Micropolar plasticity theories and their classical limits. Part I: Resulting model

Abstract

We focus attention on finite deformation micropolar plasticity theories, developed previously, which rely upon the multiplicative decomposition into elastic and plastic parts of both the macroscopic deformation gradient and the micropolar rotation tensor. The theories are thermodynamically consistent and exhibit isotropic and kinematic hardening effects. Conditions are worked out under which the micropolar continuum approaches a classical limit, i.e., a plasticity theory with symmetric Cauchy stress tensor and vanishing couple stress tensors. It turns out that, according to the assumptions made, on the one hand the elastic micropolar rotation is equal to the elastic rotation of the overall material. On the other hand, the plastic microgyration tensor is equal to the plastic material spin. Generally, the micropolar rotation is not equal to the material rotation as it is often assumed in the literature. Also, kinematic hardening rules are obtained, which are formulated by mixed Oldroyd objective time derivatives.