Numerical aspects of the eXtended Finite Element Method

The eXtended Finite Element Method (XFEM) is a very efficient way to reduce mesh dependencies when analysing crack growth. Displacements and stresses around the crack tip are calculated using additional shape functions which span the analytical displacement field around a crack tip. In this paper the following numerical aspects of the XFEM are discussed: ? The integration of the stiffness matrix has to be done accurately. Therefore singular functions have to be integrated and an error estimator must be available. We will compare the estimated error and the necessary number of integration points when using different routines. ? In case a crack truncates a very small part of a finite element the global stiffness matrix may become singular. One possibility to overcome this problem is to delete some of the enhanced degrees of freedom in the finite element analysis. Another way is to remove zero eigenvalues in the global stiffness matrix algebraically by a stabilization term. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)