基于扩展有限元法的裂纹扩展问题的研究

扩展有限元法(XFEM)是在常规有限元法(CFEM)基础上发展起来的,用来处理断裂、孔洞、夹杂等强弱不连续问题的新型数值计算方法。本文在有限元法的框架下,基于单位分解,通过在裂纹贯穿单元、裂纹尖端和材料界面等间断单元引入反映待求不连续问题的间断特性富集函数,给出扩展有限元的位移表达式,编制扩展有限元法的MATLB程序,最后基于扩展有限元法研究颗粒夹杂和孔洞对裂纹扩展路径和裂纹尖端应力强度的影响。

Developed from the conventional finite element method(CFEM),the newly emerged extended finite element method(XFEM)is dedicated to deal with the strong and weak discontinuities such as fracture,cavity and inclusion.In this paper,under the framework of finite element method(FEM),the displacement expression of the XFEM is given by introducing the enrichment function of discontinuous characteristics to the discontinuous elements such as crack penetrating element,crack tip and material interface based on unit partition.And the effects of particle inclusions and voids on the crack propagation path and the stress intensity at the crack tip are studied by writing the XFEM program in the MATLB code.