Evaluation of stress integration algorithms for elastic-plastic constitutive models based on associated and non-associated flow rules
Evaluation of stress integration algorithms for elastic-plastic constitutive models based on associated and non-associated flow rules
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DOI：
10.1016/j.cma.2015.07.014
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发表时间：
2015-10-01
影响因子：
7.2
通讯作者：
De Waele, Wim
中科院分区：
文献类型：
--
作者：
Safaei, Mohsen;Lee, Myoung-Gyu;De Waele, Wim
本文深入分析了有限变形弹塑性本构关系的四种应力积分算法。特别是，在塑性理论的连续体水平上，针对非关联流动法则（non-AFR）和关联流动法则（AFR）开发了四种积分方案。四种积分方案是（1）全隐式后向欧拉，（2）半显式凸切割平面，（3）全显式经典前向欧拉和（4）全显式前向欧拉，名为下一个增量校正误差（NICE-1），它们被实现到有限元软件ABAQUS的用户材料子程序中。通过使用不同方向和时间增量的单轴拉伸模拟来进行数值精度分析。还对单轴拉伸/压缩试验进行了相同的分析，以研究时间增量对计算的硬化曲线的影响。最后，进行了圆柱杯拉深（冲压圆柱杯的制造过程）模拟，以比较 AFR 和非 AFR 方案的计算时间和精度，以评估更现实的成形应用。通过系统的比较分析，得出以下结论： (1) 在寻找显式积分方案的最佳时间增量时应小心谨慎。 (2) 当使用相同的积分方案时，AFR 和非 AFR 的计算时间和精度没有太大差异。 (3) 对于大型板材成形应用的模拟，显式应力积分算法可能是更实用的选择，因为与完全隐式算法相比，它不会降低计算精度和效率。 (C) 2015 Elsevier B.V. 保留所有权利。
This paper presents in-depth analyses of four stress integration algorithms for finite deformation elastic-plastic constitutive relations. In particular, the four integration schemes were developed for both non-Associated Flow Rule (non-AFR) and Associated Flow Rule (AFR) in the continuum level of plasticity theory. The four integration schemes are (1) fully implicit backward Euler, (2) semi explicit convex cutting plane, (3) fully explicit classical forward Euler and (4) fully explicit forward Euler named Next Increment Corrects Error (NICE-1), which were implemented into the user material subroutines of finite element software ABAQUS. Analysis on numerical accuracy was carried out by using uniaxial tensile simulations at various orientations and time increments. The same analysis was also conducted for uniaxial tension/compression tests to investigate the effect of time increment on the calculated hardening curve. Finally, cylindrical cup deep drawing (manufacturing process which stamps a cylindrical cup) simulations were performed to compare computation time and accuracy for both AFR and non-AFR schemes for the evaluation of more realistic forming application. From the systematic comparative analyses, the following conclusions are made; (1) Caution should be exercised when finding an optimum time increment for explicit integration schemes. (2) The computation time and accuracy for both AFR and non-AFR are not much different when identical integration scheme is used. (3) For the simulation of large scale sheet metal forming applications, the explicit type stress integration algorithm can be a more practical choice considering that it does not deteriorate the computational accuracy and efficiency compared to the fully implicit algorithm. (C) 2015 Elsevier B.V. All rights reserved.