A state-of-the-art review of the X-FEM for computational fracture mechanics

This paper presents a review of the extended finite element method X-FEM for computational fracture mechanics. The work is dedicated to discussing the basic ideas and formulation for the newly developed X-FEM method. The advantage of the method is that the element topology need not conform to the surfaces of the cracks. Moreover, X-FEM coupled with LSM makes possible the accurate solution of engineering problems in complex domains, which may be practically impossible to solve using the standard finite element method.