Remarks on Invariant Modelling in Finite Strain Gradient Plasticity

Abstract

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 F_p is assumed which can be derived by an underlying thermodynamic potential involving as plastic gradient Curl F_p. 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 C_p = F^T_p Fp. This is contrary to the case of the local theory without gradients on the plastic transformation F_p in which case the same form-invariance conditions reduce the model to a dependence on C_p[3].