Hardening materials modeling in finite elastic–plastic deformations based on the stretch tensor decomposition

In this paper, finite elastic–plastic deformations of hardening materials are analyzed based on the modified multiplicative decomposition of the left stretch tensor. This decomposition is the modified form of the Metzger and Dubey’s decomposition used in the frame work of the principal axes of the left stretch tensor. For this purpose, basis-free corotational constitutive equations are derived for elastic–plastic hardening materials with the Armstrong–Frederick kinematic hardening and isotropic hardening models. The proposed governing equations are solved with different corotational rates for the simple shear problem with the material properties of the stainless steel SUS 304. The results are compared with those obtained experimentally by Ishikawa. This comparison shows a good agreement between the proposed theoretical model and the experimental data. Also, there is no significant difference in the stress results, using different corotational rates in the proposed model. As another example, the Prager kinematic hardening equation is used. In this case, the stress results using log-rate are close to those obtained by Bruhns et al., in which they used the additive decomposition of the strain rate tensor in a constitutive modeling based on the log-rate. Based on this example, it is noted that for the same corotational rate, the choice of the kinematic decomposition affects the results slightly.