Modeling of large simple shear using a viscoplastic overstress model and classical plasticity model with different objective stress rates

Large simple shear deformation, which usually has been used to test the applicability of various models, is studied by applying the classical plasticity model and the viscoplasticity theory based on overstress (VBO) with the logarithmic stress rate. Hypo-elastic, elastic-perfectly plastic, elastic-plastic linear kinematic and isotropic hardening models are employed. In addition to the logarithmic rate, the influences of the convected Truesdell and co-rotational Jaumann and Green-Naghdi rates on stress-strain behavior in simple shear are investigated. It is observed that unlike the Jaumann rate the logarithmic rate does not exhibit any oscillatory response. The responses of the logarithmic rate to every type of model discussed here are acceptable except for the elastic-perfectly plastic case. The finite viscoplasticity theory based on overstress, which has been developed by Krempl and his co-workers, with zero isotropic stress rate and nonzero hardening modulus and elastic-plastic kinematic hardening model gives the same results at the rate of 10^-5 1/s. It is shown that elastic-perfectly plastic, elastic-plastic kinematic hardening can be modeled with FVBO.