Three-dimensional basic and mixed interface problems of the mathematical theory of thermoelastic pseudo-oscillations are considered for piecewise homogeneous anisotropic bodies. Applying the method of boundary potentials and the theory of pseudodifferential equations existence and uniqueness theorems of solutions are proved in the space of regular functions C^(k+ alpha) and in the Bessel-potential (H^(s)_(p)) and Besov (B^(s)_(p,q)) spaces. In addition to the classical regularity results for solutions to the basic interface problems, it is shown that in the mixed interface problems the displacement vector and the temperature are Hölder continuous with exponent 0<alpha<1/2.

La démarche actuelle des industries aérospatiales est de diminuer le coût de lancement des engins spatiaux par une réduction de la masse des composants. Dans l’optique de cette démarche, de nouveaux matériaux sont élaborés et permettent de satisfaire aux exigences de densification, de dissipation thermique et de réduction de masse des équipements électroniques embarqués dans les satellites. Cette thèse est une contribution à l’étude de deux de ces matériaux, l’AlSi CE9F et une nuance d’alumine cofrittée à température, destinés à réaliser des boitiers hybrides de protections de composants électroniques, initialement conçus en Kovar. Les objectifs sont d’affiner les connaissances sur propriétés mécaniques des deux matériaux et de mettre en place des règles de conceptions propres à leurs comportements mécaniques. En effet, l’AlSi CE9F et l’alumine ont un comportement à rupture fragile. La détermination de leurs résistances à la rupture est alors réalisée dans le cadre de la théorie de Weibull. Des séries d’essais de flexion quatre points et trois points sont effectués. Elles permettent d’identifier les paramètres de Weibull des deux matériaux à température ambiante et de mettre en évidence les effets de volume. L’étude expérimentale est poursuivie sur l’AlSi CE9F afin de déterminer l’influence de la température sur ses propriétés mécaniques à travers deux approches. La première s’intéresse à une variation monotone de la température et la seconde à des cycles thermiques entre -50 et 125°C. Si la première étude ne montre qu’une faible évolution du module d’élasticité, la seconde démontre que les cycles thermiques contribuent à l’amélioration de la résistance à la rupture de l’AlSi CE9F. Cette augmentation de la contrainte à la rupture se traduit également par une évolution de sa microstructure. Dans un second temps, un modèle de Weibull est numériquement mis en place à partir des paramètres identifiés et du critère de la contrainte équivalente de Freudenthal. Ce critère est analysé et validé à travers l’étude de trois éprouvettes en AlSi CE9F à chargements complexes. Le modèle validé est enfin utilisé pour décrire le comportement mécanique de deux composants dans différentes configurations de sollicitation, réalisés respectivement en alumine HTCC et en AlSi CE9F. Une méthodologie de dimensionnement est alors mise en place et permettra de disposer de nouvelles règles de conception équivalentes à celles existant sur les matériaux classiques. / The aerospace companies currently want to decrease the price of spacecraft launching with a reduction of the mass components. New materials were recently developed to satisfy the rising requirements of thermal dissipation, densification and weight decrease of on-board electronic equipment intended to satellite. This thesis is a contribution to the characterization of two of these innovative materials: AlSi CE9F and a grade of alumina HTCC. These materials are designed to manufacture hybrid boxes for computing chips, originally made in Kovar. The objectives are to improve the mechanical properties knowledge of these materials and to develop a know-how design specific to their mechanical behaviours. Indeed, AlSi CE9F and alumina have brittle fracture behaviour. The strength analysis is also realized in connection with the Weibull theory. The Weibull’s parameters are identified from the four points and three points bending strength and the volume effects are highlighted. The experimental study is completed by the analysis of the temperature influence on the mechanical properties of AlSi CE9F through two approaches. The first one considers a monotonic variation of temperature and shows a minor evolution of the elastic modulus. The second one proves that thermal cycles between -50 and 125°C improve the strength value of AlSi CE9F. This increase is also reflected by an evolution of its microstructure. Secondly, a Weibull’s model is numerically established based on identified parameters and the Freudenthal’s equivalent stress criterion. The Freudenthal’s criterion is analysed and confirmed through the study of complex loading samples made in AlSi CE9F. The confirmed model is finally used to describe the mechanical behaviours of two components respectively made in AlSi CE9F and alumina HTCC, thoroughly in several loading configurations. A design methodology is developed and will bring new rules in modelling and design, closed to those existing in conventional materials.

