Dynamic Motion of Two Elastic Half-Spaces in Relative Sliding Without Slipping

Abstract

Two isotropic linear elastic half-spaces of different material properties are pressed together by a uniform pressure and subjected to a constant shearing stress, both of which are applied far away from the interface. The shear stress is arbitrarily less than is required to produce slipping according to Coulomb’s friction law. Nonetheless, it is found here that the two bodies can slide with respect to each other due to the presence off a separation wave pulse in which all of the interface sticks, except for the finite-width separation-pulse region. In this type of pulse, the separation zone has a vanishing slope at its leading edge and an infinite slope at its trailing edge. Nonetheless, the order of the singularity at the trailing edge is small enough so as not to produce an energy sink. The problem is reduced to the solution of a pair of singular integral equations of the second kind which are solved numerically using a variation of the well-known method of Erdogan et al. (1973). Results are given for various material combinations and for a range of the remote shear-to-normal-stress ratio.