基于数值流形法的三维裂纹扩展研究

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。

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

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.