Elastic–plastic multiplicative decomposition with a stressed intermediate configuration

This paper presents an extension to the elastic–plastic multiplicative decomposition to permit the origin, in stress space, to reside outside the closure of the elastic domain. In this work the classical assumption of a stress-free intermediate configuration is abandoned in favor of a new one where the intermediate configuration could be stressed. This stress is identified as the maximal unloading point in stress space, and denoted the plastic stress. To motivate the discussion, the infinitesimal plasticity model is considered first. A remarkable result is obtained, where, for the case of linear elastic response, the classical infinitesimal model is, after some reinterpretation, recovered. The fully nonlinear model is developed, and is shown to reduce to the classical one when the intermediate configuration is stress-free. The new framework is then applied to the case of J2-plasticity, where it is shown that when coupled with neo-Hookean elasticity, as in the infinitesimal case, after some reinterpretation, the classical model is recovered (i.e., the total stress is independent of the plastic stress). Numerical simulations are used to illustrate the importance of properly modeling the hardening behavior even during (external) loading in cases where load redistribution may take place.