Made available in DSpace on 2016-08-17T18:39:43Z (GMT). No. of bitstreams: 1 4433.pdf: 5330114 bytes, checksum: edb55c6ffa47a3cf94d1224982188ac2 (MD5) Previous issue date: 2011-08-30 / The hydrostatic pressure inside the cell or simply cell turgor is an important component of texture in vegetables and is directly related to firmness. The decrease in cell turgor of plant organs is also an indicator of loss of tissue water. This effect can be perceived visually by wilting accompanied by a dry appearance with the loss of brightness and color of products, which influences consumer perceptions about its quality. Within this context has been crafted technique for measuring turgor with Thermoelastic Probe® (TP) based on the principle of measuring isovolumetric. After an extensive literature review found that the published studies on TP, presented further on control theory and modeling of physical phenomena involved in the measurement of turgor. However not bring practical results, containing automated measurements of cell turgor in plants. This study aimed to fill this gap. In this direction was made improving of the method to manufacturing the sensor and a new mechanical design for TP. The attainment of the sensors is given through the steps of stretching the capillary, making the tip, sanding, filling and sealing fluid sensor. The method for obtaining the proposed sensor showed minimal utilization rate of 27.0% representing an improvement of 540% over the figures provided by the available literature. Since the new mechanical design of TP significantly improved the alignment and relative positioning of the sensor, sample and image capture system. The process of exchange of sensor and positioning of the sample for measurement of turgor was also facilitated, resulting in an average time of 5 minutes to perform these tasks. This marked a breakthrough since the previous version, users reported that this task could take up to 60 minutes. Both activities related to the new mechanical design of the ST and the improvement of the methodology for obtaining sensor thermoelastic were preparatory to the development of automatic control of turgor measurement. The automation of the measurement process was performed after the implementation of a software to detect the position of the meniscus oil / cytoplasm based on the determination of the difference in contrast between the phases formed by the fluid sensor (oil ) and intracellular fluid. For automatic control of the position of the meniscus, was implemented a Proportional Integral type controller. The proposed values for the parameters of controller allowed the control of the selected position of the meniscus and automatic - x - determination of turgor pressure in cells of onion (Allium cepa L.). In an unprecedented manner, this paper makes the first successful experiment in automatic determination of cell turgor in plant organs with Termoelastic Probe. / A pressão hidrostática no interior da célula ou simplesmente turgescência celular é um importante componente da textura em vegetais e está diretamente relacionada à firmeza. A diminuição do turgor celular dos órgãos vegetais também é um indicador da perda de água dos tecidos. Tal efeito pode ser percebido de forma visual pela murcha acompanhada por uma aparência seca com a perda do brilho e da cor dos produtos, o que influencia a percepção do consumidor sobre sua qualidade. Dentro deste contexto foi trabalhada a técnica de medição de turgor com Sonda Termoelástica®1 (ST) baseada no princípio de medição isovolumétrico. Após extensa revisão bibliográfica verificou-se que os trabalhos sobre ST publicados, apresentavam aprofundamento sobre a teoria de controle e modelagem física dos fenômenos envolvidos no processo de medição do turgor. Entretanto não traziam resultados práticos, contendo medidas automatizadas do turgor celular em vegetais. Este trabalho objetivou preencher esta lacuna. Neste sentido foi realizado o aprimoramento da metodologia de manufatura do sensor termoelástico juntamente com novo projeto mecânico da ST. A obtenção dos sensores se deu atraves das etapas de esticamento do capilar, confecção da ponta, lixamento, preenchimento com fluido sensor e selamento. O método para obtenção de sensores proposto apresentou taxa de aproveitamento mínima de 27,0 % representando uma melhoria de 540 % em relação aos valores apresentados pela literatura disponível. Já o novo projeto mecânico da ST melhorou sensivelmente o alinhamento e posicionamento relativo entre sensor, amostra e sistema de captura de imagens. O processo de troca de sensor e posicionamento da amostra para medição do turgor também foi facilitado, implicando em um tempo médio de 5 minutos para realização destas tarefas. Este fato marcou um grande avanço, visto que usuários da versão anterior relataram que esta tarefa poderia durar até 60 minutos. Tanto as atividades ligadas ao novo projeto mecânico da ST e ao aprimoramento da metodologia para obtenção de sensores termoelásticos foram predecessoras e preparatórias para desenvolvimento do controle automático da medição de turgor. A automação do 1 Sonda Termoelástica® - Equipamento patenteado pela Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA) representada pela unidade especializa: EMBRAPA Instrumentação localizada em São Carlos - SP. A Sonda Termoelástica® tem a função de medir o turgor em células de vegetais, interagindo com o citoplasma através do princípio da termoelasticidade do fluido sensor. - viii - processo de medição de turgor foi realizado após a implementação de um software para detecção da posição do menisco óleo/citoplasma baseado na determinação da diferênça de contraste entre as fases formadas pelo fluido sensor (óleo) e líquido intracelular. Para controle automático da posição do menisco, foi implementado um controlador do tipo PI. Os valores propostos para os parâmetros do controlador Proporcional Integral selecionado permitiram o controle da posição do menisco e a determinação automática da turgescência em células de cebola (Allium cepa L.). De forma inédita, este trabalho caracteriza a primeira experiência bem sucedida na determinação automática de turgor em células de órgãos vegetais com ST.

