Dilatational and shear waves induced by the frictional sliding of two elastic half-spaces

Abstract

The nominally steady-state frictional sliding of two flat elastic half-spaces is investigated. It is shown that steady sliding is compatible with the formation of a pair of body waves (dilatational and shear) in each body radiated away from the sliding interface. Each wave propagates at a different angle such that the trace velocities along the interface are equal. The angles of propagation are determined by the material properties and by the coefficient of sliding friction. The wave amplitudes are subject only to the restriction that the perturbations in interface contact pressure and relative tangential velocity satisfy the inequality constraints for unilateral sliding contact. Furthermore these waves are shown to exist for a variety of frictional sliding laws, including speed-dependent and speed-independent friction. Finally it is shown that a slip pulse can exist which allows the two bodies to undergo relative tangential motion with a ratio of applied shear to normal stress which is less than the friction coefficient.