An analytic solution to a driven interface problem

The frictional properties of sliding metal interfaces at high velocities are not well known from either an experimental or theoretical point of view. The constitutive properties and macroscopic laws of frictional dynamics at high velocities necessary for materials continuum codes have only a qualitative validity and it is of interest to have analytic problems for sliding interfaces to enable separation of model from numerical effects. The authors present an exact solution for the space and time dependence of the plastic strain near a sliding interface in a planar semi-finite geometry. This solution is based on a particular form for the strain rate dependence of the flow stress and results in a hyperbolic telegrapher equation for the plastic strain. The form of the solutions and wave structure will be discussed.