一种非统一黏塑性本构的有限元实现

在与率相关黏塑性本构模型的背应力分量中加入静态回复项通常用来更精确地描述材料应力松弛效应．本文基于包含静态回复项的非统一黏塑性本构模型，提出了对应的隐式应力积分算法．该模型可简化为两个关于偏背应力和等效应力张量的方程组，通过牛顿迭代法进行求解．在应力积分算法中采用了Return-Mapping求解策略．此外还推导出了材料的一致切线刚度矩阵来判断有限元分析收敛性．在此基础上开发出了适用于ABAQUS工程软件的UMAT用户材料子程序．文中选取了高温下镍合金材料在伴随应力松弛的循环加载路径下的试验结果来验证算法的有效性．从比较结果中可以发现：用户子程序即使在大时间增量下也具有良好的收敛性，静态回复项的引入使得模型对应力松弛效应的模拟更加准确．

FEA Implementation of Non-Unified Visco-Plasticity Model with Static Recovery

To examine the relaxation behaviors of materials, static recovery term is always incorporated in the back stress components for kinematic hardening in time-dependent plasticity model. An implicit integration algorithm for non-unified visco-plasticity model is studied. By Newton iterative strategy, two set of equations for deviatoric stress and relative stress tensors are solved. Additionally, Return-Mapping method is applied numerically, and consistent tangent stiffness modulus is used for convergence evaluation in finite element analysis. The model is implemented into the commercial software ABAQUS through the user subroutine UMAT. Dwell experiments of the nickel-based superalloy under strain-controlled cyclic loading with holding periods for relaxation at high temperature are selected to verify the method. The results indicate that the user subroutine is able to converge with satisfactory speed even at large increment, and the additional static recovery terms can improve the simulation accuracy for relaxation behaviors.