Isogeometric boundary element method for crack propagation based on Bézier extraction of NURBS

Isogeometric boundary element method (IGABEM) based on Bézier extraction of non-uniform rational B-splines (NURBS) is developed to analyze the crack propagation and the interaction between inclusions and cracks in 2D infinite isotropic medium. We use isogeometric analysis (IGA) with NURBS to describe the geometric boundaries of inclusions and cracks which can be represented exactly no matter how coarse the discretization of the studied bodies is, so there are no geometric errors. Meanwhile, the same NURBS basis functions are used to approximate the unknown boundary quantities. For the crack boundary, the collocation points are moved inside the crack elements to meet the continuity requirement, i.e., discontinuous quadratic elements are applied on the crack boundary. Then, in order to obtain accurate stress intensity factors (SIFs), special crack tip basis functions are adopted to simulate the r variation of displacements near the crack tips. Some numerical examples are given and the obtained results have been compared with the results in the references.