Finite element implementation of large deformation micropolar plasticity exhibiting isotropic and kinematic hardening effects

Micropolar theories offer a possibility to model size effects in the constitutive behaviour of materials. Typical feature of such models is that they deal with a microrotation, which is supposed to represent an independent state variable, and its space gradient. As a consequence, the stress tensor is no longer symmetric and couple stresses enter the theory. Accordingly, a micropolar plasticity law exhibiting kinematic hardening effects should account for both, a back-stress tensor and a back-couple stress tensor. This has been considered in the micropolar plasticity model developed by Grammenoudis and Tsakmakis. The purpose of the current paper is to specify some constitutive functions in this model, to elucidate the finite element implementation as well as to demonstrate its capabilities in describing size effects