A weakened form of Ilyushinʹs postulate and the structure of self-consistent Eulerian finite elastoplasticity

From a general standpoint in terms of internal variables, we formulate a general theory of self-consistent Eulerian finite elastoplasticity based on the additive decomposition of the Eulerian strain rate, i.e., D=De+Dp, as well as two consistency criteria. In this theory, the elastic behaviour is characterized by an exactly integrable elastic rate equation for De with a general form of complementary elastic potential. It is assumed that the yield function depends in a general manner on the Kirchhoff stress and the internal variables. Moreover, the plastic rate equation for Dp and the evolution equation for each internal variable are allowed to assume general forms relying on the just-mentioned variables and the stress rate. It is indicated that two consistency criteria, i.e., the self-consistency for the elastic rate equation and Pragerʹs yielding stationarity, lead to the unique choice of objective rates, i.e., the logarithmic rate.