Asymptotic solutions for generalized thermoelasticity with variable thermal material properties

Abstract

In this paper, a unified generalized thermoelastic solution with variable thermal material properties is proposed in the context of different generalized models of thermoelasticity, including thermoelasticity with one thermal relaxation time (LS theory), thermoelasticity with two thermal relaxation times (GL theory) and thermoelasticity without energy dissipation (GN theory). The unified form of governing equations is presented by introducing unifier parameters. The unified formulations are derived and given for isotropic homogenous materials with variable thermal material properties. The Laplace transform techniques and the Kirchhoff’s transformation are used to obtain general solutions for any set of boundary conditions in the physical domain. Asymptotic solutions for a specific problem of an elastic half-space with variable thermal conductivity and a specific heat, whose boundary is subjected to a thermal shock, are derived by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, some generalized thermoelastic phenomena are observed. Especially, the jumps at the wavefronts induced by the propagation of finite signal speed for the heat are clearly noticed. In addition, the effect of variable characteristics of material properties on thermoelastic behaviors is revealed by a comparison with the results obtained in the case of constant material properties.