Implementation of three-dimensional numerical manifold method for initiation and propagation simulation of brittle materials

In the present study, by utilizing the program framework of the three-dimensional numerical manifold method (3DNMM), we have achieved local crack surface tracking by embedding the crack surface at the physical cover centroid and the crack tip point. Consequently, we constructed and developed the corresponding fracture program module. Following this, we simulated the initiation and propagation processes of six typical I-type failure mechanical models, including L-shape beam, three-point beam, semi-disc, Brazilian disc and Brazilian disc with holes. We successfully replicated the initiation, propagation, and coalescence of cracks within the three-dimensional structure. The findings of this research verify that the developed fracture program can accurately forecast the crack initiation position, propagation path, and secondary crack distribution in three-dimensional structures. Furthermore, this study confirms the efficacy of the previously established 3DNMM theory in depicting discontinuous behaviors such as three-dimensional crack opening, closing, and sliding. The numerical method established in this study is anticipated to play a pivotal role in resolving complex multi-crack issues in the future, exhibiting significant application potential.