Stick-slip waves between elastic and rigid half-spaces

This paper is devoted to the construction of analytic solution of stick-slip waves crossing the interface between an elastic half-space and a rigid one under unilateral contact and Coulomb friction. The method of solution is based on the analytic continuation method of Radok's complex potentials within the framework of steady elastodynamical problems. The governing equations combined with the boundary conditions are reduced to a RiemannHilbert problem with discontinuous coe cient and closed-form expressions of the solution are derived. It is found that the existence of solutions depends on the additional velocity V which is related to the longitudinal elongation. If V is ignored (V = 0) then there is no solution, if not (V 6= 0) then it is possible to construct weakly singular solutions satisfying all stick-slip conditions except over a narrow zone where the waves exhibit a crack-like behaviour.