Elastoplasticity, second principle of thermodynamics and softening

This study deals with the elastoplastic materials that are modelled with a yield surface and an associated or non-associated flow rule. The hardening is assumed to be isotropic. The incremental behaviour equations are completed by the equations that characterize the evolution of the boundary conditions. The case of axisymmetrical conditions is sufficient to introduce the concepts of guiding and piloting, that are necessary to distinguish the passive aspects of the evolution of the boundary conditions from the active ones. This approach allows to take into account the more complex situations. This incremental problem enables the study of the existence and the uniqueness of the theoretical response and, moreover, to link this point to the respect of the second principle of thermodynamics, thanks to the Clausius–Duhem inequality and the plastic multiplier concept. It appears that even for a basic associated model it is possible to determine certain loading increments that violate the second principle. This could be interpreted as an instability of the behaviour.