  In this paper we use convex analysis and variational inequality methods to
establish an existence result for a model of infinitesimal rate-independent
gradient plasticity with kinematic hardening and plastic spin, in which the
local backstress tensor remains symmetric. The model features a defect energy
contribution which is quadratic in the dislocation density tensor Curl p,
giving rise to nonlocal non-symmetric kinematic hardening. Use is made of a
recently established Korn's type inequality for incompatible tensor fields. The
solution space for the non-symmetric plastic distortion is naturally H(Curl)
together with suitable tangential boundary conditions on the plastic
distortion. Connections to other models are established as well.
