In this paper, we introduce an implicit staggered algorithm for crystal plasticity finite element method (CPFEM) which makes use of dynamic relaxation at the constitutive integration level. An uncoupled version of the constitutive system consists of a multi-surface flow law complemented by an evolution law for the hardening variables. Since a saturation law is adopted for hardening, a sequence of nonlinear iteration followed by a linear system is feasible. To tie the constitutive unknowns, the dynamic relaxation method is adopted. A Green-Nagdhi plasticity model is adopted based on the Hencky strain calculated using a [2/2] Pad\'e approximation. For the incompressible case, the approximation error is calculated exactly. A enhanced-assumed strain (EAS) element technology is adopted, which was found to be especially suited to localization problems such as the ones resulting from crystal plasticity plane slipping. Analysis of the results shows significant reduction of drift and well defined localization without spurious modes or hourglassing.

翻译：本文提出了一种用于晶体塑性有限元方法（CPFEM）的隐式交错算法，该算法在材料本构积分层面利用动态松弛技术。解耦的本构系统由多屈服面流动法则及硬化变量演化律组成。由于采用饱和型硬化律，可依次进行非线性迭代与线性系统求解。为耦合本构未知量，采用了动态松弛方法。基于[2/2] Padé近似计算的Hencky应变，建立了Green-Naghdi塑性模型。针对不可压缩情形，精确计算了近似误差。采用增强假设应变（EAS）单元技术，该技术特别适用于晶塑性平面滑移引起的局部化问题。分析结果表明，该方法显著减小了积分漂移，且能清晰界定局部化区域，未出现虚假模态或沙漏现象。