On the equivalence between the multiplicative hyper-elasto-plasticity and the additive hypo-elasto-plasticity based on the modified kinetic logarithmic stress rate

In two theorems presented herein, we prove and subsequently demonstrate in several numerical examples involving homogeneous deformation that for isotropic materials, hyper-elasto-plasticity models based on the multiplicative decomposition of the deformation gradient coincide with an additive hypo-elasto-plasticity model (see Section 3.2) that employs the spin tensor based on the modified kinetic logarithmic rate. In the absence of strain-induced anisotropy (characterized by kinematic hardening herein), this objective stress rate coincides with the kinetic logarithmic rate recently developed by Jiao and Fish, 2017. We also show that other well-known additive decomposition models, such as those based on the Jaumann and logarithmic rates, may considerably deviate from the multiplicative model.