This work presents the Griffith-type phase-field formation at large deformation in the framework of adaptive edge-based smoothed finite element method (ES-FEM) for the first time. Therein the phase-field modeling of fractures has attracted widespread interest by virtue of its outstanding performance in dealing with complex cracks. The ES-FEM is an excellent member of the S-FEM family developed in combination with meshless ideas and finite element method (FEM), which is characterized by higher accuracy, softer stiffness, and insensitive to mesh distortion. Given that, the advantages of the phase-field method (PFM) and ES-FEM are fully combined by the approach proposed in this paper. With the costly computational overhead of PFM and ES-FEM in mind, a well-designed multi-level adaptive mesh strategy was developed, which considerably improved the computational efficiency. Furthermore, the detailed numerical implementation for the coupling of PFM and ES-FEM is outlined. Several representative numerical examples were recalculated based on the proposed method, and its effectiveness is verified by comparison with the results in experiments and literature. In particular, an experiment in which cracks deflected in rubber due to impinging on a weak interface was firstly reproduced.

中文翻译：

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一种基于边缘的自适应平滑有限元方法 (ES-FEM)，用于大变形裂缝的相场建模

这项工作首次在基于自适应边缘的平滑有限元方法（ES-FEM）的框架内提出了大变形下的格里菲斯型相场形成。其中，裂缝的相场建模因其在处理复杂裂缝方面的出色表现而引起了广泛的兴趣。ES-FEM 是结合无网格思想和有限元方法 (FEM) 开发的 S-FEM 系列的优秀成员，其特点是精度更高、刚度更软、对网格变形不敏感。鉴于此，本文提出的方法充分结合了相场法 (PFM) 和 ES-FEM 的优点。考虑到 PFM 和 ES-FEM 昂贵的计算开销，开发了一种精心设计的多级自适应网格策略，大大提高了计算效率。此外，还概述了 PFM 和 ES-FEM 耦合的详细数值实现。基于所提出的方法重新计算了几个具有代表性的数值例子，并通过与实验和文献结果的对比验证了其有效性。特别是首次再现了橡胶中裂纹因撞击弱界面而偏转的实验。