The numerical manifold method (NMM) simulates continuous and discontinuous problems in a unified framework; thus NMM has advantages in analysing crack propagation. However, calculation of the stress intensity factors (SIFs) when adopting the NMM requires additional procedures, such as the J-integral and the interaction integral. In this study, a hybrid crack element (HCE) method is incorporated into the NMM to directly obtain the SIFs; the new algorithm combines the merits of both the NMM and HCE method. In the proposed algorithm, the HCE is used in the crack-tip region while the NMM is applied in the remaining region. The SIFs at the crack-tip are calculated directly from the solution of the governing equation with less computational complexity relative to existing methods. The proposed algorithm does not require any changes to the initial mesh during crack propagation. It is verified by a few examples and the results show that the simulated crack propagation paths are in good agreement with the results from existing studies while the computational efficiency is improved due to the direct calculation of the SIFs and the consistency of the mesh system in the crack propagation process.
He, J., Liu, Q., Ma, G., & Zeng, B. (2016). An improved numerical manifold method incorporating hybrid crack element for crack propagation simulation. International Journal of Fracture, 199(1), 21-38. https://doi.org/10.1007/s10704-016-0084-z