Thermodynamical Consideration of Plastic Constitutive Equations with Work-Hardening

Abstract

According to Coleman's thermodynamics, the elastic and the plastic constitutive equations have been deduced theoretically from the Clausius-Duhem inequality. The modified thermodynamic potential and a scalar internal state variable are introduced and a yield restriction is assumed. The dependence of the internal state variable on the yield function is considered to express the isotropic work-hardening. In the elastic state the rates of stress and temperature are chosen arbitrarily, so that it is possible to obtain naturally the elastic constitutive equations. In the yield state they are restricted by the yield condition, and thus the undefinite plastic parts of strain and the entropy, which are subjected to some restriction, can be obtained. When the material is independent of the internal state variable, it reduces to a perfect plastic material. A special simple case is also discussed.