A multiscale analysis of elastic contacts and percolation threshold for numerically generated and real rough surfaces

In this paper, we present numerical investigation of the contact between an elastic solid and a randomly rough surface. In agreement with recent results, we find that the contact area vs load relation depends on the statistical parameters only through the root mean square slope of the heights distribution. Such result extends to contact pressure regimes where the area/load relation is non-linear. Moreover, we show that fractal self-affine surfaces give a good representation of real surfaces from both topographical and contact mechanics points of view. Finally, we investigate how the network of non-contact areas evolves as the real contact area is increased, finding that the percolation threshold is smaller than the one predicted by Bruggeman's theory