Modeling quasi-static crack propagation using preconditioned numerical manifold method

The numerical manifold method (NMM) is robust and effective in modeling complex fracture problems as it allows the fracture paths to intersect meshes and uses enrichments with Williams expansions to capture the tip singularities. However, mesh cutting and crack-tip enrichment lead to small cut ratios and linear dependence, respectively, for complicated fracture problems. These two situations constantly cause serious ill-conditioning issues. Therefore, ill-conditioning is extremely challenging for crack propagation modeling. A preconditioning strategy was developed previously for NMM to deal with the ill-conditioning for static crack problems (Liu et al., 2023). In this study, we employ the preconditioned numerical manifold method (PNMM) for complicated crack propagation problems. Furthermore, we use a load factor to ensure that the mechanical mechanism and fracture criterion are satisfied simultaneously for multiple crack propagation problems. Numerical examples demonstrate the remarkable stability and efficiency of PNMM for multiple crack propagation problems.