Phase-field material point method for brittle fracture

The material point method for the analysis of deformable bodies is revisited and originally upgraded to simulate crack propagation in brittle media. In this setting, phase-field modelling is introduced to resolve the crack path geometry. Following a particle in cell approach, the coupled continuum/phase-field governing equations are defined at a set of material points and interpolated at the nodal points of an Eulerian, ie, non-evolving, mesh. The accuracy of the simulated crack path is thus decoupled from the quality of the underlying finite element mesh and relieved from corresponding mesh-distortion errors. A staggered incremental procedure is implemented for the solution of the discrete coupled governing equations of the phase-field brittle fracture problem. The proposed method is verified through a series of benchmark tests while comparisons are made between the proposed scheme, the corresponding finite element implementation, and experimental results.