Chapter 7 - Development of elastoplastic and viscoplastic constitutive equations

Abstract

The requirements for the elastoplastic constitutive equations, that is, the decomposition of the deformation into the elastic and the plastic parts and the incorporation of the yield surface, are described first. In addition, the continuity and the smoothness conditions are defined, which are required for the accurate description of the elastoplastic deformation behavior. Then, the development of elastoplastic constitutive equations is reviewed: The constitutive equations based on the infinitesimal hyperelastic-based plasticity were first studied and then the hypoelastic-based plasticity was incorporated. In the meantime, various cyclic elastoplasticity models describing not only the monotonic but also the cyclic loading behavior, that is, the cyclic elastoplasticity models, have been proposed. Among them, the subloading surface model is capable of describing the monotonic and the cyclic loading behaviors rigorously. The basic concept and the formulation of the subloading surface model in the current configuration are described in detail. Further, the subloading surface model is extended to the subloading-overstress model to describe the rate-dependent deformation.