Dans cette thèse, nous présentons et étudions une nouvelle formulation du problème de contact frottant entre deux corps élastiques se basant sur la méthode de Nitsche. Dans cette méthode les conditions de contact sont imposées faiblement, grâce à un terme additionnel consistant et stabilisé par un paramètre gamma. En premier lieu, nous introduisons, l’étude effectuée en petites déformations pour une version non biaisée de la méthode. La non-distinction entre une surface maître et une surface esclave permettera à la méthode d’être plus générique et applicable directement au problème d’auto-contact. Le cadre restrictif des petites déformations nous permet d’obtenir des résultats théoriques sur la stabilité et la convergence de la méthode. Ces résultats sont complétés par une validation numérique. Ensuite, nous introduisons l’extension de la méthode de Nitsche au cadre des grandes déformations qui est d’avantage pertinent pour les applications industrielles et les situations d’auto-contact. La méthode de Nitsche est formulée pour un matériau hyper-élastique avec frottement de Coulomb et se décline en deux versions : biaisée ou non. La formulation est généralisée à travers un paramètre theta pour couvrir toute une famille de méthodes. Chaque variante particulière a des propriétés différentes du point de vue théorique et numérique, en termes de précision et de robustesse. La méthode est testée et validée à travers plusieurs cas tests académiques et industriels. Nous effectuons aussi une étude de l’influence de l’intégration numérique sur la précision et la convergence de la méthode. Cette étude couvre une comparaison entre plusieurs schémas d’intégration proposés dans la littérature pour d’autres méthodes intégrales. / In this thesis, we present and study a new formulation of frictional contact between two elastic bodies based on Nitsche’s method. This method aims to treat the interface conditions in a weak sense, thanks to a consistent additional term stabilized with the parameter gamma. At first, we introduce the study carried out in the small strain framwork for an unbiased version of the ethod. The non-distinction between a master surface and a slave one will allow the method to be more generic and directly applicable to the self-contact problem. The restrictive framework of small strain allowed us to obtain theoretical results on the consistency and convergence of the method. Then, we present the extension of the Nitsche method to the large strain case more relevant for industrial applications and situations of self-contact. This Nitsche’s method is formulated for an hyper-elastic material and declines in the two versions: biased and unbiased. We describe a class of methods through a generalisation parameter theta . Particular variants have different properties from a numerical point of view, in terms of accuracy and robustness. To prove the accuracy of the method for large deformations, we provide several academic and industrial tests. We also study the influence of numerical quadrature on the accuarcy and convergence of the method. This study covers a comparison of several integration rules proposed in the literature for other integral methods.

Aços inoxidáveis duplex (AID) são materiais amplamente utilizados para uma grande variedade de aplicações desde a indústria química, de alimentos, petroquímica, naval, farmacêutica, energia nuclear e em muitos outros campos devido à combinação de suas excelentes propriedades mecânicas e de resistência à corrosão. Particularmente na indústria petroquímica, os aços AID’s são muito utilizados como materiais estruturais para a construção de gasodutos que transportam altos volumes de CO2 e na confecção das camadas internas dos tubos flexíveis (oleodutos offshore), utilizadas na produção de óleo. A soldagem a arco dos AID’s pode acarretar, dependendo das taxas de resfriamento envolvidas, a formação de precipitados de segunda fase que degradam suas propriedades mecânicas. Um processo alternativo para evitar o problema de precipitação de fases indesejáveis é a utilização do processo de soldagem/reparo por fricção com pino consumível (SFPC). O objetivo do presente trabalho é a caracterização metalúrgica e mecânica de juntas de solda de aço inoxidável duplex UNS S31803 obtidas através dos processos SFPC e de soldagem de costura por fricção (SCF). Na soldagem SCF, o objetivo do estudo foi a verificação da influência do passo de soldagem na formação e alteração das estruturas e nas propriedades mecânicas. Os resultados dos