Combined thermodynamics approach for anisotropic, finite deformation overstress models of viscoplasticity

An anisotropic finite deformation thermodynamic framework is developed that admits most of the models within the class of unified viscoplasticity approaches, applying to representations of the behaviors of polymers, metals and their composites. The importance of changing natural configurations as a driver for dissipation is emphasized, as is the specification of constitutive behaviors via the energy and dissipation functions. In a sequential application of thermodynamic approaches, Caratheodory’s lemma is first applied to establish traditional potential relations for the stress and entropy, followed by application of the Coleman–Noll approach to deduce that evolution functions related to the rates of the independent variables must be associated with reversible, non-dissipative changes. The principal of maximum dissipation is lastly applied to deduce the flow rule, identify dissipative behaviors, and deduce interrelationships between the independently-specified energy and dissipation functions. A simplified case is described that illustrates these interrelationships and their compatibilities with the proposed framework.