An extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase‐field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction‐correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two‐ and three‐dimensional quasistatic fracture are provided to demonstrate the approach.

中文翻译：

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扩展/广义相场有限元方法用于裂纹扩展与局部局部富集

提出了一种基于相场法模拟准静态裂纹扩展的扩展/广义有限元方法（XFEM / GFEM）。该方法依赖于与两个不同尺度相关的解的近似值：整体尺度，即结构化并用粗糙网格离散化；局部尺度封装裂隙区域，即用精细网格离散化。使用稳定的XFEM / GFEM在全球范围内嵌入位移场和损伤场。所提出的方法可以容纳在荷载阶跃之间演化的近似空间，同时为结构问题保留固定的背景网格。另外，采用了一种预测校正算法来促进载荷步中约束裂缝区域的动态演化。