A review on XIGA method for computational fracture mechanics applications

•Detailed discussion on basic concepts of IGA and XIGA.•Comprehensive overview of the applications of XIGA in the area of fracture.•Advancements of XIGA to model the weak and strong flaws in structure.•Presents studies on crack growth due to complex, static & dynamic loading. This paper is devoted to a state-of-the-art review on extended Isogeometric Analysis (XIGA) for computational fracture mechanics. The basic knowledge and formulations of the recently developed XIGA method are discussed in the present work, which includes over one hundred ninety publications that have appeared in the literature. XIGA is a numerical approach that enjoys the benefits of both, extended finite element method (XFEM) and isogeometric analysis (IGA) method. XIGA method has proved its advantage over the other contemporary methods for the reason that it creates a tight link between the computer-aided design (CAD), geometry, meshing, and the analysis. This method accurately explicates the geometry and the solutions by employing the same basis functions for the modeling, in conjunction with the analysis, known as non-uniform B-splines (NURBS). This contributes in creation of an exact and precise method for solving complex engineering problems i.e. XIGA. The ability to model crack evolution without re-meshing is one of the key advantages of XIGA. In this method, crack-tip enrichment functions are employed to capture the singularity in the crack-tip stress field and Heaviside functions are used to model the crack face. It is found that XIGA is able to cope up with the multifaceted fracture problems in complex domain. Attention is also paid to numerous crack problems in different material under various loading conditions and the penalties stemming from the use of XIGA. The numerical results of the researches from the literature based on contribution of XIGA are compared and described, that clearly indicates that XIGA has the potential to solve complex engineering fracture mechanics problems with efficacy and accuracy when compared with other conventional FEA formulations.