L'objectif de la thèse est d'analyser le comportement mécanique de matériaux granulaires composites bidimensionels en terme de textures granulaires en utilisant deux approches : étude expérimentale par "thermoelastic stress analysis" et étude numérique par dynamique moléculaire. Les systèmes granulaires composites sont préparés à l'aide de cylindres en polyoxyméthylène (POM) et polyéthylène haute densité (PEHD), présentant un rapport de rigidité de 4 entre eux. Différents rapports de diamètres et de nombres de particules sont considérés. Les résultats expérimentaux et numériques sont en bon accord à l'échelle macroscopique. En particulier, le réseau fort (qui est ici caractérisé par des contraintes hydrostatiques supérieures à la valeur moyenne) contient moins de 50% des particules, et présente une distribution décroissance exponentielle quel que soit le type de particules considéré pour l'analyse (particules souples, particules rigides, toutes les particules). De plus, la distribution des contacts entre particules rigides (contacts POM-POM) est anisotrope et tend à s'organiser dans le sens de la direction du chargement extérieur appliqué, tandis que les autres types de contact agissent principalement pour maintenir le système en équilibre. / The main objective of our dissertation is to analyze the mechanical behavior of two-dimensional composite granular materials through the granular textures. Thermoelatic stress analysis experiments and molecular dynamics simulations are used for this purpose. The composite granular systems are prepared from polyoxymethylene (POM) and high-density polyethylene (HDPE) cylinders with a stiffness ratio of about 4 between them. Different configurations in terms of ratios of diameter size and ratio of particle numbers are systematically investigated. Experimental and numerical results are good correlated at the macroscopic scale. In particular the strong network, which is here characterized by hydrostatic stresses higher than the mean value, consists of less than 50% of all particles, and exhibits an exponential decay whatever the type of particles considered for the analysis (soft, stiff, or both types). In addition, the contact distributions between stiff particles (POM-POM contacts) is anisotropic with an effort to arrange parallel to the direction of the external applied load, whereas the other types of contacts just act to sustain the granular system in equilibrium.

La thermographie infrarouge est un moyen d'analyse du comportement mécanique des matériaux. Elle a connu un essor considérable depuis les années 80 avec l'apparition des premiers capteurs. Deux techniques principales ont pu être développées ; la calorimétrie quantitative et l'analyse des contraintes par thermoélasticité (TSA en anglais). Jusqu'à aujourd'hui, la majorité des travaux a été réalisée sur les métaux et les polymères. Le présent manuscrit relève le challenge d'appliquer ces techniques aux matériaux verres, en développant une méthodologie de débruitage des films thermiques, permettant de conserver la résolution spatiale des mesures thermiques. Cela permet de caractériser de forts gradients dans des champs de variations de température de faible intensité. Cette méthodologie a été utilisée pour débruiter des films thermiques d'échantillons de verre soumis à un chargement mécanique cyclique. Dans un premier temps, elle a été appliquée pour étudier la réponse thermique d'une empreinte à l'échelle microscopique. Dans un second temps, elle a été utilisée pour remonter à des champs de contraintes et de sources de chaleur à l'échelle macroscopique. Ce travail ouvre de nouvelles perspectives à l'étude du comportement thermomécanique des matériaux fragiles présentant une faible réponse thermique sous sollicitation mécanique et de forts effets de gradients spatiaux. Les applications visées sont la fissuration et l'identification de paramètres constitutifs. / The infrared thermography is used to analyse the mechanical behavior of materials. Since the 80's, it has rised with the appearance of the first sensors. Two principal techniques has been developed; the quantitative calorimetry and the thermoelastic stress analysis (TSA). Until today, most of the works has been carried out on metals and polymers. This manuscript takes-up the challenge of applying these techniques to glassy materials by developing a methodology to denoise infrared movies, which allows to preserve the spatial resolution of the thermal measurement. It allows to caracterise high gradients of low temperature variation fields. This methodology has been used to denoised thermal movies of glass samples submitted to a cyclic mechanical test. In a first time, it has been applied to study the thermal response of an imprint at the microscopic scale. In a second time, stress and heat sources fields have been determined at the macroscopic scale. This work provides new possibilities to study the thermomechanical behavior of brittle materials which present a low thermal response and high spatial gradients under mechanical loading. The target applications are the cracking phenomenom and the identification of constitutive parameters.

