The extended finite element method(XFEM) is a new numerical method of modeling strong as well as weak discontinuities within a standard finite element framework. The principle 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. This enrichment strategy allows the use of a mesh independent of the discontinuity geometry. Numerical aspects of the XFEM are studied

including the representing of interface and the determination of enriched node and enriched model by level set method by level set method

the selection of enriched domain at the crack tip

the determination of quadrature domain for J integration and the quadrature scheme.