Crack growth prediction by manifold method

The prediction of crack growth is studied by the manifold method. The manifold method is a new numerical method proposed by Shi. This method provides a unified framework for solving problems dealing with both continuums and jointed materials. It can be considered as a generalized finite-element method and discontinuous deformation analysis. One of the most innovative features of the method is that it employs both a physical mesh and a mathematical mesh to formulate the physical problem. The physical mesh is dictated by the physical boundary of a problem, while the mathematical mesh is dictated by the computational consideration. These two meshes are interrelated through the application of weighting functions. In this study, a local mesh refinement and auto-remeshing schemes are proposed to extend the manifold method. The proposed model is first verified by comparing the numerical results with the benchmark solutions, and the results show satisfactory accuracy. The crack growth problems and the stress distributions are then investigated. The manifold method is proposed as an attractively new numerical technique for fracture mechanics analysis.