A finite-volume implementation of the phase-field model for brittle fracture with adaptive mesh refinement

The phase-field method (PFM) has advantages in modeling crack propagation in rock-like materials by treating the crack surface as a continuous function, therefore avoiding dealing with the sharp discontinuous displacement field. This study presents an implementation of PFM using the finite volume method (FVM) to discretize the governing equations for the conservation of linear momentum and the evolution of phase field. The coupled equations are solved by an iterative staggered scheme. The adaptive mesh refinement (AMR) technique is further employed to improve computational efficiency, which is relatively easy to achieve in FVM as the method can naturally handle unstructured meshes with hanging nodes in both two- and three-dimensional problems, as opposed to the finite element method (FEM). Several classical crack propagation problems, including the singleedge notched tension and shear tests, the L-shaped panel test, and the test on a notched plate with a hole, are simulated and compared with available experimental and FEM results, which demonstrate that the FVM-based PFM can model crack propagation accurately and effectively and could be more efficient than the FEM-based PFM.