We propose a relatively simple and mesh-independent approach to model crack branching and merging using the Shifted Fracture Method (SFM), within the class of Shifted Boundary Methods. The proposed method achieves mesh independency by accurately accounting for the area of the fracture surface, in contrast to traditional element-deletion/node-release techniques. In the SFM, the true fracture is embedded into the computational grid, but the fracture interface conditions are modified (shifted) by means of Taylor expansions to the surrogate fracture composed of full edges/faces in two/three dimensions. This avoids numerical integration on cut elements, so that the data structures and geometrical treatment of cut elements are simple, while mesh-independent results and accurate fracture approximations are still maintained. We demonstrate the capabilities of the proposed approach in a number of prototypical numerical experiments.

中文翻译：

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使用移位断裂方法进行裂纹分支和合并仿真


我们提出了一种相对简单且独立于网格的方法，使用移位边界法 （Shifted Boundary Methods） 中的移位断裂法 （SFM） 来模拟裂纹分支和合并。与传统的单元删除/节点释放技术相比，所提出的方法通过准确考虑断裂表面的面积来实现网格独立性。在 SFM 中，真正的裂缝被嵌入到计算网格中，但裂缝界面条件通过泰勒展开来修改（移动）到由二维/三维完整边/面组成的代理裂缝。这避免了对切割单元进行数值积分，因此切割单元的数据结构和几何处理很简单，同时仍然保持了与网格无关的结果和精确的断裂近似值。我们在许多原型数值实验中证明了所提出的方法的能力。