Application Of The Extend Finite Element Method To Fracture Mechanics

The extended finite element method (XFEM) is a numerical method for modeling discontinuities within a standard finite element framework. The principle of XFEM consists in enriching the basis of the classical finite element method by some singular functions around the crack tip and by a step function along the crack line to take into account the discontinuity of the displacement field across the crack. The major difference between XFEM and the conventional finite element method (CFEM) is that the mesh in XFEM is independent of the internal geometry and physical interfaces, such that meshing and re-meshing difficulties in discontinuous problems can be overcome. The major contents are as follows:(1) The several basic theory of fracture mechanics and the method of stress intensity factors (SIFs) are introduced, implementations formulation of interaction energy integrals are suggested to compute SIFs in XFEM.(2) The elementary theory of XFEM and the improved XFEM are introduced. Implementation procedures and formulations of the XFEM are described in detail.(3) The computation flow chart which XFEM simulate crack growth is presented. Some critical problem of programming have solved, such as the location of crack, the quadrature scheme, the enriched node of crack tip and the loading application problem.(4) Through example have carried on SIFs and determined some parameters and simulated crack growth of mode I problem and compound of I and II problem. It is verified that application of the improved XFEM to fracture mechanics not only relaxes the prohibitive requirements for mesh density and crack growth without remeshing , but also save the computation time and can obtain the quite high precision.