ensaios foram comparados com as propriedades obtidas do material base (MB) “como recebido”. A partir das juntas soldadas obtidas por fricção, foram extraídos corpos de prova para ensaios de microtração e Charpy para avaliação da resistência mecânica e da resistência ao impacto. Análises da microestrutura em microscopia ótica (MO) e perfis de microdurezas ao longo da região de solda também foram realizadas. Verificou-se que os processos de soldagem SFPC e SCF provocam um intenso refinamento de grão na zona de mistura (região da interface entre material do pino e da base), modificando a estrutura lamelar de grãos alongados da matriz ferrítica/austenítica, ocasionado por uma ação conjunta de aquecimento e deformação plástica oriunda do processo de solda por fricção. Os resultados dos ensaios de microtração indicam que as juntas soldadas aumentaram sua resistência mecânica com relação ao material base, fato que se deve ao aumento da quantidade da ferrita na zona termomecanicamente afetada (ZTMA), à formação de nitretos de cromo no centro dos grãos ferríticos e ao refino de grão. O aumento da quantidade de ferrita na ZTMA ocorre devido às altas taxas de resfriamento envolvidas no processo de soldagem e verificados por análise térmica. As elevadas taxas de resfriamento dificultam a difusão do nitrogênio que tem um importante papel no equilíbrio de fases da estrutura duplex (ferrita-austenita), na soldagem. O nitrogênio aprisionado no interior do grão ferrítico produz nitretos de cromo deixando de agir como elemento gamagênico aumentando a quantidade da fase ferrita. As juntas soldadas verificadas apresentaram tenacidade aceitável de acordo com o exigido pela norma ASTM A923. / Duplex stainless steels (DSS) are materials widely used for a variety of applications from the chemical, food, petrochemical, marine, pharmaceutical, nuclear industry and other fields due to the combination of their excellent mechanical properties and corrosion resistance. Particularly in the petrochemical industry, the DSS’s steels are extensively used as structural materials for the construction of gas pipelines that carry high volumes of CO2 and making the inner layers of flexible pipes (pipelines offshore) used in offshore oil production. The arc welding of DSS's can lead, depending on cooling rates involved, the formation of second phase precipitates which degrade their mechanical properties. An alternative method to avoid the problem of precipitation of unwanted phase is to use the welding process Friction Hydro Pillar Processing (FHPP). The aim of this work is the metallurgical and mechanical characterization of joints welds of UNS S31803 duplex stainless steel obtained through FHPP processes and Friction Taper Stitch Welding (FTSW). In FTSW welding, the objective of the study was to verify the influence of the welding step on the formation and alteration of structures and mechanical properties. The test results were compared with the properties of the obtained base material "as received". From the welds joints obtained by friction welding, specimens for microtensile testing and charpy were extracted to evaluate the mechanical strength and toughness. Microstructural analysis in optical microscopy (OM) and scanning electron microscopy (SEM) and microhardness profiles along the weld region were also performed. It was found that the welding process FHPP and FTSW causes an intense grain refinement in bonding zone, modifying the lamellar structure of elongate grains of matrix ferritic/austenitic, caused by action of heating and plastic deformation arising from the welding process by friction. The results of the microtensile tests indicate that the welded joints increased their mechanical resistance with respect to the base material, due to the increase in the amount of the ferrite in the thermomechanically affected zone (ZTMA), the formation of chromium nitrides in the center of ferritic grains and grain refining. The increase in the amount of ferrite in the ZTMA occurs due to the high cooling rates involved in the welding process and verified by thermal analysis. The high cooling rates difficult the nitrogen diffusion, which plays an important role in the phase equilibrium of the duplex structure (ferrite-austenite) in welding. The nitrogen trapped inside the ferritic grain produces chromium nitrides ceasing to act as gamogenic element by increasing the amount of the ferrite phase. The welds joints verified also had acceptable ductility and toughness according required by standard ASTM A923.

