An adaptive mesh refinement strategy for 3D phase modeling of brittle fracture

In order to improve the calculation accuracy and efficiency of the phase field method (PFM), an adaptive mesh refinement strategy suitable for 3D problems is proposed. The refined area is selected in terms of both the phase field value and the phase field increment value. The transition area is then chosen based on the transition element determination algorithm. The corresponding areas are refined using three basic and two advanced refinement templates. The new mesh is made up of hexahedrons and has no hanging nodes. The improved backtracking algorithm based on distance judgment is used in 3D adaptive mesh refinement and has proven its capacity to increase calculation efficiency. The accuracy and applicability of PFM to low-quality meshes with 3D adaptive mesh refinement are verified through benchmark tests, and the errors are all within 1%. Compared with the global refinement mesh, the number of elements in the PF model with 3D adaptive mesh refinement is reduced by more than 80%, and the computational efficiency is increased by 16 times. Combined with virtual crack insertion technology, mode I-II-III fracture is successfully simulated. The accurate and efficient calculation of cracked structures is realized. 3D multi-level adaptive mesh refinement is preliminary developed, and compared with single-level adaptive mesh, the computational efficiency is about two times higher, which provides a po-tential way to solve the efficient simulation of crack propagation in large-volume structures.