Interfacial elastic waves and frictional slip instabilities

Elasticity theory permits several interfacial wave solutions. In anti-plane elasticity, the Love wave occurs in bonded contact of an elastic layer on a dissimilar elastic half-space. In in-plane elasticity, the slip wave (also called the generalized Rayleigh wave) exists at a freely slipping interface between dissimilar elastic half-spaces, and the Stoneley wave occurs in bonded contact of dissimilar elastic half-spaces. It is shown that these interfacial elastic waves are often destabilized when frictional slipping occurs. Simple friction models such as the Coulomb law, as well as experimentally motivated rate- and state-dependent friction laws will be considered. With the Coulomb law, destabilization of the slip wave occurs at short wavelengths. Regularization procedures in such cases will be discussed. Long wavelength Love and Stoneley waves are also shown to be destabilized in slow sliding when a rate- and state-dependent friction law acts at the interface, indicating that the quasi-static limit is not attained in slow sliding.