Finite deformation plasticity and viscoplasticity laws exhibiting nonlinear hardening rules Part II: Representative examples

We consider two finite deformation plasticity models, which differ mainly in the evolution equation governing the response of kinematic hardening. Both models reduce to the same constitutive law in the case of small deformations. The aim of the paper is to discuss these models by calculating the predicted responses for some representative loading conditions. The numerical calculations needed are performed by using an efficient time-integration algorithm which has been developed with a view to implementation in the ABAQUS finite element code. Generally, there are some differences between the predicted responses and in particular between the second-order effects predicted by the two models. For some simple deformation processes, e.g. simple shear and simple torsion, the differences concerning second-order effects exhibit some kind of regularities, which are independent of material parameters. Also, even if boundary value problems are considered where global deformations are small, significant differences can exist between the predicted model responses according to the finite deformation and the limiting small deformation theory.