  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.
