On the propagation of transients through thermoviscoelastic media

Abstract

We examine the propagation of thermal and mechanical transients through general linear thermoviscoelastic media. A linear theory of heat conduction in deformable materials with memory is employed to study the one-dimensional problem of a homogeneous thermoviscoelastic half-space subjected to thermal and mechanical disturbances at its boundary. A ray series approach is used to generate asymptotic wave front expansions for the temperature, strain, and stress response of the medium to the disturbances. General properties of the propagation process are obtained simply and directly. As an example, we specialize the solution to the case of a medium where the conduction of heat obeys Cattaneo’s law and the viscoelastic response is that of a standard linear solid. The propagation of transients through this material is depicted graphically for various values of the thermal and mechanical parameters.