Structured mesh refinement in MLS-based numerical manifold method and its application to crack problems

The numerical manifold method (NMM) is suitable for both continuity and discontinuity problems due to its two cover systems, namely the mathematical cover and the physical cover. However, the use of these two cover systems makes it difficult to implement local mesh refinement in conventional NMM. In this paper, a structured mesh refinement is proposed for crack problems within the framework of MLS-based NMM. In order to balance both accuracy and efficiency, an eccentric domain of influence is suggested near the transition region, where the domain size is determined by surrounding elements. The visibility criterion used in element-free Galerkin method is introduced to describe the discontinuity near the crack tip. The main advantage of the proposed method is that it can solve complex crack problems straightforwardly without introducing any extra degree of freedom. Several examples are tested to demonstrate the effectiveness of the proposed method for crack problems.