EXTENDED FINITE ELEMENT METHOD WITH NONLINEAR GEOMETRY AND ITS APPLICATION IN FRACTURE MECHANICS

Abstract

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.