Modeling of finite strain viscoplasticity based on the logarithmic corotational description

Abstract

It has been proven that the deformation rate is identical to the logarithmic corotational rate of the spatial logarithmic strain. Based on the logarithmic corotational description we present an extension of a Chaboche infinitesimal viscoplastic law for finite strain cases. An additive decomposition of the logarithmic corotational rate of the logarithmic strain, implicitly included in an internal dissipation inequality, is applied to the extension. Functionally, this additive decomposition corresponds to the additive decomposition of the material time derivative of the logarithmic strain used in infinitesimalinelastic problems. Using the additive decomposition and replacing the material time derivatives of all second-order tensors in the infinitesimal viscoplastic law with the corresponding logarithmic corotational rates, we arrive at a new finite viscoplastic law with nonlinear isotropic and kinematic hardening. The numerical algorithms suitable for the finite element implementation of this law are formulated and several numerical examples are presented. These numerical examples prove that the finite viscoplastic law and the algorithms are effective and reliable.