The Clausius-Duhem inequality and the structure of rate-independent plasticity

This paper is concerned with a derivation of the thermodynamic restrictions on a class of inelastic constitutive assumptions that reflect the general response of rate-independent, inelastic materials with a yield condition. The procedure of Coleman and Noll, utilizing the Clausius-Duhem Inequality is used. it is shown that a constitutive statement for the stress and entropy response, similar in form to hyperelastic materials, can be derived from the Clausius-Duhem Inequality without making any special, additional assumptions. The results obtained are well-known in the literature, and have been put to practical use (e.g. numerical implementations of elasto-plastic and damaged materials) in the recent past; it is hoped that this work provides a sound logical basis for the use of such results.