Variational Gradient Plasticity: Local-Global Updates, Regularization and Laminate Microstructures in Single Crystals

This work summarizes recent results on the formulation and numerical implementation of gradient plasticity based on incremental variational potentials as outlined in a recent sequence of work [Mie14, MMH14, MWA14, MAM13]. We focus on variational gradient crystal plasticity and outline a formulation and finite element implementation of micromechanically-motivated multiplicative gradient plasticity for single crystals. In order to partially overcome the complexity of full multislip scenarios, we suggest a new viscous regularized formulation of rate-independent crystal plasticity, that exploits in a systematic manner the longand short-range nature of the involved variables. To this end, we outline a multifield scenario, where the macro-deformation and the plastic slips on crystallographic systems are the primary fields. We then define a long-range state related to the primary fields and in addition a short-range plastic state for further variables describing the plastic state. The evolution of the short-range state is fully determined by the evolution of the long-range state, which is systematically exploited in the algorithmic treatment. The model problem under consideration accounts in a canonical format for basic effects related to statistically stored and geometrically necessary dislocation flow, yielding micro-force balances including non-convex cross-hardening, kinematic hardening and size effects. Further key ingredients of the proposed algorithmic formulation are geometrically exact updates of the short-range state and a distinct regularization of the rate-independent dissipation function that preserves the range of the elastic domain. The model capability and algorithmic performance is shown in a first multislip scenario in an fcc crystal. A second example presents the prediction of formation and evolution of laminate microstructure.