The actual contact between solid surfaces is generally rough and time dependent. The stresses induced by the rough contact can only be correctly described using a detailed 3D model. Even finer details are required in the case of surface coatings. Consequently, the rough coated contact problem is strongly multi-scale: the characteristic dimensions of the contact, the coating and the roughness range from the millimeter to the nanometer. A straightforward discretisation of this multi-scale problem would exceed the memory and CPU capacity of current (and next generation) computers. This paper proposes an efficient numerical model that can handle this multi-scale problem: using 109 points and locally refined grids. The proposed model is based on multigrid techniques within a finite difference frame work. Localised refinement is implemented to optimize memory requirement and computing time. Validation of the solver is performed through a comparison with analytical results for simple cases. The algorithm performance is analyzed through a parametric study describing the influence of layer thickness (0.01 < t/a < 10) and mechanical properties (0.005 < Ec/Es < 10) of the coating on the contact parameters (Ph, a). A linear graded coating, used as a solution to avoid interfacial problems, is then compared to a coating with constant properties. A quantitative analysis of the evolution of the maximum tensile stress with depth is conducted in both cases.

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