This paper presents an adaptive strategy for phase-field simulations with transition to fracture. The phase-field equations are solved only in small subdomains around crack tips to determine propagation, while an XFEM discretization is used in the rest of the domain to represent sharp cracks, enabling to use a coarser discretization and therefore reducing the computational cost. Crack-tip subdomains move as cracks propagate in a fully automatic process. The same computational mesh is used during all the simulation, with an $h$-refined approximation in the elements in the crack-tip subdomains. Continuity of the displacement between the refined subdomains and the XFEM region is imposed in weak form via Nitsche's method. The robustness of the strategy is shown for some numerical examples in 2D and 3D, including branching and coalescence tests.

中文翻译：

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一种无需重新网格划分的裂纹扩展 XFEM 相场组合计算模型

本文提出了一种具有过渡到断裂的相场模拟的自适应策略。相场方程仅在裂纹尖端周围的小子域中求解以确定传播，而在域的其余部分使用 XFEM 离散化来表示尖锐裂纹，从而能够使用更粗的离散化，从而降低计算成本。裂纹尖端子域随着裂纹在全自动过程中传播而移动。在所有模拟过程中使用相同的计算网格，在裂纹尖端子域中的元素中使用 $h$ 细化近似。细化子域和 XFEM 区域之间位移的连续性通过 Nitsche 方法以弱形式强加。对于 2D 和 3D 中的一些数值示例，包括分支和合并测试，显示了该策略的稳健性。