On the coupled heat equation of linear thermoelasticity

The presence of the coupling term in the coupled heat equation of linear thermoelasticity is quite undesirable. Beyond causing heat transfer to be coupled to the deformation, it is shown that it causes the internal energy to be singular in the isothermal limit where it does not go over continuously to its pure theory of elasticity form. This is very much unlike classical fluid mechanics in which the isothermal limit is regular in so far as the internal energy is concerned. It is shown that as long as the deformation does not contain high frequency vibrations, the coupling term can be dropped and the singularity can be removed. This is proven by a careful order of magnitude analysis of the governing equations and is a valid approximation for the overwhelming majority of phenomena. It is a desirable approximation to make that has been commonly made in the literature in the past anyhow. The full implications of these results for research in thermoelasticity are thoroughly discussed.