Abstract
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.
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Mauthe, S., Miehe, C. (2015). Variational Gradient Plasticity: Local-Global Updates, Regularization and Laminate Microstructures in Single Crystals. In: Conti, S., Hackl, K. (eds) Analysis and Computation of Microstructure in Finite Plasticity. Lecture Notes in Applied and Computational Mechanics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-18242-1_4
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