Material point method for the propagation of multiple branched cracks based on classical fracture mechanics

Abstract

The material point method (MPM) combines the advantages of both mesh-free and grid-based methods for simulating complex cracking problems without the limitations of the grid. However, the conventional MPM cannot deal with cracks directly because of the continuous nodal velocity field. Therefore, in this study, the conventional MPM is improved using three new algorithms to simulate the propagation of multiple branched cracks. The first proposed algorithm is the phantom node method using a particle cutting technique, which allows discontinuity of the velocity field around arbitrary cracks, and the second one is the multi-crack contact algorithm to deal with the contact problem between multiple objects cut by multiple cracks, avoiding crack penetration. The last one is particle interaction integral method based on classical fracture mechanics to get the dynamic stress intensity factors (DSIF) and realize the crack propagation. And all algorithms are validated by comparing with the extended finite element method. Subsequently, uniaxial compression tests of three rock samples with different pre-existing cracks are simulated using the extended MPM. Three types of crack coalescence are found, and the simulated results agree with the previous experimental results, which demonstrate the feasibility and flexibility of the proposed extended MPM for simulating the propagation of multiple branched cracks.