Numerical computation of the crack development and SIF in composite materials with XFEM and SFEM

The lifetime of most engineering structures and components is known to depend on the presence of defects, such as holes, cracks, or voids usually introduced during a manufacturing process. In many cases, the crack growth, extension and propagation within a body, still remains a challenging problem in fracture mechanics. The present paper proposes the application of the level set method combined with the numerical extended finite element method (XFEM) to predict the fracture direction of propagation within a specimen, and to compute the stress intensity factor for cracked plates under different loading conditions. This technique avoids the difficulty of remeshing when tracking the moving interface positions during the cracking process. The combined XFEM formulation is first reviewed and then applied to different examples. The numerical results provided by the XFEM are straightforwardly compared with the theoretical predictions from the handbooks and the numerical solutions found with a strong formulation finite element method (SFEM) based on the generalized differential quadrature (GDQ) approach. The good agreement between the theoretical and numerical results confirms the accuracy of the proposed formulation to treat fracture mechanics.