The finite element method has been widely used to solve different problems in the field of fracture mechanics. In the last two decades, new methods have been developed to improve the accuracy of the solution in 2D linear elastic fracture mechanics problems, such as the extended finite element method (XFEM) or the phantom node method (PNM). The goal of this work is to quantify the differences between some numerical approaches: standard finite element method (FEM), mechanical property degradation, interelemental crack method with multi-point constraints, XFEM and PNM. We explain the different techniques analysed together with their advantages and disadvantages. We compare these numerical techniques to model fracture using problems of reference with known solutions, evaluating their behaviour in terms of convergence with respect to the element size and accuracy of the stress intensity factor (SIF), stresses ahead the crack tip and crack propagation prediction. Some of the new techniques have shown a better accuracy in SIF calculation or stress fields ahead the crack tip and other lead to high errors in local results estimations. However, all methods reviewed here can predict crack propagation for the problems of reference of this work, showing good accuracy in crack orientation prediction.

中文翻译：

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使用有限元的二维 LEFM 中的一些裂缝建模方法之间的比较

有限元方法已被广泛用于解决断裂力学领域的不同问题。在过去的二十年中，已经开发出新的方法来提高二维线弹性断裂力学问题的求解精度，例如扩展有限元法 (XFEM) 或虚拟节点法 (PNM)。这项工作的目标是量化一些数值方法之间的差异：标准有限元法 (FEM)、机械性能退化、具有多点约束的元素间裂纹法、XFEM 和 PNM。我们解释了分析的不同技术及其优缺点。我们使用已知解决方案的参考问题将这些数值技术与模拟断裂进行比较，根据单元尺寸和应力强度因子 (SIF) 的精度、裂纹尖端前的应力和裂纹扩展预测的收敛性来评估它们的行为。一些新技术在 SIF 计算或裂纹尖端前的应力场中显示出更好的准确性，其他导致局部结果估计的高误差。然而，本文综述的所有方法都可以预测裂纹扩展，作为本文的参考问题，在裂纹取向预测方面表现出良好的准确性。