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A phase-field fracture model for brittle materials based on COMSOL

DOI：10.7511/jslx20210413002

 作者 单位 E-mail 张文兵 上海海事大学 海洋科学与工程学院, 上海 201306河海大学 水利水电学院, 南京 210098 zhangwb@shmtu.edu.cn 沈振中 河海大学 水利水电学院, 南京 210098 徐力群 河海大学 水利水电学院, 南京 210098 张宏伟 河海大学 水利水电学院, 南京 210098 甘磊 河海大学 水利水电学院, 南京 210098 李舸航 上海市堤防泵闸建设运行中心, 上海 200080

相场法通过一系列微分方程描述材料断裂过程,避免了繁琐的裂纹面追踪,在模拟裂纹的萌生、扩展和分叉等方面具有优势。介绍了基于相场法的脆性材料断裂模型,给出了脆性材料断裂问题相场法控制方程的推导过程,提出了基于分步迭代法在COMSOL中实现脆性材料相场断裂模型的方法。再现了脆性材料单元模型和单边缺口平板受拉及受剪作用下的开裂过程,模拟的裂纹扩展路径与已有文献的结果相近,验证了程序的合理性。针对脆性材料相场断裂模型包含的诸多参数,采用Morris法对影响荷载-位移关系的脆性材料断裂模型参数进行了全局敏感性分析,结果表明,杨氏模量(E)、临界能量释放率(Gc)和位移增量(Δux)是影响模型荷载-位移关系输出结果的主要参数。基于COMSOL实现的相场断裂模型能够有效模拟脆性材料的裂纹萌生和扩展断裂过程,模型参数E,Gc和Δux对材料断裂性能的提升或模型参数反演效率的提高具有重要影响。

The phase-field method (PFM) describes the material fracture process through a series of differential equations,which avoid tedious crack surface tracing and have advantages in simulating crack initiation,propagation,and bifurcation.This paper introduced a fracture model for brittle materials based on the PFM,gave the derivation process of the governing equations of the PFM for the brittle material fracture problem,and proposed a method to implement the phase-field fracture model for brittle materials in COMSOL based on the staggered algorithm.The cracking process of the brittle material one element model and the single-edge notched plate subjected to tensile and shear are reproduced,and the simulated crack propagation path is consistent with the results of the existing literature,which verifies the rationality of the computer program.For many parameters involved in the phase-field fracture model of brittle materials,a global sensitivity analysis based on the Morris method is carried out to identify the main factors of the phase-field fracture model pertinent to the load-displacement relationship.The results show that the Young’s modulus (E),critical energy release rate (Gc) and displacement increment (Δux) are the main parameters that affect the output results of the load-displacement relationship.The phase-field fracture model implemented in COMSOL can effectively simulate the crack initiation and propagation in brittle materials,and the model parameters E,Gc and Δux have an important impact on the improvement of the fracture performance of the material and the efficiency of the inversion of the model parameters.