Some basic theorems on a recent model of linear thermoelasticity for a homogeneous and isotropic medium

Abstract

This paper investigates a thermoelasticity theory based on the recent heat conduction model proposed by Quintanilla (Mech Res Commun 2011; 38: 355–360). Taylor’s expansion of this model leads to an interesting problem of heat conduction. Serious attention has been paid by researchers in the last few years to investigating various heat conduction models. We have considered this newly proposed model of heat conduction given by Quintanilla and employed for coupled thermoelastic problems. We derive the basic governing equations for a homogeneous and isotropic medium and aim to derive some important theorems. Firstly, the uniqueness theorem of a mixed initial and boundary value problem of linear thermoelasticity in the present context is proved. A variational principle is derived for the basic governing equations of motion on the basis of a functional in the context of the present problem. A reciprocity theorem is established by using Laplace transformation. Furthermore, generalization of Somigliano and Green’s theorem for this model is proved on the basis of our reciprocity relation.