Finite-element analysis of contact between elastic self-affine surfaces

Finite element methods are used to study contact between elastic solids with self-affine surfaces. The total contact area rises linearly with load at small loads. There is a constant mean pressure in the contact regions that is proportional to the rms slope of the surface. The constant of proportionality is nearly independent of Poisson ratio and roughness exponent and lies between previous analytic predictions. The contact morphology is also analyzed. Connected contact regions have a fractal area and perimeter. The probability of finding a cluster of area $a_c$ drops as $a_c^{-\tau}$ where $\tau > 2$ and increases with decreasing roughness exponent. The distribution of pressures shows an exponential tail that is also found in many jammed systems. These results are contrasted to simpler models and experiment.