On the transient planar contact problem in the presence of dry friction and slip

This article models a plane strain dynamic contact problem for an infinite elastic body. Contact is established for x > 0 under the action of a time-dependent remote compressive load, and the system is subjected to a time-dependent remote tangential load. The two faces of the contact interface can slide relative to one other to accommodate mismatches between the shear stresses and the existing Coulomb friction. This is shown to be a cause of interfacial waves of slip, which this article models by deriving the general expression for the corrective traction due to an arbitrary slip distribution. This is achieved using a variant of the Wiener-Hopf technique. Combined with existing closed-form expressions for the interfacial tractions due to compressive and shear loads, this enables the formulation of the elastodynamic extension to the stick-and-slip problem of the Cattaneo-Mindlin type. Exploiting self-similarity a simple numerical algorithm is detailed for solving the resulting Volterra integral equations of the first kind. The solution is shown to display a number of features entirely missed in static problems: slip waves are shown to exist irrespective of the magnitude of the applied loads and the friction coefficient; a regime of reverse and forward slip is also shown to exist for low friction coefficients, brought about by the interfacial Rayleigh waves. The practical implications of these solutions are discussed.