Abstract
The constitutive equations for an ideal plastic material are derived naturally from the Clausius-Duhem inequality and the yield function. An admissible thermodynamic process must satisfy the inequality. If there is no restriction on the stress and temperature rates in the elastic state, then we obtain the elastic constitutive equations. However, if they are related in the yield state by means of the yield criterion, then the constitutive equation may contain a term that corresponds to the plastic flow of the ideal plastic material. The isotropic case is considered, and we obtain Hook's law, the thermal isotropic expansion, and the Levy-St. Venant flow rule.
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