In this paper, we present a phase-field method combined with an explicit cycle jump scheme for simulating low-cycle fatigue fracture in brittle materials in both two and three dimensions. In order to improve the computation efficiency, an adaptive local mesh refinement strategy, which features a predictor–corrector scheme and an adaptive criterion, is developed. The incompatible meshes due to local refinement are directly treated within the framework of variable-node elements. The predictor–corrector scheme is employed to pre-refine the mesh before the nucleation. In order to reduce the number of computation cycles, an explicit cycle jump scheme is developed which extrapolates the toughness states over a few cycles. Aiming to further enhance the computation efficiency for three-dimensional problems, the number of elements is decreased by introducing the effective fracture toughness. Several representative two- and three-dimensional numerical examples are presented to demonstrate the robustness, efficiency, and accuracy of the proposed framework.

中文翻译：

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使用可变节点单元和显式循环跳跃方案的疲劳裂纹扩展的自适应相场建模


在本文中，我们提出了一种与显式循环跳跃方案相结合的相场方法，用于模拟二维和三维脆性材料的低周疲劳断裂。为了提高计算效率，开发了一种自适应局部网格细化策略，该策略具有预测校正器方案和自适应准则。由于局部细化而​​导致的不兼容网格直接在可变节点单元的框架内处理。预测器-校正器方案用于在成核之前预细化网格。为了减少计算周期的数量，开发了一种显式的周期跳跃方案，该方案可以推断几个周期内的韧性状态。为了进一步提高三维问题的计算效率，通过引入有效断裂韧性来减少单元数量。提出了几个有代表性的二维和三维数值示例，以证明所提出的框架的鲁棒性、效率和准确性。