Size effects in finite deformation micropolar plasticity

Micropolar theories offer a possibility to model size effects in the constitutive behavior 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 [

1

], [

2

].

To be more specific, we assume the multiplicative decomposition to apply for both the deformation gradient tensor of the macroscopic continuum and the micropolar rotation tensor of the assigned microstructure. From these, we obtain additive decompositions for the strain and curvature tensors as well as their associated rates. A yield function is assumed which reflects isotropic and kinematic hardening effects. The stress tensor and the back-stress tensor in the yield function are supposed to obey the structure of the so-called Mandel stress tensor within the framework of classical (non-polar) plasticity. All constitutive equations are defined in such a manner that the second law of thermodynamics is fullfilled in every admissible process.

The capabilities of the constitutive theory are demonstrated by means of finite element calculations. To this end, the micropolar plasticity model is implemented into finite element code ABAQUS. Details of the implementation are given in Grammenoudis and Tsakmakis [

2

]. Here, a discussion of the influence of hardening on size effects is given, with reference to torsion deformation (see Grammenoudis and Tsakmakis [

3

]).