Abstract The displacement-based methods for the extraction of the Stress Intensity Factors (SIFs) were created decades ago and, since them, they have been used in a wide range of numerical analysis, most of them based on standard 2D Finite Element Method (FEM). Although the accuracy of the SIFs computed by the displacement-based methods generally be inferior compared with the energy release methods, the use of the former methods have been motivated by its simplicity, ease of implementation and low computational cost, even though it may yield less accurate SIFs when compared with the latter methods. A major use of the SIFs is the prediction of the crack path direction in crack propagation analysis. The modelling of crack propagation is the most frequent application of the Generalized Finite Element Method (GFEM) and Extended Finite Element Method (XFEM) and a large number of crack propagation models presented in literature uses energy release methods for SIFs evaluation. Very few works using displacement-based methods for the computation of the SIFs have been published in literature in the context of the GFEM and XFEM. This paper presents a propagation model for an explicit non-planar 3D crack in a GFEM/XFEM background. The proposed model uses the Displacement Correlation Method (DCM) for the SIFs extraction. Some crack propagation problems are investigated and the resultant crack paths are compared with reported results from literature. This work demonstrates that the model here proposed generates very reasonable crack paths even for relatively coarse meshes using linear elements.

中文翻译：

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广义/扩展有限元方法中基于位移的显式非平面3D裂纹扩展模型

摘要 用于提取应力强度因子 (SIF) 的基于位移的方法是在几十年前创建的，从那时起，它们已被广泛用于数值分析，其中大多数基于标准的 2D 有限元方法 (FEM) ）。尽管与能量释放方法相比，基于位移的方法计算的 SIF 的准确性通常较差，但使用前一种方法的动机是其简单、易于实现和计算成本低，即使它可能产生较少的与后一种方法相比，准确的 SIF。SIF 的一个主要用途是在裂纹扩展分析中预测裂纹路径方向。裂纹扩展建模是广义有限元方法 (GFEM) 和扩展有限元方法 (XFEM) 最常见的应用，文献中提供的大量裂纹扩展模型使用能量释放方法进行 SIF 评估。在 GFEM 和 XFEM 的背景下，使用基于位移的方法计算 SIF 的作品很少发表在文献中。本文介绍了 GFEM/XFEM 背景中显式非平面 3D 裂纹的传播模型。所提出的模型使用位移相关方法 (DCM) 进行 SIF 提取。研究了一些裂纹扩展问题，并将由此产生的裂纹路径与文献报道的结果进行了比较。