In order to examine relaxation behaviors of materials, static recovery term is always conducted in the backstress components for kinematic hardening in time-dependent plasticity model. Implicit integration algorithm for non-unified visco-plasticity model is derived. Plastic strain is divided into two parts: the visco-plastic strain, which is calculated based on the viscosity function, and the steady strain which only depends on the equivalent deviatoric backstress. Using the Newton iterative strategy, two sets of equations for deviatoric stress and relative stress tensors are solved. Additionally, the return mapping method is applied in numerical method, and consistent tangent stiffness modulus is progressed for convergence in finite element analysis. The model is implemented into commercial software ABAQUS as user subroutine UMAT. Dwell experiments of 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 attains convergence with good speed even at large increment, and the additional static recovery terms can improve the simulation for relaxation behaviors.

为了检查材料的松弛行为，在时变塑性模型中，总是在背应力组件中进行静态恢复项以进行运动硬化。推导了非统一粘塑性模型的隐式积分算法。塑性应变分为两部分：基于塑性函数计算的粘塑性应变和仅取决于等效偏向背应力的稳态应变。使用牛顿迭代策略，求解了偏应力和相对应力张量的两组方程。此外，将返回映射方法应用于数值方法，并在有限元分析中进行一致的切线刚度模量收敛。该模型已作为用户子例程UMAT实施到商业软件ABAQUS中。选择了镍基高温合金在应变控制的循环载荷下，具有在高温下保持弛豫的保持时间的实验，以验证该方法。结果表明，即使子程序增加很大，用户子程序也可以达到良好的收敛速度，并且附加的静态恢复项可以改善松弛行为的仿真。