A thermodynamic framework is presented for the theory of Viscoplasticity Based on Overstress (VBO) developed by Krempl and co-workers (Krempl, E., and Ho, K., 2001, in Lemaitre Handbook of Materials Behavior Models, Academic Press, New York, pp. 336–348; 2000, in Time Dependent and Nonlinear Effects in Polymers and Composites, ASTM STP 1357, Schapery, R. A., and Sun, C. T., eds., ASTM, West Conshohocken, PA, pp. 118–137; Cernocky, E. P., and Krempl, E., 1979, Int. J. Non-Linear Mech., 14, pp. 183–203; Gomaa et al., 2004, Int. J. Solids Struct., 41, pp. 3607–3624), for anisotropic materials and small deformations. A Caratheodory-based approach is applied to demonstrate the existence of entropy and absolute temperature, as previously described by Hall (2000, Compos. Sci. Technol., 60, pp. 2581–2599). The present framework indicates that the stress rate-dependent term in the established growth law for the equilibrium stress cannot contribute to the dissipation, and is therefore referred to here as the elastic equilibrium stress rate. A new temperature rate-dependent term is obtained for the same growth law, which is also required to be dissipationless. These terms are therefore identified with dissipationless changes of the stored energy and∕or entropy. In general, the traditional, and thermodynamically justified, forms for the potential functions that arise in the present nonequilibrium treatment lead to dissipationless contributions from internal variable growth law terms that are linear in the rates of the controllable variables. Similar indications, without first establishing entropy and absolute temperature existence, were noted in the modeling of Lehmann (1984, in The Constitutive Law in Thermoplasticity, T. Lehmann, ed., Springer, New York).
