Kinematic hardening in large strain plasticity

TLDR: In this paper, a finite strain hyper elasto-plastic constitutive model capable of describing non-linear kinematic hardening as well as nonlinear isotropic hardening is presented.

Abstract: A finite strain hyper elasto-plastic constitutive model capable to describe non-linear kinematic hardening as well as nonlinear isotropic hardening is presented. In addition to the intermediate configuration and in order to model kinematic hardening, an additional configuration is introduced - the center configuration; both configurations are chosen to be isoclinic. The yield condition is formulated in terms of the Mandel stress and a back-stress with a structure similar to the Mandel stress. It is shown that the non-dissipative part of the plastic velocity gradient not governed by the thermodynamical framework and the corresponding quantity associated with the kinematic hardening influence the material behaviour to a large extent when kinematic hardening is present. However, for isotropic elasticity and isotropic hardening plasticity it is shown that the non-dissipative quantities have no influence upon the stress-strain relation. As an example, kinematic hardening von Mises plasticity is considered, which fulfils the plastic incompressibility condition and is independent of the hydrostatic pressure. To evaluate the response and to examine the influence of the non-dissipative quantities, simple shear is considered; no stress oscillations occur. (Less)