Elastic instabilities at a sliding interface

I consider a semi-infinite elastic solid sliding on a flat hard substrate. I present a linear instability analysis to determine when the steady sliding motion becomes unstable with respect to infinitesimal perturbations. I consider a general case where the interfacial frictional shear stress depends not only on the sliding velocity but also on a state variable. I show that when the pressure in the contact area between the solids is constant, no linear instability occurs if the kinetic friction coefficient increases monotonically with the sliding velocity, $d{\mu }_{\mathrm{k}}{/dv}_0>0.\mathrm{}$ However, when the pressure at the interface varies spatially, elastic instabilities may also occur when $d{\mu }_{\mathrm{k}}{/dv}_0>0.\mathrm{}$ I discuss the physical origin of this effect, and suggest that these instabilities may be precursors of the Schallamach waves.