Incipient sliding of rough surfaces in contact: a multiscale numerical analysis

In this paper, the Cattaneo theory of frictional contact is extended to elastic half-spaces in contact through rough disordered interfaces. The discrete version of the Cattaneo theorem is provided, and represents the basis of a multiscale numerical contact algorithm. Mathematical surfaces with imposed roughness, as well as experimentally digitised ones, are analysed. By means of a numerical method, the evolution of the contact domain, at different resolution, is investigated. Roughness of the interfaces provides lacunarity of the contact domains, whose fractal dimension is always smaller than 2.0. When a tangential force is applied, the extent of the stick area decreases in the same way as the contact area develops with increasing pressure, and the slip area is found to be proportional to the tangential force, as predicted by Cattaneo theory. The evolution of the shear centroid, as well as the amount of dissipated energy up to full-sliding, are provided. Finally, it is shown that, at a sufficient level of discretization, the distribution of contact pressures is multifractal.