We present a remeshing‐free brittle fracture simulation method under the assumption of quasi‐static linear elastic fracture mechanics (LEFM). To achieve this, we devise two algorithms. First, we develop an approximate volumetric simulation, based on the extended Finite Element Method (XFEM), to initialize and propagate Lagrangian crack‐fronts. We model the geometry of fracture explicitly as a surface mesh, which allows us to generate high‐resolution crack surfaces that are decoupled from the resolution of the deformation mesh. Our second contribution is a mesh cutting algorithm, which produces fragments of the input mesh using the fracture surface. We do this by directly operating on the half‐edge data structures of two surface meshes, which enables us to cut general surface meshes including those of concave polyhedra and meshes with abutting concave polygons. Since we avoid triangulation for cutting, the connectivity of the resulting fragments is identical to the (uncut) input mesh except at edges introduced by the cut. We evaluate our simulation and cutting algorithms and show that they outperform state‐of‐the‐art approaches both qualitatively and quantitatively.

中文翻译：

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用于模拟脆性断裂的位移相关 XFEM

我们在准静态线弹性断裂力学 (LEFM) 假设下提出了一种免重新网格化脆性断裂模拟方法。为了实现这一点，我们设计了两种算法。首先，我们基于扩展有限元方法 (XFEM) 开发了近似体积模拟，以初始化和传播拉格朗日裂纹前沿。我们将断裂的几何图形明确地建模为表面网格，这使我们能够生成与变形网格的分辨率分离的高分辨率裂纹表面。我们的第二个贡献是网格切割算法，它使用断裂面生成输入网格的片段。我们通过直接操作两个表面网格的半边数据结构来做到这一点，这使我们能够切割一般表面网格，包括凹多面体和邻接凹多边形的网格。由于我们避免了用于切割的三角剖分，因此所得片段的连接性与（未切割的）输入网格相同，除了切割引入的边缘。我们评估了我们的模拟和切割算法，并表明它们在定性和定量上都优于最先进的方法。