The first objective of this dissertation is to present hybrid numerical-analytical approaches and reduced-order models to simulate microelectromechanical systems (MEMS) in multi-physics fields. These include electric actuation (AC and DC), squeeze-film damping, thermoelastic damping, and structural forces. The second objective is to investigate MEMS phenomena, such as squeeze-film damping and dynamic pull-in, and use the latter to design a novel RF-MEMS switch. In the first part of the dissertation, we introduce a new approach to the modeling and simulation of flexible microstructures under the coupled effects of squeeze-film damping, electrostatic actuation, and mechanical forces. The new approach utilizes the compressible Reynolds equation coupled with the equation governing the plate deflection. The model accounts for the slip condition of the flow at very low pressures. Perturbation methods are used to derive an analytical expression for the pressure distribution in terms of the structural mode shapes. This expression is substituted into the plate equation, which is solved in turn using a finite-element method for the structural mode shapes, the pressure distributions, the natural frequencies, and the quality factors. We apply the new approach to a variety of rectangular and circular plates and present the final expressions for the pressure distributions and quality factors. We extend the approach to microplates actuated by large electrostatic forces. For this case, we present a low-order model, which reduces significantly the cost of simulation. The model utilizes the nonlinear Euler-Bernoulli beam equation, the von K´arm´an plate equations, and the compressible Reynolds equation. The second topic of the dissertation is thermoelastic damping. We present a model and analytical expressions for thermoelastic damping in microplates. We solve the heat equation for the thermal flux across the microplate, in terms of the structural mode shapes, and hence decouple the thermal equation from the plate equation. We utilize a perturbation method to derive an analytical expression for the quality factor of a microplate with general boundary conditions under electrostatic loading and residual stresses in terms of its structural mode shapes. We present results for microplates with various boundary conditions. In the final part of the dissertation, we present a dynamic analysis and simulation of MEMS resonators and novel RF MEMS switches employing resonant microbeams. We first study microbeams excited near their fundamental natural frequencies (primary-resonance excitation). We investigate the dynamic pull-in instability and formulate safety criteria for the design of MEMS sensors and RF filters. We also utilize this phenomenon to design a low-voltage RF MEMS switch actuated with a combined DC and AC loading. Then, we simulate the dynamics of microbeams excited near half their fundamental natural frequencies (superharmonic excitation) and twice their fundamental natural frequencies (subharmonic excitation). For the superharmonic case, we present results showing the effect of varying the DC bias, the damping, and the AC excitation amplitude on the frequency-response curves. For the subharmonic case, we show that if the magnitude of the AC forcing exceeds the threshold activating the subharmonic resonance, all frequency-response curves will reach pull-in. / Ph. D.

Three-dimensional basic and mixed interface problems of the mathematical theory of thermoelastic pseudo-oscillations are considered for piecewise homogeneous anisotropic bodies. Applying the method of boundary potentials and the theory of pseudodifferential equations existence and uniqueness theorems of solutions are proved in the space of regular functions C^(k+ alpha) and in the Bessel-potential (H^(s)_(p)) and Besov (B^(s)_(p,q)) spaces. In addition to the classical regularity results for solutions to the basic interface problems, it is shown that in the mixed interface problems the displacement vector and the temperature are Hölder continuous with exponent 0<alpha<1/2.

Im Fokus dieser Arbeit stehen Dämpfungseffekte schwingfähiger Mikroelektromechanischer Systeme (MEMS), die nach dem kapazitiven Wirkprinzip arbeiten. Die verschiedenen Dissipationsprozesse und die zugehörigen analytischen Modelle sowie numerischen Berechnungsmöglichkeiten auf physikalischer Ebene werden vorgestellt und mit eigenen experimentellen Ergebnissen verglichen. Der Schwerpunkt liegt dabei auf der fluidischen Dämpfung im Kontinuum und bei leichter Verdünnung, was bei den meisten kapazitiven MEMS den dominierenden Verlusteffekt darstellt.:1 Überblick 2 Grundlagen zur Beschreibung von Mikrosystemen 3 Herstellung und Charakterisierung 4 Fluidische Dämpfung 5 Weitere dissipative Effekte mikromechanischer Systeme 6 Zusammenfassung und Ausblick / This thesis focuses on damping effects of vibrational micro-electromechanical systems (MEMS) with capacitive working principle. The different dissipation processes and the associated analytical models as well as numerical calculation possibilities on a physical level are presented and compared to own experimental results. The main emphasis is on fluidic damping in the continuum regime and with slight rarefaction, which is the dominant loss effect in most capacitive MEMS.:1 Überblick 2 Grundlagen zur Beschreibung von Mikrosystemen 3 Herstellung und Charakterisierung 4 Fluidische Dämpfung 5 Weitere dissipative Effekte mikromechanischer Systeme 6 Zusammenfassung und Ausblick

