Abstract

While the regular Finite Element Method (FEM) is well developed and robust, it is not particularly well suited to model evolving discontinuities, since the construction of a discontinuous space requires the element topology to be aligned with the geometry of the discontinuity. This in turn requires regeneration of the mesh as the discontinuity evolves, resulting in projection errors and a significant computational cost. The eXtended Finite Element Method (XFEM) is a new technique which was developed recently to account for the evolving discontinuities in the crack growth problems. In XFEM, special functions (discontinuous and near tip functions) are added to the regular FEM to model the discontinuities without regenerating the mesh. Using this property in XFEM, and assuming Linear Elastic Fracture Mechanics (LEFM) concept, the damage tolerance analysis to determine the time or the number of loading cycles required for a smaller pre-existent crack to grow to critical size can be accomplished more efficiently than that in the regular FEM. The derived XFEM-formulation has been effectively implemented and in-house computer code has been developed to find the stress intensity factors and to model the crack growth efficiently without re-meshing the structure. Numerous benchmark 2-D problems with cracks located at different locations and inclined in different angles have been investigated and the results are validated with those available in the literature. Finally, the potential application of XFEM in damage tolerance analysis has been demonstrated.