A canonical rate-independent model of geometrically linear isotropic   gradient plasticity with isotropic hardening and plastic spin accounting for   the Burgers vector
  In this paper we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor Curl(p) giving rise to a non-symmetric nonlocal backstress, and isotropic hardening response only depending on the accumulated equivalent plastic strain. The model is fully isotropic and satisfies linearized gauge-invariance conditions, i.e., only true state-variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn's inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain sym(p) and standard isotropic hardening. 
Francois Ebobisse, Klaus Hackl and Patrizio Neff
math.AP