THERMOMECHANICAL DERIVATION OF NONCOAXIAL PLASTIC CONSTITUTIVE-EQUATIONS CONSIDERING SPINS OF OBJECTIVE STRESS RATES

Elasto-plastic constitutive equations which take into account yield-ve rtex effects are important in the study of localization instabilities of plastic deformations. However, they have never been discussed therm omechanically. In this paper, a method of deriving the above equations is proposed which is based on the second law of thermodynamics and th e principle of maximal entropy production rate. Elastic strain as a st rain measure which is conjugate to the objective stress rate is separa ted from total strain so that the Clausius-Duhem inequality, in which the Gibbs function is introduced as an elastic potential, can be alway s satisfied. The strain rate and stress rate are expressed by the same objective rate in the rate form of the elastic constitutive equation obtained. The plastic constitutive equation is derived using the princ iple of maximal dissipation rate. Since this equation is regarded as a flow rule in which the complementary dissipation function assumes the role of a plastic potential, it is indicated that the yield-vertex ca n exist on the dissipation surface. Furthermore, the spin which should be used in the objective stress rate is selected by taking into accou nt not only usual requirements but also thermomechanical ones.