Le but de cette thèse pluridisciplinaire est d’étudier le problème de l’interaction fluide-structure à partir du point de vue mathématique et physique. Des problèmes d’interaction d’un fluide visqueux avec une structure élastique décrivent, par exemple, des interactions entre le manteau terrestre et de la croûte terrestre, le sang et la paroi vasculaire dans un vaisseau sanguin, etc. En génie l’interaction fluide visqueux-structure apparaît lors de la formation de solution colloïdale quand un laser passe à travers le fluide influençant le substrat (ablation laser dans un liquide). Fusion sélective au laser (FSL) est utilisée pour étudier le comportement des contraintes résiduelles en dépendance des propriétés thermoélastiques et mécaniques du matériau et des formes variées des cordons rechargés. A partir du point de vue mathématique le système couplé “flux fluide visqueux – plaque mince élastique” en 3D lorsque l’épaisseur de la plaque, E, tend vers zéro, tandis que la densité et le module de Young du matériau élastique sont d’ordre 1 et E-3, respectivement, est considéré. Le solide est couché par le fluide qui occupe un domaine épais. La modélisation multi-échelle est effectuée pour la partie élastique. Le développement asymptotique complet est construit lorsque E tend vers zéro. L’existence, la régularité et l’unicité de la solution pour le problème initial sont étudiées au moyen de techniques variationnelles. La méthode de décomposition asymptotique partielle du domaine est appliquée pour le système couplé. L’erreur de la méthode est évaluée / The goal of this multi-disciplinary thesis is to study the fluid-structure interaction problem from mathematical and physical viewpoints. Viscous fluid-structure interaction problems describe, for example, interactions between the Earth mantle and the Earth crust, the blood and the vascular wall in a blood vessels, etc. In engineering viscous fluid-structure interaction appears during colloidal solution formation when a laser pierce through the fluid influencing the substrate (laser ablation in a liquid). Selective laser melting (SLM) is used to study the behavior of residual stresses depending on the thermoelastic and mechanical properties of the material and on various forms of reloaded beads. From mathematical point of view the coupled system “viscous fluid flow-thin elastic plate” in 3D when the thickness of the plate, E, tends to zero, while the density and the Young’s modulus of the plate material are of order 1 and E-3, respectively, is considered. The plate lies on the fluid which occupies a thick domain. The multi-scale modeling is performed for the elastic part. The complete asymptotic expansion is constructed when E tends to zero. The existence, the regularity and the uniqueness of the solution for the original problem are studied by means of variational techniques. The method of asymptotic partial domain decomposition is applied for the coupled system. The error of the method is evaluated

A new nonlinear fracture analysis framework is developed for the mode-I and II fracture response of thick-section fiber reinforced polymeric (FRP) composites. This framework employs 3D micromechanical constitutive models for the nonlinear material behavior along with cohesive elements for crack growth. Fracture tests on various cracked geometries are used to verify the prediction of the failure loads and the crack growth behavior. A commercially available pultruded E-glass/polyester and vinylester thick-section FRP composite material was used to demonstrate the proposed fracture approach along with the nonlinear constitutive modeling. A new Infra-red thermography technique is derived to measure the surface strain field near the crack tip in the linear response range. Mode I and II fracture toughness tests for pultruded composites are also examined using the eccentrically loaded, single-edge-notch tension, ESE(T), single-edge-notch tension, SEN(T), and a butterfly specimen with an Arcan-type fixture. Material nonlinearity and crack growth effects were observed during the tests and investigated using the proposed analysis framework. The effect of material orthotropy on the stress intensity factor solutions was addressed using the virtual crack closure technique. The analytic and experimental results support the use of the ESE(T) specimen for the measuring the mode-I fracture toughness and the butterfly shaped specimen for measuring the mode-II toughness. The calibrated cohesive models were able to predict the measured crack growth in both modes I and II for various crack geometries. A mixed mode failure criterion is proposed and verified with test results. Examples are presented for using this criterion and crack growth analyses. The experimental and analytical results of this study can form a foundation for using fracture-based methods for the design of structures using these materials.