Cyclic micro-slip and energy dissipation on elastic rough interfaces

A numerical model based on the solution of the normal contact between elastic half-spaces and subsequent post-processing according to the Mindlin and Deresiewicz solution for cyclic tangential loading is presented. Thanks to a recent extension of the Cattaneo-Mindlin analogy to the solution of tangential contact between non-convex domains, the proposed approach enables the study of cyclic micro-slip and energy dissipation between elastic bodies with general shapes in contact. In order to make the procedure straightforward and as general as possible, a non-dimensional formulation, based only on the normal contact load displacement curve, is proposed. The cyclic behaviour of the tangential contact of self-affine fractal surfaces, like those generated by fracture of concrete or rock, is described with several examples. An interpretation of the behavior of cyclic micro-slip in the framework of shakedown phenomenon is finally proposed.