Remarks on Invariant Modelling in Finite Strain Gradient Plasticity

I discuss invariance conditions arising in 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 flow rule for Fp is assumed which can be derived by an underlying thermodynamic potential involving as plastic gradient Curl Fp. The proposed formulation is supposed to be forminvariant w.r.t. arbitrary superposed rigid rotations of the reference, intermediate and spatial configuration but the model is not spin-free due to the nonlocal dislocation interaction and cannot be reduced to a dependence on the plastic metric Cp = FTp Fp. This is contrary to the case of the local theory without gradients on the plastic transformation Fp in which case the same form-invariance conditions reduce the model to a dependence on Cp[3]