Numerically robust algorithmic formulations suitable for rate-independent crystal plasticity are presented. They cover classic local models as well as gradient-enhanced theories in which the gradients of the plastic slips are incorporated by means of the micromorphic approach. The elaborated algorithmic formulations rely on the underlying variational structure of (associative) crystal plasticity. To be more precise and in line with so-called variational constitutive updates or incremental energy minimization principles, an incrementally defined energy derived from the underlying time-continuous constitutive model represents the starting point of the novel numerically robust algorithmic formulations. This incrementally defined potential allows to compute all variables jointly as minimizers of this energy. While such discrete variational constitutive updates are not new in general, they are considered here in order to employ powerful techniques from non-linear constrained optimization theory in order to compute robustly the aforementioned minimizers. The analyzed prototype models are based on (1) nonlinear complementarity problem (NCP) functions as well as on (2) the augmented Lagrangian formulation. Numerical experiments show the numerical robustness of the resulting algorithmic formulations. Furthermore, it is shown that the novel algorithmic ideas can also be integrated into classic, non-variational, return-mapping schemes.

翻译：提出了适用于率无关晶体塑性的数值稳健算法公式化方法。这些方法涵盖了经典局部模型以及基于微形态方法引入塑性滑移梯度的梯度增强理论。所发展的算法公式化依赖于（关联性）晶体塑性的潜在变分结构。更精确地说，遵循所谓的变分本构更新或增量能量最小化原理，以连续时间本构模型为基础的增量定义能量作为新颖数值稳健算法公式化的起点。该增量定义势能允许将所有变量共同求解为该能量的极小化器。尽管此类离散变分本构更新并非全新概念，但在此处应用非线性约束优化理论的强大技术来稳健计算上述极小化器。分析的原型模型基于：（1）非线性互补问题（NCP）函数；（2）增强拉格朗日公式化。数值实验证明了所得算法公式化的数值稳健性。此外，还展示了新颖算法思想可集成至经典的非变分回映映射方案中。