Subsonic slip waves and steady sliding at the interface between two anisotropic elastic half-spaces in frictional contact with stick–slip

Abstract

The theoretical study is presented on the existence and behaviors of slip waves along a frictionally contact interface between two similar or dissimilar anisotropic solids which are pressed together by remote pressure and meanwhile sheared by remote shearing traction. We consider the wave motion in a symmetry plane perpendicular to the interface and thus the in-pane motion is uncoupled with the anti-plane motion. The external loads may or may not lead to steady rigid sliding between two solids, while the separation of the interface is excluded by assuming the applied pressure is large enough. The local stick–slip motion without local separation at the frictionally contact interface caused by the perturbed slip waves is studied. The Stroh formalism, together with the concept of the surface impedance tensor is employed. The boundary value problem involving unknown slip/stick zones is cast to a Hilbert singular integral equation with an unknown integral interval. The explicit solutions representing the slip waves are obtained. The existence and behaviors of such slip waves are discussed based on theoretical and numerical analysis. For the case of no initial steady sliding between two solids (i.e., the applied shearing traction is lower than the interface friction force), slip waves which are singular at one end of the slip zone may propagate. For the case of initial steady sliding (i.e., the applied shearing traction can break the interface friction), no such slip waves exist.