Thermodynamics of Some Viscoplastic Material Models With Internal Variables

Abstract

The thermodynamic restrictions for elastic-viscoplastic material models with evolution equations for the internal variables involving rates of external variables are derived. Compatibility with the Clausius-Duhem entropy inequality (Second Law) is required and this yields non-classical potential relations and a residual dissipation inequality.For two viscoplastic models (Robinson et al., Krempl et al.), which involve external variable rates in the evolution equations and which have not been embedded in a thermodynamic frame, the consistence with the non-classical potential relations is discussed. Further, the evaluation of the residual dissipation inequality is done for a thermodynamic extension of an early version of the Robinson model. Necessary and sufficient conditions for the material data are obtained to insure a non-negative mechanical dissipation. The results demonstrate that the model is formally consistent with the Second Law.

A review of some plasticity and viscoplasticity constitutive theories

“…As discussed in Chaboche (1996), it will lead to an unconventional definition for the elastic strain, due to the use of a reversible term in the evolution equation of the internal state variable. Such discussion was also given, in other terms in Lubliner (1973), Freed et al (1991), Malmberg (1990). Recent efforts have been made by Hall et al (2005) to interpret the stress rate dependent term as a dissipationless contribution.…”