The problem of a rigid punch sliding on an elastic or a viscoelastic layer

Abstract

The problem of a rigid punch moving over a general anisotropic viscoelastic medium is considered both for the case where the medium is a finite layer and where it is an infinite half-space. Formal equations are derived, using Fourier Transform techniques, for the most general case where no assumptions are made concerning the shape of the punch. However, attention is then focussed on the case where the punch is uniformly infinite in one direction. Both the general inertial problem and the non-inertial approximation are considered for the half-plane problem. Previously known results are shown to emerge from the general formalism with relative ease. The general viscoelastic problem is shown to be formally identical to the isotropic problem treated in [1] though algebraically far more complex. In the non-inertial approximation, however, the extra complexity is not great, and in particular, if all the viscoelastic functions are assumed to have similar time behaviour, the resulting equations are essentially no more complex than the isotropic equations solved in [2]. For this case, the relationship between the hysteretic friction coefficients along the two axes of anisotropy on an orthotropic medium is quantified. Displacementtraction relationships are given for an isotropic layer, including inertial effects and some numerical results are given for the thick elastic layer problem.