Implicit constitutive relations in thermoelasticity

In this paper, after a brief discussion on the implicit constitutive relations used in thermoelasticity, based on Fox’s [1] work, we derive a general implicit relation for the heat flux vector. In the section following that we use the methodology suggested by Rajagopal [2] and [69] whereby we derive a class of implicit constitutive relations for q and we show that by selecting appropriate functions appearing in the formulation, we can obtain as special cases the Fourier heat conduction and the Maxwell–Cattaneo–Fox model. We do not discuss the implications of the second law of thermodynamics.