Pulse propagation in heat-conducting elastic materials

The influence of second-order effects on the propagation of a weak dilatational stress pulse in a heat-conducting elastic material is investigated. As a first approximation, the problem is studied using the linear theory of thermoelasticity. It is found that thermal diffusion dominates the wave motion, and a time is reached when second-order terms must be considered. The wave motion is then found to be isentropic and the shock structure is governed by Burgers's equation. Solutions to this equation are obtained and the influence of heat-conduction on pulse propagation in elastic materials is discussed, with some numerical results being presented for copper. Also, previous work in linear thermoelasticity theory is clarified and related to known results in linear and nonlinear elastodynamics.