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We generalize the Persson contact mechanics and rubber friction theory to thecase where both surfaces have surface roughness. The solids can be rigid,elastic or viscoelastic, and can be homogeneous or layered. We calculate thecontact area, the viscoelastic contribution to the friction force, and theaverage interfacial separation as a function of the sliding speed and thenominal contact pressure. We illustrate the theory with numerical results for arubber block sliding on a road surface. We find that with increasing slidingspeed, the influence of the roughness on the rubber block decreases, and fortypical sliding speeds involved in tire dynamics it can be neglected.

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