Application of the linearly independent numerical manifold method in modeling the complex crack problems

摘要

Numerical manifold method (NMM) is very suitable for modeling the transition from continuum to discontinuum by virtue of its advanced finite cover technique. Compared with the 0-order NMM, higher-order displacement functions are more suitable for modelling the crack problems as the result that the latter usually shows higher precision than the former under the same mesh density. However, the higher-order NMM may be suffering with the linear dependence problems, such as the 1-order NMM which adopts 1-order polynomials as its cover functions. Xu et al. (2015) has proposed a new higher-order NMM which has no linear dependence problems and has been applied to solve simple crack problems. In the paper, it is applied to solve the complex problems such as the multiple branched and intersecting cracks in order to show its advantageous features. The excellent results show that the proposed method is also excellent in even treating the complex problems.