L'étude par continuation des solutions périodiques et quasi-périodiques est appliquée à plusieurs modèles issus du violon. La continuation pour un modèle à un degré de liberté avec friction régularisée permet de montrer la préservation, par rapport à la friction de Coulomb, des bifurcations de cycle limite (une vitesse maximale et une force minimale permettant le mouvement de Helmholtz) et de propriétés globales de la branche de solution (croissance de l'amplitude avec la vitesse, décroissance de la fréquence avec la force normale). L'équilibrage harmonique est évalué sur la friction régularisée et a des propriétés de convergence intéressantes (erreur faible, monotone, à décroissance rapide). La continuation sur un modèle à deux modes donne accès aux solutions de registres supérieurs, dont la stabilité coïncide avec l'expérience. La valeur retenue pour l'inharmonicité peut modifier fortement le diagramme de bifurcation. Une nouvelle méthode de continuation des solutions quasi-périodiques est proposée. Elle associe l'EH étendu à deux pulsations avec la Méthode Asymptotique Numérique. Une attention particulière est portée à la rapidité des calculs, face à la croissance rapide de la taille des systèmes à inverser. Un modèle de friction prenant en compte la température au point de contact est reformulé à l'aide d'une dérivée fractionnaire. Nous proposons une méthode de continuation de solutions périodiques de systèmes contenant des dérivées ou intégrales fractionnaires. Nous établissons une condition suffisante pour que les cycles asymptotiques du cadre causal (Caputo) soient solutions du cadre que nous avons choisi. / The continuation of periodic and quasi-periodic solutions is performed on several models derived from the violin. The continuation for a one degree-of-freedom model with a regularized friction shows, compared with Coulomb friction, the persistence of limit cycle bifurcations (a maximum bow speed and a minimum normal force allowing Helmholtz motion) and of global properties of the solution branch (increase of amplitude with respect to the bow speed, decrease of frequency with respect to the normal force). The Harmonic Balance Method is assessed on this regularized friction system and shows interesting convergence properties (the error is low, monotone and rapidly decreasing). For two modes the continuation shows higher register solutions with a plausible stability. A stronger inharmonicity can greatly modify the bifurcation diagram. A new method is proposed for the continuation of quasi-periodic solutions. It couples a two-pulsations HBM with the Asymptotic Numerical Method. We have taken great care to deal efficiently with large systems of unknowns. A model of friction that takes into account temperature of the contact zone is reformulated with a fractional derivative. We then propose a method of continuation of periodic solutions for differential systems that contain fractional operators. Their definition is usually restricted to causal solutions, which prevents the existence of periodic solutions. Having chosen a specific definition of fractional operators to avoid this issue we establish a sufficient condition on asymptotically attractive cycles in the causal framework to be solutions of our framework.

Dans le domaine des matériaux métalliques, les techniques d’assemblage par soudageconduisent à des réductions de masse et de coûts importantes susceptibles d’intéresserles industries aéronautiques. Néanmoins, les procédés de soudage classiquespar fusion ne s’appliquent pas aux dernières générations d’alliages d’aluminium aéronautiques.Dans ce contexte, le procédé de soudage Friction Stir Welding présentedes atouts considérables, de nature à rendre compétitives les structures métalliquesface à la montée en puissance des matériaux composites.L’objectif de cette thèse est double. Il s’agit d’une part d’améliorer notre compréhensiondu procédé de soudage Friction Stir Welding Bobbin Tool puis dans undeuxième temps de proposer une méthodologie visant à prédire les paramètres desoudage optimaux.Afin de mener à bien ces objectifs, des essais de soudage ont été menés pour troisalliages d’aluminium aéronautique, incluant deux alliages d’aluminium-lihtium, etdeux épaisseurs, représentatives d’une jonction de peau de fuselage. Les résultatsd’essais ont par la suite été exploités et ont permis de mettre en évidence des corrélationsentre paramètres de soudage, température, puissance et malaxage du noyausoudé.Dans un troisième temps, afin de supporter la démarche expérimentale, des outilsde simulation ont été utilisés. Un modèle thermo-fluide local a été développé afinde simuler les phénomènes de malaxage dans le noyau soudé. A l’échelle globale, unmodèle thermique a permis de reproduire fidèlement les phénomènes de diffusion dela chaleur dans la structure. Enfin, le couplage des deux modèles a montré qu’il étaitpossible de simuler puis de prédire un domaine de soudabilité. / In the field of metallic materials, welding technologies can provide significantmass reductions and cost savings to aircraft industries. Nevertheless, classical fusionwelding processes can not be applied to last generations of aeronautical aluminiumalloys. In this context, Friction Stir Welding offers many advantages and can helpmetallic parts to face the build up of composite materials.This thesis has mainly two objectives. We aim first at improving our understandingof Friction Stir Welding with Bobbin Tool and then at proposing a kind ofmethodology able to predict optimal welding parameters.Welding trials were carried out using three aeronautical aluminium alloys includingtwo aluminium lithium and two thicknesses representative of a fuselagejunction. Results were analyzed and some correlations were found between weldingparameters, temperature and stirring of the weld nugget.This work was also supported by several modeling tools. A local thermo-fluidapproach has been used to simulate stirring of the material in the weld nugget. Aglobal thermal model has been used to simulate heat diffusion in the structure. Then,a coupled approach of these previous modeling tools shows that it was possible tonumerically predict a processing window.

