The Sliding With Coulomb Friction of a Rigid Indentor Over a Power-Law Inhomogeneous Linearly Viscoelastic Half-Plane

Abstract

In a previous paper, the title problem was solved for a homogeneous power-law linearly viscoelastic half-plane. Such material has a constant Poisson’s ratio and a shear modulus with a power-law dependence on time. In this paper, the shear modulus is assumed also to have a power-law dependence on depth from the half-plane boundary. As in the earlier paper, only a quasi-static analysis is presented, that is, the enertial terms in the equations of motion are not retained and the indentor is assumed to slide with constant speed. The resulting boundary value problem is reduced to a generalized Abel integral equation. A simple closed-form solution is obtained from which all relevant physical parameters are easily computed.