The thermodynamics of Maxwellian materials

Abstract

In this paper, we study the thermodynamics of a class of nonlinear dissipative materials frequently called Maxwellian materials. Using the Clausius-Duhem inequality, we establish the restrictions on the constitutive equations and show that in non-equilibrium situations the stress behaves in a manner similar to an internal state variable. We further show that the stress relaxation function for the material must satisfy a dissipation inequality, and that, if all equilibrium states of the material are asymptotically stable, the stress relaxation function is an odd function of the overstress σ − ̄∗*, where ̄∗* is the equilibrium stress. In addition, we consider the instantaneous and equilibrium responses of the material and prove that in these situations both the stress and the temperature are deriveable from the internal energy function. Finally, we consider briefly an example of a specific constitutive model and close with a discussion of an alternative formulation of the general theory in which the roles of stress and temperature are interchanged.