General contact mechanics theory for randomly rough surfaces with application to rubber friction

We generalize the Persson contact mechanics and rubber friction theory to the case where both surfaces have surface roughness. The solids can be rigid, elastic, or viscoelastic and can be homogeneous or layered. We calculate the contact area, the viscoelastic contribution to the friction force, and the average interface separation as a function of the sliding speed and the nominal contact pressure. We illustrate the theory with numerical results for the classical case of a rubber block sliding on a road surface. We find that with increasing sliding speed, the influence of the roughness on the rubber block decreases to the extent that only the roughness of the stiff counter face needs to be considered.