O objetivo deste trabalho, foi investigar o comportamento tribológico do par cerâmico alumina - nitreto de silício no deslizamento em água com pH controlado e em uma suspensão com diferentes concentrações de sílica coloidal em água, e verificar a possibilidade de atingir um coeficiente de atrito da ordem de milésimos (&#956; < 0,01), aqui chamado de ultra baixo coeficiente de atrito (UBCA) e verificar se a mudança do pH do meio, ou a alteração da concentração de sílica na água, diminui o runningin, tempo necessário para o sistema entrar em regime estacionário, do coeficiente de atrito. Os ensaios foram realizados na configuração de ensaio tribológico esfera contra disco, no qual a esfera foi de nitreto de silício e o disco de alumina, sob carga normal de 54 N e velocidade de deslizamento de 1 m/s. A água utilizada nos ensaios foi destilada e deionizada, e a sílica coloidal amorfa, sem porosidade e de tamanho médio de partícula de 12 nanômetros foi a Aerosil® 200. A esfera de nitreto de silício, adquirida comercialmente, e o disco de alumina, foi proveniente de trabalhos anteriores. Todos os materiais foram caracterizados quanto a densidade. Algumas propriedades mecânicas como dureza, módulo de elasticidade e tenacidade à fratura foram determinadas. Nos ensaios lubrificados com água onde o pH foi controlado, o sistema atingiu o regime com valores de coeficiente de atrito da ordem de milésimos, exceto quando o pH da água era muito baixo ou muito alto. Em hidrossol o coeficiente de atrito chegou a unidades de milésimos, mas quando se aumenta a concentração de sílica coloidal, também, aumenta o desgaste nas superfícies. O disco de alumina sempre apresentou menor desgaste do que a esfera de nitreto de silício, em todas as condições estudadas. / The objective of this work was to investigate the tribological behavior of the ceramic pair alumina-silicon nitride, sliding on the water with controlled pH and in a suspension with different concentrations of colloidal silica in water, and verify the possibility of achieving a friction coefficient in the order of thousandths (&#956; < 0.01), here called ultra low friction coefficient (ULFC) and verify if the change of pH or changing the concentration of silica in the water, decreases the running-in, time required for the system reach the steady state of friction coefficient. The tests were conducted in a pin on disc setup in which the ball was made on silicon nitride and the disc of alumina, under normal load of 54 N and a sliding velocity of 1 m/s. The water used in the experiments was distilled and deionized. The amorphous silica, without porosity and average particle size of 12 nanometers was Aerosil ® 200. The ball of silicon nitride, was purchased commercially, and the alumina disk was recycled from previous works, all materials were characterized by density. Some mechanical properties such as hardness, elastic modulus and fracture toughness were determined. In tests with controlled pH water the system has reached the friction coefficient of the order of thousandths, except when the pH of the water was too low or too high. In hydrossol the friction coefficient reached units of thousandths, but when increasing the concentration of colloidal silica also increases the wear in the surfaces. The alumina disc always showed less wear than the ball of silicon nitride, in all conditions studied.

Esta tese tem por objetivo a aplicação do processamento por atrito linear na liga de titânio Ti-6Al-4V. Derivado da solda por atrito linear, é um processo recente desenvolvido na década de 90 para união de alumínio. Sua aplicação em outros tipos de materiais como aços e ligas de alto desempenho, em especial o titânio, tem interessado a industria. A metodologia utilizada nesta tese para avaliar o processamento por atrito linear, consistiu na execução de ensaios mecânicos de tração em condições mistas em chapas da liga de titânio Ti-6Al-4V. A máquina utilizada para o processamento das chapas foi um centro de usinagem CNC convencional, adaptado com dispositivos especiais. Além dos ensaios de tração em condições mistas, foram executadas medições de microdurezas nas regiões atingidas pelo processo, avaliação das microestruturas resultantes e medições de tensão residual para uma caracterização mais ampla do processo. As microestruturas na região processada são caracterizadas por uma estrutura totalmente transformada. As temperaturas de pico na região processada excederam a temperatura -transus durante o processamento e a transformação da fase + ocorreu durante a fase de resfriamento. A transformação da fase para resultou na formação de agulhas de fase nos contornos e pelo interior dos grãos da fase . Pequenas regiões com estrutura equiaxial de grãos ( globular) foram observados na zona de processamento. A abordagem dos resultados quantitativos foi feita de forma estatística, visando identificar os parâmetros de maior interação com os resultados observados. Foi identificado nesta tese que a rotação da ferramenta apresentou a maior influência nos resultados de tensão residual, microdureza e tensão de escoamento. Uma importante contribuição à modelagem da tensão de escoamento para materiais anisotrópicos é proposta, baseado em um critério de escoamento ortotrópico. Equações complementares baseadas nos testes mistos de tração e cisalhamento são propostas para modificar o modelo