Transverse and normal interfacial stiffness of solids with randomly rough surfaces.

Using a theoretical approach and computer simulations, we calculate the normal stiffness K(perpendicular) and the transverse stiffness K(parallel) of the interface between two contacting isotropic solids with randomly rough surfaces and Poisson ratio ν. The theoretical predictions for K(perpendicular) agree well with the simulations. Moreover, the theoretical result for the ratio K(perpendicular)/K(parallel) is (2 - ν)/(2 - 2ν), as predicted by Mindlin for a single circular contact region. Finally, we compare the theory to experimental ultrasonic data.