Viscothermoelasticity with finite wave speeds: thermomechanical laws

Abstract

The development of constitutive equations of linear viscothermoelasticity, free of the paradox of infinitely fast propagation of heat, is in the focus of this work. Two models from hyperbolic thermoelasticity—theory with one relaxation time and theory with two relaxation times—provide the stepping-stone. The setting for these models is offered, respectively, by the primitive thermodynamics of Edelen and the thermodynamic orthogonality of Ziegler, in both cases involving internal parameters. The telegraph-like heat conduction is governed in the first case by the Maxwell–Cattaneo model and in the second by the Fourier law. In the first case, temperature and its first derivative appear in the thermomechanical constitutive relation, whereas in the second case also the second derivative is present.