In this paper, we propose 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-Naghdi 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法（CPFEM）的隐式交错算法，该算法在本构积分层面采用了动态松弛技术。本构系统的解耦形式包含一个多表面流动法则以及一个硬化变量的演化定律。由于硬化采用了饱和定律，因此可以采用先非线性迭代再求解线性系统的顺序流程。为关联本构未知量，采用了动态松弛方法。基于$[2/2]$帕德近似计算的亨基应变，采用了格林-纳格迪塑性模型。对于不可压缩情况，近似误差可精确计算。本文采用了增强假定应变（EAS）单元技术，该技术特别适用于局部化问题，例如由晶体塑性平面滑移产生的问题。结果分析表明，该方法能显著减小漂移现象，并产生清晰明确的局部化效果，且无虚假模态或沙漏模式出现。