中文摘要：

该文将扩展有限元方法应用到几何非线性及断裂力学问题中,并研制开发了扩展有限元Fortran程序。扩展有限元法其计算网格与不连续面相互独立,因此模拟移动的不连续面时无需对网格进行重新剖分。该文推导了几何非线性扩展有限元法的公式,在常规有限元位移模式中,基于单位分解的思想加进一个阶跃函数和二维渐近裂尖位移场,反映裂纹处位移的不连续性,并用2个水平集函数表示裂纹;采用拉格朗日描述方程建立了有限变形几何非线性扩展有限元方程;采用多点位移外推法计算裂纹应力强度因子并通过最小二乘法拟合得到更精确的结果。最后给出的大变形算例表明该文提出的几何非线性的断裂力学扩展有限元方法和相应的计算机程序是合理可行的,而且对于含裂纹及裂纹扩展的问题,扩展有限元法优于传统的有限元法。

英文摘要：

A extended finite element（X-FEM） method and corresponding Fortran code are developed in the modeling and simulation for nonlinear geometry and fracture mechanics problems.X-FEM can model a domain without explicitly meshing the crack surface.This method can treat an arbitrary crack independent of the mesh and crack growth.The X-FEM formulas with nonlinear geometry are deduced.In order to model the crack discontinuity,a Heaviside step function and a two-dimensional asymptotic crack-tip displacement field are added to the traditional finite element approximation for the local enrichment based on the theory of partition of unity.The crack is described by two level set functions.The X-FEM computational algorithm is presented in the framework of Lagrangian description in order to model the arbitrary discontinuities in large deformations.The stress intensifying the factors of a crack are calculated by using the multi-point displacement extrapolation method and least square fitting.Finally,a numerical example is presented to demonstrate the accuracy and efficiency of the X-FEM and the FORTRAN code in large deformation crack problems.It is found that X-FEM is superior to the traditional FEM in the modeling and simulation of crack being and crack growth program.