On finite deformation elasto-plasticity

Abstract

Some fundamental kinematical and kinetical results in finite elasto-plastic deformations of crystalline solids are reviewed. It is shown that essentially all existing elasto-plasticity concepts lead rigorously to total strain rate measures which are additively decomposed to an elastic and a plastic contribution, provided that the corresponding total, elastic and plastic strain rates are conjugate to the same stress measure. Furthermore, this additivity follows from the conservation of energy which further shows that, under the most general setting, the plastic strain rate may include a “workless” additive part which renders the Eulerian plastic strain rate tensor noncoaxial with the Cauchy stress tensor even when an isotropic yield function is assumed. Various Lagrangian and Eulerian strain measures, their rates and the corresponding conjugate stress measures are examined, and it is established that the additive decomposition of the strain rate holds independently of the particular choice of the strain measure or the ground state. Finally, a conflicting theory by Lee [33,36], who claims to have shown that the usual additive decomposition of the strain rate to an elastic and a platic part is in “error”, is reviewed, and it is shown that this theory also leads to an additive strain rate decomposition, and that Lee's conflicting conclusion stems from misinterpretation. Certain undesirable features of this theory, which emerge from a decomposition of the “total” deformation gradient into an elastic and a plastic part, are discussed and it is concluded that the commonly accepted physically based incremental theories of elasto-plasticity, either phenomenological or microscopically based, present distinct advantages.