Transactions of Materials and Heat Treatment

Title：Application of constant stiffness method and tangent stiffness method in numerical simulation for metal materials

Authors： Xu Cheng Li Gui Fang Xuebin

Unit： Wuhan University of Science and Technology

KeyWords： constant stiffness method tangent stiffness method UMAT subroutine FORTRAN language incremental step

ClassificationCode：TG389

year,vol(issue):pagenumber：2023,48(2):257-263

Abstract：

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.

Funds：

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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