On the stability of transient bimaterial contact in the presence of dry friction and slip

An analytic formulation for the study of planar elastodynamic contact in bimaterial interfaces subject to dry friction and slip is presented. Using the Wiener–Hopf technique, explicit analytical expressions for the elastic waves scattered by a planar contact interface are derived. Two cases are studied: (1) the uncoupled problem where it is assumed that normal and tangential loads cause, respectively, no tangential and vertical displacements; (2) the fully coupled problem, where they do. In both cases, an analytic formulation for determining the magnitude of the regions of stick and slip expected at the interface is offered. This provides a complete analytic account of the interfacial tractions and, as a results, serves to model the elastic wave scattering by contact interfaces, a problem of interest in fields as disparate as geophysics, non-destructive testing, and fracture mechanics. The uncoupled problem is shown to be inconsistent: the magnitude of the reciprocal displacements caused by the normal/tangential loads is non-negligible, and of the same magnitude as the interfacial slip distribution itself. The coupled problem is shown to lead to a matricial Wiener–Hopf problem the scattering kernel of which is non-commutative; an Abrahams approximation reliant on the Padé approximants is used to study the problem. It is shown that in many circumstances, the bimaterial contact interface is bound to detach locally, even when the far-field, steady-state solutions would predict otherwise. This is brought about by interfacial loading mismatches brought about by the coupling, and is shown to be affected by various factors: weak pressure loads, the friction coefficient, the disparity in the elastic constants of the media under contact. An useful analytic criteria for detachment is offered.