Exact solution of the coupled thermo–viscoelastic problem for the semi-infinite space

Abstract

We present an exact analytical solution of the periodic time-dependent thermo-viscoelastic problem for the infinite half space with traction-less surface and a volume heat source arising from laser penetration. We take into account the extension of the heat source, the mutual dependence of heat transfer and elasticity and the viscosity of the material, to describe damping of elastic waves, and in particular surface waves for periodic driving. The solution of the heat equation (including temperature change caused by compression/dilatation of the material) is also provided and a numerical example for aluminium, where this is demonstrated, is given.