Thermoplastic materials with combined hardening

The constitutive equations of a rate-independent thermoplastic material at large deformations are presented. The compatibility of the model with the second law of thermodynamics is examined. The entropy function is constructed explicitly under general conditions. For isotropically hardening materials a complete description of the entropy functions is given, and for ideal thermoplastic materials a condition ensuring the uniqueness of the entropy is presented. Also, the validity of the non-isothermal generalization of Il'yushin's condition is established