锻压技术

常刚度法和切线刚度法在金属材料数值仿真中的应用

英文标题：Application of constant stiffness method and tangent stiffness method in numerical simulation for metal materials

作者：许成李贵方学彬

单位：武汉科技大学

分类号：TG389

出版年,卷(期):页码：2023,48(2):257-263

摘要：

对常刚度法和切线刚度法两种非线性有限元计算方法进行对比研究。通过FORTRAN语言编写UMAT子程序将两种算法嵌入至ABAQUS软件中，再结合AA7075-T6铝合金试样的单轴拉伸实验及其数值模拟结果，分析单元尺寸、增量步对这两种算法的计算效率、精度及稳定性的影响。结果表明：在不同增量步和单元尺寸下，常刚度法的计算效率更高，但若以计算的精度作为标准，则切线刚度法的计算效率更高。在相同单元尺寸下，增量步越小，算法精度越高，但常刚度法的波动更大。由于增量步影响占主导，若增量步非常小，则单元尺寸对常刚度法精度的影响甚微，反之影响较大，而切线刚度法的精度受单元尺寸的影响很小。综合分析可知，切线刚度法的计算稳定性更高，为相关UMAT子程序开发人员提供了依据和参考。

Two nonlinear finite element calculation methods of constant stiffness method and tangent stiffness method were compared and studied, and two algorithms were embedded into ABAQUS software by writing UMAT subroutine in FORTRAN language. Then, the influences of element size and incremental step on the calculation efficiency, accuracy and stability of the two algorithms were analyzed by the uniaxial tensile test and numerical simulation results of AA7075-T6 aluminum alloy samples. The results show that the calculation efficiency of the constant stiffness method is higher at different incremental steps and element sizes. However, if the calculation precision is taken as the standard, the calculation efficiency of the tangent stiffness method is higher. With the same element size, the smaller the incremental step is, the higher the precision of the algorithm is, but the greater the fluctuation of the constant stiffness method is. Since the influence of the incremental step is dominant, if the incremental step is very small, the element size has little effect on the precision of the constant stiffness method, otherwise, the effect is greater. However, the calculation precision of the tangent stiffness method is slightly affected by the element size. Thus, the comprehensive analysis shows that the stability of the tangent stiffness method is higher, which provides a basis and reference for developers of relevant UMAT subroutine.

基金项目：

华中科技大学材料成形与模具技术国家重点实验室开放基金资助项目(P2020-019)

作者简介：许成(1998-), 男, 硕士研究生，E-mail：xuchengmode@163.com；通信作者：李贵(1983-), 男, 博士, 副教授，E-mail：leegui2030@wust.edu.cn

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