On undamped heat waves in an elastic solid

TLDR: In this article, the authors focused on the thermal properties of the constitutive response functions in the context of both nonlinear and linear theories, and provided an easy comparison of the one-dimensional version of the equation for the determination of temperature in the linearized theory.

Abstract: This paper is concerned with thermoelastic material behavior whose constitutive response functions possess thermal features that are more general than in the usual classical thermoelasticity. After a general development of the constitutive equations in the context of both nonlinear and linear theories, attention is focused on the latter. In particular, the one-dimensional version of the equation for the determination of temperature in the linearized theory provides an easy comparative basis of its predictive capability: In one special case where the Fourier conductivity is dominant, the temperature equation reduces to the classical Fourier law of heat conduction, which does not permit the possibility of undamped thermal waves; however,'in another special case in which the effect of conductivity is negligible, the equation has undamped thermal wave solutions without energy dissipation.