High Order Extended Finite Element Method for Cracked Domains

Computer simulation of fracture processes remains a challenge for many industrial modelling problems. In a classical finite element method, the non-smooth displacement near the crack tip is captured by refining the mesh locally. The number of degrees of freedom may drastically increase, especially in three dimensional applications. Moreover, the incremental computation of a crack growth needs frequent remeshings. Reprojecting the solution on the updated mesh is not only a costly operation but also it may have a troublesome impact on the quality of results. In the last few years, Moës, Dolbow and Belytschko1 introduced a numerical methodology which has been developed by the name of XFEM eXtended Finite Element Method. Not only finite elements are enriched with the asymptotic crack tip displacement solutions, but also with