›› 2018, Vol. 39 ›› Issue (S1): 488-494.doi: 10.16285/j.rsm.2017.2529

• 数值分析 • 上一篇    下一篇

基于数值流形法的三维裂纹扩展研究

杨石扣1,张继勋2,任旭华2   

  1. 1. 河海大学 力学与材料学院,江苏 南京 211100; 2. 河海大学 水利水电学院,江苏 南京 210098
  • 收稿日期:2017-12-20 出版日期:2018-07-20 发布日期:2018-09-02
  • 通讯作者: 任旭华,男,1963年生,博士,教授,博士生导师,主要从事高坝及复杂地基、地下结构稳定、水工建筑物除险加固技术等方面的研究。E-mail: renxh@hhu.edu.cn E-mail: yangshikou@126.com
  • 作者简介:杨石扣,男,1985年生,博士,主要从事水工地下结构工程研究。
  • 基金资助:

    国家自然科学基金项目(No. 51739006, No. 51209078);中国博士后科学基金项目(No. 2017M611678)。

Study of three-dimensional crack propagation based on numerical manifold method

YANG Shi-kou1, ZHANG Ji-xun2, REN Xu-hua2   

  1. 1. College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 211100, China; 2. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, Jiangsu 210098, China
  • Received:2017-12-20 Online:2018-07-20 Published:2018-09-02
  • Supported by:

    This work was supported by the National Natural Science Foundation of China(51739006, 51209078) and the Project funded by China Postdoctoral Science Foundation (2017M611678).

摘要: 基于数值流形法(NMM)进行三维裂纹扩展分析研究,编写了相应的C++程序。充分发挥数值流形法在非连续变形分析领域的优势,不需要扩展有限元中的水平集和阶跃函数概念,应用数值流形法计算结果分析裂纹尖端线的破坏状况,对已有的非局部求迹法和三角形推进法进行简化和扩展,提出一种简化算法确定最终的新裂纹扩展面。应用简化算法对水平钱币型裂纹扩展问题进行数值模拟和对比分析研究。计算结果表明,基于数值流形法的三维裂纹扩展算法是可行的,采用简化处理之后,克服原有算法的不足,大大减少了新裂纹尖端线和新裂纹面的数目,降低了计算网格对新裂纹面的影响,提高了计算效率和扩大了应用范围。

关键词: 数值流形法(NMM), 三维裂纹扩展, 裂纹尖端线, 三角形推进法

Abstract: The problem of three-dimensional crack propagation is analyzed by the numerical manifold method(NMM) and the corresponding program with C++ is produced. By fully taking advantage of NMM in the area of discontinuous deformation analysis, the concepts of level set(LS) and Heaviside function in the extended finite element method(XFEM) are not required to be used. The result obtained from NMM is used to analyze failure state of each crack tip line. The exiting nonlocal crack tracing method and triangle tracing method are simplified and extended; and then a new tracing method is proposed to determine the final crack face. A block with a horizontal penny-shaped crack under tensile loading is simulated. The results show that the 3D crack propagation simulation based on NMM is feasible. After the simplification and extension, the shortcoming of original algorithm is overcome. The numbers of new crack tip line and new crack face are greatly reduced; and the influence of mesh on new crack surface is reduced; therefore the computational efficiency can be improved and the application can be expanded.

Key words: numerical manifold method(NMM), three-dimensional crack propagation, crack tip line, triangle tracing method

中图分类号: 

  • O 346.1

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