ortotrópico. O intuito deste modelo é indicar em que condições o material tem seu regime de escoamento atingido, podendo servir de base para simulações práticas de peças em condições similares. / This thesis aims at the application of friction stir processing (FSP) in Ti-6Al-4V titanium alloy. Derived from friction stir welding (FSW), it is a recent process developed in the 90s for aluminum joining. Its application to other types of materials such as steel and high performance alloys, in particular titanium, has interested industry. The methodology applied in this thesis to evaluate FSP, consisted in the execution of tensile test at mixed conditions to Ti-6Al-4V sheets 4. The machine used for processing the sheet was a conventional CNC milling machine, assembled with special fixture devices. In addition to tensile tests, measurements have been performed to the regions affected by the process such as evaluation of microhardness, microstructure and residual stress condition. The microstructures at the processed region are characterized by a transformed structure. The peak temperatures, in the processed region, exceeded the -transus temperature during the processing and transformation of the phase + occurred during the cooling phase. This transformation resulted in the formation of boundary and intergranular phase (Widmanstätten) at the grains. Small regions of equiaxed grain structure (globular ) were observed in the processed zone. The approach to the quantitative results was made in statistical form aiming to identify the parameters interaction with the observed results. It was identified in this thesis that the tool spinning rotation showed the highest influence on the results of residual stress, hardness and yield strength. An important contribution to the modeling of anisotropic materials yield stress is proposed based on an orthotropic yield criterion. Additional equations based on the mixed tests for tensile and shear are proposed to modify the orthotropic model. The purpose of this model is to indicate the conditions under which the material has reached its yield regime, and may be a basis for practical simulations in similar conditions.

L’objectif de l’étude est l’intégration de la méthode acoustique dans les analyses des étoffes. Par l’étude du phénomène du bruit généré par le frottement, nous avons pu concevoir et réaliser un instrument expérimental simulant le mouvement de l’avant-bras humain. Les méthodes utilisées pour l’obtention des paramètres du mouvement de l’avant-bras humain, sont des méthodes expérimentales basées sur la capture vidéo du mouvement et le traitement des séquences de ces vidéos enregistrées. Cet instrument nous a permis de tester plusieurs supports textiles destinés à l’habillement, pour extraire leur empreinte acoustique. La méthode de mesure par cet instrument consiste en l’obtention des spectres sonores obtenus par le frottement de deux échantillons de même support textile, qui seront ensuite traités et analysés pour avoir le niveau sonore et l’empreinte de la matière textile. Les résultats obtenus par cet instrument, selon des paramètres des essais fixés au préalable, montrent que le bruit généré par frottement textile /textile, devient plus intense, au fur et à mesure que la vitesse augmente (de la marche à la course) et l’intensité de ce bruit dépend aussi de la nature de la matière constituant le support textile. Ces résultats peuvent être révélateurs d’informations importantes sur les caractéristiques de tissu. Les essais de validation de cet instrument ont été faits en prenant uniquement des variations de vitesses de mouvement et de surface de frottement. Ainsi, cet instrument aide à créer un frottement similaire à la condition réelle du frottement de l’avant-bras. Dans cet esprit, on peut envisager d’utiliser cet instrument pour d’autres matériaux souples dans différentes conditions de vitesse, de surface et de pression de frottement et donc d’usage. / The objective of this study is to explore the possibilities to use acoustic method for fabric analysis. An experimental instrument was designed to study the noise generated by friction during body movement. It also allows simulating the motion of human forearm. Parameters of forearm movement were obtained by analyzing several recorded videos in sequences. Several clothing products have been tested by this instrument. The principle of this method is to obtain sound spectra created by friction between two same types of samples those have been further analyzed for the noise level and footprint of textile material. Different parameters of machine have been set before performing tests. Results depict for some fabrics that value of noise generated increases with the increase of movement speed (from walking to running). Intensity of noise mainly depends on nature of fabric’s raw material and can be influenced by speed and surface. These results indicate some very important information regarding fabric characteristics. The instrument has been validated and tested by changing two variables that are movement speed and surface friction maintaining pressure a constant. This instrument creates friction similar to real time friction produced during the movement of arm while walking or running. By using this concept, this instrument can be used for other flexible materials at different speeds, pressure and friction.

