Crack propagation with the extended finite element method and a hybrid explicit-implicit crack description

A method for two-dimensional and three-dimensional crack propagation that combines the advantages of explicit and implicit crack descriptions is presented. An implicit description in the frame of the level set method is advantageous for the simulation within the extended finite element method (XFEM). The XFEM has proven its potential in fracture mechanics as it provides accurate solutions without any remeshing during the crack simulation. On the other hand, an explicit representation of the crack, for example, by means of a polyhedron, enables a simple update of the crack during the propagation. A key aspect in the proposed method is the introduction of three level set functions that are computed exactly from the explicit representation. These functions imply a coordinate system at the crack front and serve as a basis for the enrichment. Furthermore, a simple model for the crack propagation is presented. One of the biggest achievements of the proposed method is that two-dimensional and three-dimensional crack simulations are treated in a consistent manner. That is, the extension from two to three dimensions is truly straightforward.