Abstract 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.

中文翻译：

---

XIGA方法在计算断裂力学中的应用综述

摘要 本文致力于对用于计算断裂力学的扩展等几何分析 (XIGA) 进行最新评论。在目前的工作中讨论了最近开发的 XIGA 方法的基本知识和公式，其中包括在文献中出现的 190 多篇出版物。XIGA 是一种数值方法，它同时具有扩展有限元方法 (XFEM) 和等几何分析 (IGA) 方法的优点。XIGA 方法证明了其优于其他当代方法的优势，因为它在计算机辅助设计 (CAD)、几何、网格划分和分析之间建立了紧密的联系。该方法通过对建模采用相同的基函数并结合分析来准确地说明几何和解，称为非均匀 B 样条 (NURBS)。这有助于创建用于解决复杂工程问题的精确方法，即 XIGA。无需重新划分网格即可模拟裂纹演化的能力是 XIGA 的主要优势之一。在该方法中，裂纹尖端富集函数用于捕捉裂纹尖端应力场中的奇异性，并使用 Heaviside 函数对裂纹面进行建模。发现XIGA能够处理复杂域中的多方面断裂问题。还关注了不同材料在不同载荷条件下的众多裂纹问题以及因使用 XIGA 导致的惩罚。比较和描述了基于 XIGA 贡献的文献研究的数值结果，