mais adequado é fundamental para inspecionar defeitos em dutos revestidos de interesse. Para os casos analisados, a saber, SH0 e SH1 com comprimentos de onda de 25 mm, 20 mm, 15 mm e 10 mm, os modos de mais adequados são SH1 em 25mm - 285 kHz, SH0 em 20 mm - 160 kHz, SH0 em 15 mm - 210 kHz, SH1 em 15 mm - 330 kHz, SH0 em 10 mm - 310 kHz e SH1 em 10 mm - 400 kHz, apresentando atenuação aproximada de 21 dB/m, 3 dB/m, 15 dB/m, 13 dB/m, 4 dB/m e 17 dB/m, respectivamente, e clara identificação do defeito através de sua refletividade. Portanto, o presente estudo é útil no projeto de um setup experimental confiável ao analisar um duto cujo revestimento possui propriedades viscoelásticas. / [en] Shear horizontal (SH) ultrasonic guided waves are commonly used for non-destructive evaluation of plates and pipes. In steel pipes, a coating layer is often applied to the outer surface in order to prevent it from corrosion. The applied coating layer presents considerably lower acoustic impedance than the pipe main material, namely, steel, nevertheless, its presence significantly affects the propagation characteristics of SH guided wave modes, since one deals with a multilayered waveguide problem. Due to the viscoelastic properties of the coating layer, ultrasonic guided wave modes that adequately propagate in an equivalent bare pipe can become an unsuitable choice in a coated pipe, due to high attenuation, rendering pipe inspection unfeasible. In this thesis, it was investigated which SH guided wave modes are more adequate for circumferential inspections of a coated pipe of interest, namely, a 6.35 mm thick steel pipe and a polyethylene coating whose thicknesses varies. A semi-analytical model was used to calculate the dispersion and attenuation curves and a finite element numerical model was further exploited to investigate the propagating modes in coated waveguided under the presence of defects. Results show that, in the analyzed cases, at the high-frequency-thickness regime, the quasi-SH0 mode at 10 mm wavelength is the most suitable choice for an evaluation with no previous knowledge of the specimen. However, with knowledge of the characteristics of the evaluated specimen, it is possible to select other modes that can have a lower attenuation. Therefore, a careful selection of the most suitable operating mode is paramount in order to inspect a defect with ultrasonic guided waves in pipes with coating. Considering the studied cases, namely, SH0 and SH1 at of 25 mm, 20 mm, 15 mm, and 10 mm wavelength, the most suitable SH guided wave modes are SH1 at 25mm - 285 kHz, SH0 at 20 mm - 160 kHz, SH0 at 15 mm - 210 kHz, SH1 at 15 mm - 330 kHz, SH0 at 10 mm - 310 kHz and SH1 at 10 mm - 400 kHz, showing approximated attenuation of 21 dB/m, 3 dB/m, 15 dB/m, 13 dB/m, 4 dB/m and 17 dB/m, respectively, and clear defect identification by mean of its reflectivity. Therefore, the present study is useful in order to design a reliable experimental setup when analyzing a pipe whose coating has viscoelastic properties.

