A Multi Resolution Study on the Behavior of Fractal Interfaces with Unilateral Contact Conditions

In this paper, the influence of the resolution of fractal interfaces to the contact area is investigated by taking into account shear displacements. The paper is based on fractal approaches for the modeling of the multiscale self-affine topography of these interfaces where unilateral contact conditions are assumed to hold. More specifically for every value of the shear displacement a solution is taken in terms of normal forces and displacements at the interface, for different values of the resolution delta and for different values of normal forces. At each scale a classical Euclidean problem is solved. This procedure is applied for the simulation of a unilateral contact problem between two elastic bodies and between two bodies with elastoplastic behavior with hardening. In both cases the same fractal interface is adopted and the same multi-resolution analysis has been performed.