Thermodynamics of Materials with Memory

We now apply thermodynamic principles to field theories with memory. For general nonlinear, nonisothermal theories, we assume that a free energy is given, this being the fundamental constitutive assumption. Applying a generalization of the approach of Coleman [36], Coleman and Mizel [38], Gurtin and Pipkin [130], we derive the constitutive equations for the theory in Section 5.1. Also, fundamental properties of free energies are derived. Furthermore, some observations are made on the case of periodic histories and in relation to constraints on the nonuniqueness of free energies. In Section 5.2, an expression for the maximum recoverable work is given for general materials, together with an integral equation for the process yielding this maximum. Finally, in Section 5.3, we discuss how free energies can be constructed from combinations of simpler free energies.