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X-FEM Applied to Three-Dimensional Curvilinear Crack Front

A three-dimensional extended finite element algorithm coupled with the level set method is developed for curvilinear crack front problems. This method does not need to force the discontinuities to be in conformity with the mesh. In order to compute the pointwise stress intensity factors along the curvilinear crack front, an orthogonal curvilinear coordinate system is constructed at the intersection point between the crack front and a surface of the crack front element. As the crack surface is expressed by the level set method, no explicit meshing of the crack geometry emerges on the crack front. This makes the domain integral more difficult. An independent grid of hexahedral cells around the crack front needs to be built as the virtual extension domain for accomplishing the domain integral. To assess the accuracy of the approach, an example with semi-elliptic crack surface is considered. The results show excellent agreement with the results calculated by the standard finite element method and those obtained from the literature.