LINEAR DYNAMIC THERMOELASTICITY - A SURVEY.

This survey presents a historical development of linear dynamic thermoelasticity over the last 30 years. A linear theory of unsteady heat conduction is combined with elastodynamics to describe thermomechanical processes in a solid body. Because of the complicated structure of the governing equations, only a few one-dimensional initial-boundary value problems have thus far been solved in a form that allows their complete analysis. A relatively large number of problems that have been solved successfully concern periodic thermoelastic disturbances. The reason is that the periodicity hypothesis allows the reduction of the governing equations to the classical Helmholtz equations with complex-valued wave numbers and to application of the methods of classical elastodynamics to solution of actual problems. The survey also includes descriptions of fundamental results and of a basic system of field equations for dynamic thermoelasticity with relaxation times. Suggestions concerning areas of the theory that are critically in need of further investigations are given.