Algorithm for generation of physical cover and contact loops based on loop updating

The numerical manifold method has been successful in solving continuous and discontinuous problems in a unified way, but the precondition is to generate the physical cover and contact loops correctly. For problem domains invariant during analysis, at first, the generation process of the physical cover and contact loops is expounded, where an algorithm for searching for loops, as the core of NMM pre-processing, is emphasized. Furthermore, a new algorithm much closer to the nature of NMM for the generation of physical cover and contact loops during the crack growth is proposed based on the concept of updating physical patch loops and contact loops. In theory, it is suitable for the cases of arbitrary crack growth length, and the crack tips are allowed to stop at any point of the manifold element, which has eliminated the mesh dependence to a great degree. Finally, the robustness and correctness of the proposed method is confirmed by an example of multiple crack growth.