In this paper, crack growth in orthotropic materials subjected to dynamic loading is numerically studied using an adaptive phase-field method. The study starts with a coarse structured mesh and the adaptive refinement strategy based on a user-defined threshold on the phase-field variable is proposed for computational efficiency, and variable-node elements are employed to treat the hanging nodes as a result of local adaptive refinement. The Hughes-Hilbert-Taylor (HHT) time integration scheme is adopted for temporal discretization. The directionality of orthotropic materials is represented by a penalized second-order structural matrix, which is incorporated in the crack face energy density. Through numerical examples, the influence of the material orientation on the dynamic crack growth in orthotropic materials is studied and the reliability of the proposed framework is validated.

中文翻译：

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使用可变节点单元的自适应相场建模正交各向异性脆性材料的动态裂纹扩展

在本文中，使用自适应相场方法对动态载荷作用下正交各向异性材料的裂纹扩展进行了数值研究。该研究从粗结构网格开始，为了提高计算效率，提出了基于用户定义的相场变量阈值的自适应细化策略，并采用变量节点元素将悬挂节点视为局部自适应的结果细化。采用休斯-希尔伯特-泰勒（HHT）时间积分方案进行时间离散化。正交各向异性材料的方向性由惩罚二阶结构矩阵表示，该矩阵包含在裂纹面能量密度中。通过数值算例，研究了材料取向对正交各向异性材料动态裂纹扩展的影响，并验证了所提出框架的可靠性。