L'objectif de cette thèse est d'observer l'impact des coups de couteaux sur différents tissus en aramide et d'analyser les facteurs influents. On peut se défendre d'une attaque mais une blessure ne peut être complètement évitée. L'objectif est d'absorber un maximum d'énergie, de façon à réduire le risque de blessure. Les mécanismes de perforation par une lame sont complexes. L'étude a révélé une demande dans ce domaine, car la plupart des solutions proposent des armures lourdes contenant du textile. Cet assemblage de matériaux a des inconvénients, comme le poids trop élevé et le manque de souplesse. D'autres chercheurs recommandent des solutions textiles parce qu'elles sont souples et déjà utilisées dans le domaine balistique. Les recherches menées pour cette thèse ont pour but de contribuer au développement de types de textile résistant aux coups de couteaux. C'est la raison pour laquelle, non seulement les propriétés de la matière textile doivent être analysées, mais aussi l'attaque au couteau en elle-même, pour développer une meilleure protection. Il a été démontré que beaucoup de facteurs influent sur le niveau de protection et rendent sa perception difficile. Des recherches ont été réalisées pour évaluer les paramètres de test, qui sont définis dans le test standard, mais aussi pour ceux qui n'y sont pas définis. / The research goal of this thesis is to examine various aramid fabrics with regard to their stabbing behaviour and to find influencing factors to this. An attack can only be inhibited, but an injury cannot be completely prevented. The goal is always to absorb as much energy as possible, so that the penetration is thus reduced and the risk of injury decreases. The stab mechanism is a complex and variable process. The review showed the demand on research in this area, because the most solutions involve hard body armour parts in combination with fibrous materials. This material combinations show many disadvantages with regards to the high weight and the missing flexibility. Other researchers also recommend textile solutions, because they are flexible and in the field of ballistic panels they are already used. The investigations carried out within this thesis are done to contribute to the development of pure textile stab-resistant panels. Therefore the interdependencies between the physical properties of the material but also the mechanism during a stab attack have to be recognized, to developed higher protection levels. It was shown, that the multitude of factors causes the problem to define a level of protection. General investigations were done to analyse the test parameters, which are defined in the test standard but also this one, which are missing.

Ce travail de thèse est une contribution au développement des méthodes d’acoustique non linéaire pour le contrôle non destructif et l’imagerie de défauts de type contact dans les solides.Dans ce travail, des modifications sont proposées pour deux méthodes récentes de contrôle non destructif par acoustique non linéaire : l’interférométrie de coda couplée au retournement temporel, et l’imagerie non linéaire par ultrasons aériens. Le principal avantage de la première méthode est sa sensibilité extrême liée à l’accumulation des effets induits par des changements, même faibles, des propriétés de l’échantillon durant la formation de la coda. La deuxième méthode apporte une approche complémentaire en permettant de réaliser un contrôle sans contact. Les techniques développées ont été testées sur des échantillons présentant des défauts artificiels à des emplacements connus. Les performances de chacune des méthodes ont été étudiées.La deuxième partie de ce travail porte sur la description théorique des non-linéarités acoustiques de contact et leur utilisation pour le développement d’une boite à outils numériques permettant la simulation d’ondes acoustiques dans des structures complexes contenant des contacts internes. Un model physique décrivant le décalage tangentiel de deux corps en contact en présence de friction est proposé. Il aboutit à une solution analytique pour la relation présentant une hystérésis entre les déplacements de contact normal et tangentiel et les chargements. Ce modèle est utilisé comme condition aux frontières pour les surfaces de contact internes (défauts) dans un modèle de propagation d’ondes acoustiques utilisant un logiciel d’éléments finis commercial / This PhD thesis work contributes to the development of nonlinear elastic methods for non-destructive testing and imaging of contact-type defects in solids.In this work, two modifications of recent nonlinear nondestructive testing methods are suggested: the coda wave interferometry combined with the nonlinear time reversal principle and air-coupled nonlinear ultrasonic imaging. The principal advantage of former technique is in its extremely high sensitivity owing to the fact that weak changes in sample's parameters are accumulated and finally greatly amplified during the formation of the coda wave. The other technique has a complimentary strength and offers a possibility of a remote detection. The developed techniques are tested on samples with artificially fabricated defects at known locations. The performance of each method is accessed and the potential for obtaining robust nonlinear images is demonstrated.The second part of the work is concerned with a theoretical description of contact acoustical nonlinearity and its use for creating of a numerical toolbox capable of simulating wave propagation in complex structures containing internal contacts. A physical model describing the tangential shift of two contacting bodies in the presence of friction has been proposed. Its result is an analytical computer-assisted solution for hysteretic relationships between normal and tangential contact displacements and loads. The contact model and derived load-displacement relationships are used as boundary conditions posed at the internal boundaries (contact surfaces) in a finite element wave propagation model programmed via commercial software

