基于扩展有限元法数值模拟双材料界面裂纹问题  

Numerical simulation of bimaterial interface cracks using extended finite element

作　　者：苏毅 陈庆远 SU Yi;CHEN Qinyuan(School of Aeronautical Engineering,Zhengzhou University of Aeronautics,450046 Zhengzhou,China)

机构地区：[1]郑州航空工业管理学院航空工程学院,郑州450046

出　　处：《应用力学学报》2023年第6期1308-1314,共7页Chinese Journal of Applied Mechanics

基　　金：河南省高等学校重点科研计划资助项目(No.18B590003);河南省科技攻关资助项目(No.212102310004,222102320165,232102220028,232102240037)。

摘　　要：扩展有限元法通过在间断区域引入富集函数,在处理强弱不连续问题上较有限元法有极大的优势。本研究给出了基于扩展有限元法的双材料界面裂纹位移逼近方程及相互作用积分的数值离散方法和单元刚度矩阵的积分策略,材料界面弱不连续性用改进扩展有限元模拟,裂纹贯穿部分用强不连续的Heaviside函数模拟,裂纹尖端分别用2种不同渐近裂纹尖端富集函数模拟,用Matlab编制相应的扩展有限元程序。算例表明,数值模拟结果和参考文献的结果拟合的较好。The extended finite element method(XFEM)has a great advantage over the finite element method(FEM)in dealing with strong and weak discontinuities by introducing enrichment function into discontinuities.In this paper,bimaterial interface craks have been simulated using extended finite element method(XFEM).The displacement approximation equation of bimaterial interface crack is given.The integral method of the interaction integral and the integral strategy of element stiffness matrix are presented.Material discontinuity has been modeled by modified extended finite element method,and the crack penetration is simulated by Heaviside function,the crack tip is simulated by two different asymptotic crack tip enrichment functions,and the corresponding propagation extended finite element program is compiled by Matlab.Good agreement between the numerical results and the reference solutions for bimaterial interface cracks problems is realized.

关 键 词：扩展有限元法 改进扩展有限元 Heaviside函数 渐近裂尖富集函数 相互作用积分 应力强度因子 

分 类 号：O346.1[理学—固体力学]