Functionally graded materials (FGMs) are advanced materials and their main characteristic is microstructure and composition variation over the volume of the specimen. This variation of the composition results in changing of material properties in the component. In FGMs usually there are two different types of powder materials such as metal and ceramic powders which are mixed to build up the graded region. These grade layers are placed between the metal and ceramic layers and by this approach a smooth and gradual transient from metal to ceramic can be achieved.Sintering is the main technique to manufacture these types of materials. During the sintering process, cooling of the specimen from sintering temperature to room temperature results in generation of thermal residual stresses within the material. These thermal stresses may cause crack propagation and failure of the material.Distribution analysis of these thermally induced stresses within the material has been carried out in this thesis work. Finite element package ABAQUS has been used in order to simulate the distribution of the thermal residual stresses in the materials. In order to achieve the optimal design for different geometries the parametric study also has been performed. For example influence of number of layers, mixing ratio and porosity has been investigated.Based on the finite element results for cylindrical and cuboid models, non-linear composition variation for both geometries has no improving effect in terms of induced thermal residual stresses. Porous material shows less thermal stress than non-porous material. As the amount of porosity for individual layer was considered in simulation process, this approach resulted in decreasing of thermal stresses within the material. Moreover, non-uniform thickness of graded layers was not beneficial for stress reduction. This variation of thickness results in increasing of thermal residual stresses within the material.

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