Phase‐field modeling, which introduces the regularized representation of sharp crack topologies, provides a convenient strategy for tackling 3D fracture problems. In this work, an adaptive isogeometric‐meshfree approach is developed for the phase‐field modeling of brittle fracture in a 3D polycrystalline material. The isogeometric‐meshfree approach uses moving least‐squares approximations to construct the equivalence between isogeometric basis functions and meshfree shape functions, thus inheriting the flexible local mesh refinement scheme from a meshfree method. This refinement scheme is improved by introducing an error estimator that includes both the phase field and its gradient. With the present approach, numerical implementations of the adaptive phase‐field modeling that introduces the anisotropy of fracture resistance in polycrystals are proposed. In this way, propagating cracks can be dynamically tracked, and the mesh near cracks is refined in a meshfree manner without requiring a priori knowledge of crack paths. Furthermore, the intergranular and transgranular crack propagation patterns in polycrystalline materials can be simulated by the present approach. A series of numerical examples that deal with the isotropic and anisotropic fracture are investigated to demonstrate the robustness and effectiveness of the proposed approach.

中文翻译：

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通过自适应等几何无网格方法对3D多晶材料中的脆性断裂进行相场建模

相场建模引入了尖锐裂纹拓扑的正则化表示形式，为解决3D断裂问题提供了便捷的策略。在这项工作中，开发了一种自适应等几何无网格方法，用于在3D多晶材料中进行脆性断裂的相场建模。等几何无网格方法使用移动最小二乘近似来构造等几何基函数与无网格形状函数之间的等价关系，从而从无网格方法继承了灵活的局部网格细化方案。通过引入一个包括相位场及其梯度的误差估计器，可以改进这种改进方案。使用目前的方法 提出了引入多晶体抗裂性各向异性的自适应相场模型的数值实现。以此方式，可以动态地跟踪正在传播的裂纹，并且不需要先验知识的裂纹路径就可以以无网格的方式细化裂纹附近的网格。此外，可以通过本方法模拟多晶材料中的晶间和晶间裂纹扩展模式。研究了一系列处理各向同性和各向异性裂缝的数值例子，以证明该方法的鲁棒性和有效性。可以通过本方法模拟多晶材料中的晶间和晶间裂纹扩展模式。研究了一系列处理各向同性和各向异性裂缝的数值例子，以证明该方法的鲁棒性和有效性。可以通过本方法模拟多晶材料中的晶间和晶间裂纹扩展模式。研究了一系列处理各向同性和各向异性裂缝的数值例子，以证明该方法的鲁棒性和有效性。