Slip dynamics at an interface between dissimilar materials

It has been shown recently that steady frictional sliding along an interfac e between dissimilar elastic solids with Coulomb friction acting at the int erface is ill-posed for a wide range of material parameters and friction co efficients. The ill-posedness is manifest in the unstable growth of interfa cial disturbances of all wavelengths, with growth rate inversely proportion al to the wavelength. We first establish the connection between the ill-pos edness and the existence of a certain interfacial wave in frictionless cont act, called the generalized Rayleigh wave. Precisely, it is shown that for material combinations where the generalized Rayleigh wave exists, steady sl iding with Coulomb friction is ill-posed for arbitrarily small values of fr iction. Tn addition, intersonic unstable modes and supersonic steady-state modes exist for sufficiently large values of the friction coefficient. Seco ndly, regularization of the problem by an experimentally motivated friction law is studied. We show that a friction law with no instantaneous dependen ce on normal stress but a simple fading memory of prior history of normal s tress makes the problem well-posed. (C) 2001 Published by Elsevier Science Ltd.