[pt] A necessidade de transmitir energia e dados através de barreiras metálicas tem sido cada vez maior em aplicações industriais, onde não é possível a penetração de cabos elétricos, ou o uso de ondas eletromagnéticas, tais como, por exemplo, em sistemas de sensoriamento de cimentação em poços de petróleo. Ondas acústicas podem ser uma solução para esse problema, porque não são afetadas pelo efeito gaiola de Faraday, além de possuírem baixa atenuação ao atravessarem metais. Diversos esforços foram feitos para realizar a transmissão de dados através de camadas metálicas, com abordagens que variam em composição do canal acústico, taxa de transmissão, transmissão simultânea de dados e energia e complexidade dos circuitos empregados; existe, porém, carência de trabalhos que envolvam camadas metal-fluído-metal. Este trabalho apresenta uma possível solução utilizando ondas acústicas como meio de transportar energia e dados em um canal composto de barreiras com duas camadas metálicas e uma de fluído. Aqui propõe-se uma inovadora técnica de controle automático de ganho e um melhor aproveitamento da largura de banda do canal acústico, que permite maior taxa de transmissão de dados. É ainda proposta uma técnica para controle dinâmico da portadora enviada ao lado passivo do sistema. Inicialmente, foi feita uma análise de um modelo numérico, baseado em trabalhos anteriores, fundamentado na propagação de ondas acústicas e baseado na analogia acustoelétrica. Em seguida, desenvolveu-se um sistema eletrônico para receber / transmitir energia e dados digitais, modulados em frequência, de um lado ao outro do sistema. Por fim, análises experimentais foram feitas utilizando como canal acústico, um conjunto de duas placas planas de aço (de 5 mm) separadas por uma camada de fluído (de 100 mm) e dois transdutores alinhados axialmente, realizando a transferência de energia e dados digitais modulados em frequência. O sistema foi capaz de realizar a transferência de dados a uma taxa de 19200 bps e simultaneamente uma transferência de energia de 66 mW, com essa energia foi possível alimentar o modulo eletrônico e um sensor de pressão e temperatura. Durante os testes foi constatado um aproveitamento de 5,5 por cento da energia aplicada ao canal, e foi possível atingir uma taxa de erro de bit de 5 por cento em um teste com 2 h e 30 min de duração, utilizando o canal acústico com camadas de múltiplos materiais propostos. O sistema de controle de portadora funcionou adequadamente, permitindo uma redução de consumo de até 53 por cento. O controle automático de ganho permitiu uma redução de 50 por cento na taxa de erro de decodificação. Demonstra-se, então, a viabilidade de tais sistemas de controle propostos, os quais podem ser úteis em casos onde existam variações nas características acústicas do canal em questão que, em conjunto com a transferência não intrusiva, pode prover solução para sistemas de sensoriamento. / [en] The need for energy and data transmission through metallic barriers is increasing in industrial applications, where the penetration of electrical waves or the use of electrical waves is not possible. An example of such a scenario is the monitoring of cementing in wellbore applications. Acoustic waves are promising to solve this problem, since they are not affected by the Faraday cage effect, in addition, they present low attenuation when propagating in metals. Several efforts have been made to carry out data transmission through metallic layers, with approaches that vary in composition of the acoustic channel, transmission speed, simultaneous transmission of data and energy and the complexity of the circuits used, but there is a lack of works involving metal-fluid-metal layers. This work presents a possible solution using acoustic waves as a mean of transporting energy and data in a channel composed of barriers with two metallic layers and one fluid layer. Here, it is proposed a novel technique for automatic gain control and better use of the available bandwidth of the acoustic channel, which allows higher data transmission speed. Also, a technique for dynamic control of the carrier sent to the passive side of the system is proposed. Initially, an analysis with a numerical model was made, following previous works, which is based on the propagation of acoustic waves and relying on the acoustoelectric analogy. Then, an electronic system was developed to receive/transmit power and digital data, frequency modulated, from one side of the system to the other. Finally, experimental analyzes were performed using as an acoustic channel, a set of two flat steel plates (5 mm) separated by a fluid layer (100 mm) and a pairs of axially aligned transducers, performing the energy transfer and frequency modulated digital data. The system was able to transfer data at a rate of 19200 bps and simultaneously a transfer of energy of 66 mW, with this energy it was possible to feed the inside block module and a pressure and temperature sensor. During the tests, it was verified that 5.5 per cent of the energy applied to the channel was used, and it a bit error rate down to of 5 per cent was reached in a test with 2 h and 30 min of duration, using the multi-layered acoustic. The automatic carrier control system worked as expected and allowed one to reduce energy consumption in 53 per cent. The automatic gain control allowed one to reduce the error rate in 50 per cent. These control systems prove the feasibility of the proposed system and further show the usefulness of the system in scenarios that are subject to variations in the acoustic characteristics of the channel.