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软薄膜材料裂纹相互作用的断裂相场模拟

PHASE-FIELD SIMULATION OF CRACK INTERACTIONS IN SOFT THIN-FILM MATERIALS

  • 摘要: 水凝胶、橡胶等软材料因其优异的高延展性、可逆变形及良好的能量吸收性能, 在学术研究和工业应用中均展现出广阔的前景. 然而, 断裂仍是此类材料中最常见且最具破坏性的失效模式之一, 准确预测裂纹的萌生、扩展及最终破坏对于保证工程结构的安全与可靠性至关重要. 本文在有限应变框架下建立了适用于超弹性薄膜(如 PDMS)的断裂相场模型, 以揭示裂纹相互作用机制及材料参数对裂纹演化路径的影响. 模型系统阐述了控制方程的推导、数值求解方法以及自适应网格策略, 实现了高精度与高效率的兼顾. 通过单边缺口试样的模拟与实验对比, 验证了该模型在裂纹扩展形貌及力–位移响应预测方面的准确性. 进一步地, 针对双边非对称裂纹, 系统分析了材料应变软化与硬化特性、初始裂纹长度及垂直间距对裂纹偏转行为的影响. 研究结果表明, 裂纹间的应力场耦合作用会显著改变裂纹尖端的应力分布, 导致扩展路径发生明显偏转, 而初始裂纹长度对裂纹轨迹影响较小. 总体而言, 该模型能够有效表征薄膜材料中多裂纹的演化过程, 为柔性聚合物及其他非线性材料的断裂预测提供了可靠的数值工具与理论依据.

     

    Abstract: Soft materials such as hydrogels and rubbers have attracted increasing attention in both fundamental research and industrial applications due to their exceptional stretchability, reversible deformability, and outstanding energy dissipation capability. However, fracture remains one of the most prevalent and destructive failure modes in such materials, and accurately predicting crack initiation, propagation, and ultimate rupture is crucial for ensuring the safety, reliability, and longevity of soft-structure systems. In this study, a finite-strain phase-field model for thin-film fracture is developed to elucidate the underlying mechanisms of crack interaction and to investigate how material parameters influence crack evolution paths. The proposed model, specifically formulated for hyperelastic thin films such as polydimethylsiloxane (PDMS), provides a comprehensive framework that incorporates the derivation of governing equations, numerical solution strategies, and an adaptive mesh refinement scheme, thereby achieving an optimal balance between computational accuracy and efficiency. The predictive capability of the model is verified through direct comparison between numerical simulations and experimental tensile tests on single-edge-notched specimens, demonstrating strong consistency in both crack propagation morphology and load–displacement responses. Furthermore, for double-edge asymmetric configurations, the model is employed to systematically analyze the influence of strain softening and hardening behavior, initial crack length, and vertical spacing on crack deflection. The results reveal that stress-field coupling between interacting cracks significantly modifies the local stress distribution near crack tips, inducing pronounced path deviation, while the initial crack length has only a minor effect on trajectory evolution. Overall, the proposed model effectively captures multi-crack evolution behavior in thin films, offering a robust theoretical and numerical foundation for fracture prediction in flexible polymers and other nonlinear materials.

     

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