Nonlinear Interaction of an Elastic Pulse With a Frictional Contact Interface Between Two Anisotropic Dissimilar Media

Abstract

The paper analyses the interaction of an elastic pulse of arbitrary form with a frictional contact interface between two anisotropic solids which are pressed together and at the same time loaded by the in-plane and anti-plane shearing tractions. The incident pulse is assumed strong enough to break friction so that localized separation and slip take place. Coulomb friction, which causes the non-linear coupling between the in-plane and anti-plane motions, is supposed along the contact interface. The sub-critical angle incidence is first considered. By using Fourier analysis, the problem is reduced to a set of algebraic equations. A method to get the solution of the equations with determination of the slip/stick/separation zones is developed. As an example, the detailed computation for the case of an incident parabolic stress pulse is carried out. Numerical results of the interface tractions and the slip velocities are presented for two contacting half-spaces of the same materials in the same orientation. The super-critical angle incidence is discussed. In this case the problem is cast to a set of non-linear Cauchy singular integral equations whose solution is still an open question in mathematics.