Extended Finite Element Method ( X - Fem ) for Two - and Three - Dimensional Crackmodelingn

The nite element method is now well established as a robust and reliable numerical technique in many areas of solid mechanics. There are however problems where the use of the nite element method is cumbersome like the modeling of moving discon-tinuities due to the need to update the mesh to match the geometry of the discontinuity. Even for stationary cracks, in three-dimensional solids, contsructing a mesh that matches the geometry of the crack is not trivial for non-symmetric loading cases. Recently, a new technique for modeling cracks in the nite element framework has been introduced. A standard displacement-based approximation is enriched near a crack by incorporating both a discontinuous eld and the near crack front asymptotic elds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robust-ness of the proposed technique. Two-dimensional crack growth analysis are shown and stress intensity factors for planar three-dimensional crack obtained with the X-FEM are compared to available reference solutions from the literature.