The $\Delta$EVPSC model is a general elasto-visco-plastic self-consistent constitutive formalism based on a Homogeneous Effective Medium (HEM) approach that accounts explicitly for microstructural features such as slip, twinning, and crystallographic texture. $\Delta$EVPSC is improved with respect to the original model reported in (Jeong and Tomé, 2020) by introducing an intermediate linearization scheme, which leads to better predictive accuracy of intergranular stress and strain distributions in the polycrystal. The $\Delta$EVPSC model is interfaced with a commercial finite element solver Abaqus/standard as a user-defined material subroutine ($\Delta$EVPSC-FE). $\Delta$EVPSC-FE shows superior numerical stability and, when using parallel computation and 40 CPU core units, it reduces the computation time by a factor 20 compared to using a single CPU core unit for a structure consisting of 512 solid elements. The $\Delta$EVPSC-FE model is applied to FE analyses of Zr and low-carbon steel bars subjected to a sequence of bending, stress-relaxation, and unloading. It is shown that the hereditary effect is responsible for the spring-forward motion during the early stage of unloading, while the elastic recovery mainly drives the subsequent spring-back.

这 $\Delta$EVPSC 模型是基于均质有效介质 (HEM) 方法的一般弹-粘-塑性自洽本构形式，该方法明确考虑了滑移、孪晶和晶体纹理等微观结构特征。 $\Delta$通过引入中间线性化方案，EVPSC 相对于 (Jeong 和 Tomé，2020) 中报告的原始模型进行了改进，从而提高了多晶中晶间应力和应变分布的预测精度。这$\Delta$EVPSC 模型与商业有限元求解器 Abaqus/standard 接口，作为用户定义的材料子程序（$\Delta$EVPSC-FE）。 $\Delta$EVPSC-FE 显示出卓越的数值稳定性，并且在使用并行计算和 40 个 CPU 核心单元时，与使用单个 CPU 核心单元相比，由 512 个实体单元组成的结构可将计算时间减少 20 倍。这$\Delta$EVPSC-FE 模型适用于 Zr 和低碳钢筋经过弯曲、应力松弛和卸载序列的有限元分析。结果表明，在卸载的早期阶段，遗传效应是导致弹簧向前运动的原因，而弹性恢复主要驱动随后的回弹。