Generalised Thermo-Elasticity When the Material Coupling Parameter Equals Unity

Abstract

Analytical solutions of three problems using the theory of generalised thermo-elasticity are presented for the case when the material coupling parameter equals unity (lambda =1). The problems considered are (1) Constant velocity impact, (2) Daniloviskaya's problem, and (3) Step in strain. Solutions are presented for the case of thin bars (one dimensional stress) and are obtained using Laplace transform. There is a great simplification in the equations of generalised thermo-elasticity when the material coupling parameter equals unity, which permits the straight forward inversion of the transformed solutions. The solutions obtained are more general which includes the effect of relaxation time also. The important feature of this paper is that the solutions of coupled theory can be readily obtained simply by putting the relaxation constant equals to zero (Beta=0).