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Numerically robust algorithmic formulations suitable for rate-independentcrystal plasticity are presented. They cover classic local models as well asgradient-enhanced theories in which the gradients of the plastic slips areincorporated by means of the micromorphic approach. The elaborated algorithmicformulations rely on the underlying variational structure of (associative)crystal plasticity. To be more precise and in line with so-called variationalconstitutive updates or incremental energy minimization principles, anincrementally defined energy derived from the underlying time-continuousconstitutive model represents the starting point of the novel numericallyrobust algorithmic formulations. This incrementally defined potential allows tocompute all variables jointly as minimizers of this energy. While such discretevariational constitutive updates are not new in general, they are consideredhere in order to employ powerful techniques from non-linear constrainedoptimization theory in order to compute robustly the aforementioned minimizers.The analyzed prototype models are based on (1) nonlinear complementarityproblem (NCP) functions as well as on (2) the augmented Lagrangian formulation.Numerical experiments show the numerical robustness of the resultingalgorithmic formulations. Furthermore, it is shown that the novel algorithmicideas can also be integrated into classic, non-variational, return-mappingschemes.

Rate-Independent Gradient Crystal Plasticity Theory -- Robust Algorithmic Formulations based on Incremental Energy Minimization