Summary: We propose a model of finite strain gradient plasticity including phenomenological Prager-type linear kinematical hardening and nonlocal kinematical hardening due to dislocation interaction. Based on the multiplicative decomposition, a thermodynamically admissible flow rule for \(F_p\) is described involving as plastic gradient Curl \(F_p\). The formulation is covariant with respect to rigid rotations superposed on the reference, intermediate and spatial configurations, but the model is not spin-free due to the nonlocal dislocation interaction and cannot be reduced to a dependence on the plastic metric \(C_p=F_p^TF_p\).
The linearization leads to a thermodynamically admissible model of infinitesimal plasticity involving only the Curl of the nonsymmetric plastic distortion \(p\). Linearized spatial and material covariance under constant infinitesimal rotations is satisfied. Uniqueness of strong solutions of the infinitesimal model is obtained if two nonclassical boundary conditions on the plastic distortion \(p\) are introduced: \(\dot p\cdot\tau=0\) on the microscopically hard boundary \(\Gamma_D\subset\partial\Omega\), and [Curl\(p]\cdot\tau=0\) on the microscopically free boundary \(\partial\Omega\setminus\Gamma_D\), where \(\tau\) are the tangential vectors at the boundary \(\partial\Omega\). A weak reformulation of the infinitesimal model allows for a global in-time solution of the rate-independent initial-boundary value problem. The method is based on a mixed variational inequality with symmetric and coercive bilinear form. We use a new Hilbert space suitable for dislocation density-dependent plasticity.