Cette thèse étudie les instabilités dynamiques des milieux granulaires modèles saturés à l’aide d’un appareil triaxial classique. Les instabilités englobent la liquéfaction et les effondrements en compression isotrope drainée, les frottements saccadés en compression triaxiale drainée. Ces instabilités apparaissent spontanément à des contraintes effectives de confinement imprévisibles. Elles sont accompagnées de très rapides et très fortes surpressions interstitielles, malgré un drainage approprié; ce que ne présentent pas les milieux granulaires naturels. En compression isotrope drainée (consolidation), des effondrements locaux naissent instantanément. En compression triaxiale drainée, on observe de larges frottements saccadés quasi-périodiques caractérisés par des déformations volumiques et axiales contractantes. De temps en temps, ces effondrements et frottements saccadés locaux peuvent se développer en liquéfaction menant à une destruction complète de la structure granulaire. Les données à haute résolution temporelle issues de ce travail ont permis la découverte d’une nouvelle famille de liquéfaction dynamique et statique. L’étude des émissions acoustiques passives a permis l’identification de signature spectrale caractéristique. Pour les frottements saccadés, la phase de glissement peut être interprétée comme une consolidation dynamique, limitée par l’unique surface en dessous de la ligne critique de rupture dans le plan des contraintes effectives. La séquence temporelle précise des événements exclut que la pression interstitielle soit la cause principale des instabilités. Cependant, le rôle important de la surpression interstitielle est démontré dans des relations quantitatives entre les incréments de contraintes, et de déformations et l’éphémère surpression interstitielle stabilisée développée pendant la phase de glissement. Cela montre finalement la nature quasi-déterministique de ces instabilités dynamiques. Ces relations empiriques sont basées uniquement sur l’amplitude maximale de l’accélération verticale de très courte durée et sont gouvernées indépendamment par la pression de confinement et par l’indice des vides. La similarité de la surpression interstitielle entre différentes instabilités suggère fortement quelques mécanismes similaires de déclenchement, probablement à partir de ré-arrangements de la micro-structure granulaire. / This thesis reports a laboratory study on the dynamic instabilities of model saturated granular material using a triaxial apparatus. The term instability consists of isotropic collapse and liquefaction under isotropic compression and of stick-slip under triaxial compression in drained condition. The instabilities spontaneously occur at unpredictable effective stress with unexpected buildup of excess pore pressure irrespective of fully drained condition, contrasting with the instability-free behaviour of natural granular materials. In isotropic compression, instantaneous local collapse happens and in triaxial compression, very large and quasi-periodic stick-slip occurs with sudden volumetric compaction and axial contraction. Sometimes, these local failures (collapse and stick-slip) can develop into total liquefaction failure, destroying completely the granular structure. High time-resolved data permit the discovery of a new family of dynamic and static liquefaction. Passive acoustic measurements allow the identification of typical spectral signature. For stick-slip phenomenon, the slip phase with constant duration of stress drop can be interpreted as dynamic consolidation at constant deviatoric stress, limited by a unique boundary inside the critical state line in the effective stress plane. The precise temporal sequence of mechanical measurements excludes the generated pore pressure as the main cause of the instabilities. However, the role of pore pressure is emphasised by consistent quantitative relations between the amplitude of incremental stresses, incremental strains and the ephemeral stabilised excess pore pressure developed during the dynamic event, leading to the quasi-deterministic nature of granular instabilities. These empirical relations are based only on the short-lived maximum vertical acceleration and governed separately by the confining pressure and the initial void ratio. The similarity of pore pressure evolution for different kinds of instability strongly suggests some common speculative triggering mechanisms, probably originated from different rearrangements of the granular micro-structure.