Contact mechanic problems are multi-scale and involve numerous physical phenomena. These problems have been studied since the end of the XIXth century and major developments have been made during the XXth century due to the necessity for engineers to predict material behavior under tribological loads. Currently, industrial demands and technological breakthroughs drive people to consider three-dimensional simulations to study this behavior under thermo-mechanical loads. The objectives are multiple: reduce of the size of structures, increase of material resistance, improvement of fatigue life... These simulations, which often require high numerical costs in terms of memory size and CPU time, have to be performed on super computers. In this context, this work proposes an innovative model based on multigrid methods using a local refinement strategy in order to perform these simulations at a low numerical cost. The model is based on the Lamé elasticity equations and the Fourier heat equation which have been discretized using a finite difference framework. The obtained linear system is solved using the Gauss-Seidel iterative method coupled with multigrid techniques. These methods allow an acceleration of the convergence speed, using different grids and transfer operators. In order to obtain an optimum convergence speed and decrease the required memory size, local refinement strategies and optimization techniques have been used. Several calculations required hundred millions of points, can be solved on a personal computer within a few hours. Applications focus on the use of a coating or innovative materials which allow improvements in terms of fatigue life. The model has been validated against results found in the literature. Parametric studies allowed to analyse the influence of the coating thickness, the Young's modulus ratio or the use of a graded layer on the stress field and on the coating/substrate system behaviour under contact loads. Similar studies have been performed under thermal loads. Special attention has been paid to the material property variations along all space directions. It has lead us to consider a material microstructure which is composed of grains with their individual properties. The influence of the microstructure on the fatigue life phenomenon is clearly highlighted using statistical Weibull charts. The dispersion observed in the numerical results tends to be similar to experiments found in the literature.
