On the thermodynamic framework of generalized coupled thermoelastic-viscoplastic-damage modeling

A complete potential based framework utilizing internal state variables is put forth for the derivation of reversible and irreversible constitutive equations. In this framework, the existence of the total (integrated) form of either the (Helmholtz) free energy or the (Gibbs) complementary free energy are assumed a priori. Two options for describing the flow and evolutionary equations are described, wherein option one (the fully coupled form) is shown to be over restrictive and the second option (the decoupled form) provides significant flexibility. As a consequence of the decoupled form, a new operator, that is, the compliance operator, is defined, which provides a link between the assumed Gibb's and complementary dissipation potential and ensures a number of desirable numerical features, for example, the symmetry of the resulting consistent tangent stiffness matrix. An important conclusion reached is that although many theories in the literature do not conform to the general potential framework outlined, it is still possible in some cases, by slight modifications of the employed forms, to restore the complete potential structure.