A new implementation of the numerical manifold method (NMM) for the modeling of non-collinear and intersecting cracks

The numerical manifold method (NMM), based on the finite covers, unifies the continuum analyses and discontinuum analyses without changing a predefined mathematical mesh of the uncracked solid, and has the advantages of being concise in theory as well as being clear in concept. It provides a natural method to analyze complex shaped strong discontinuities as well as weak discontinuities such as multiple cracks, intersecting cracks, and branched cracks. However, the absence of an effective algorithm for cover generation, to date, is still a bottle neck in the research and application in the NMM. To address this issue, a new method for the generation of the finite covers in the NMM is proposed, for the modeling of cracks. In the present algorithm for cover generation, the physical lines such as joints and cracks are described by geometric functions, the mathematical cover is naturally partitioned into different regions by the physical lines, and the regions belonging to a same physical cover, which contains the end points of the physical lines are identified by a simple calculation of the function values of the physical lines. The present method is simple and robust, and is also very fast because it avoids the usage of the complex geometrical algorithms, and the time-consuming judgment of the point-polygon relations, which are commonly used in the previous literature. Several linear elastic fracture problems are analysed here, to demonstrate the validity and the robustness of the proposed algorithms.