An adaptive phase field modeling of fatigue crack growth using variable-node elements and explicit cycle jump scheme

In this paper, we present a phase-field method combined with an explicit cycle jump scheme for simulating low-cycle fatigue fracture in brittle materials in both two and three dimensions. In order to improve the computation efficiency, an adaptive local mesh refinement strategy, which features a predictor-corrector scheme and an adaptive criterion, is developed. The incompatible meshes due to local refinement are directly treated within the framework of variable-node elements. The predictor-corrector scheme is employed to pre-refine the mesh before the nucleation. In order to reduce the number of computation cycles, an explicit cycle jump scheme is developed which extrapolates the toughness states over a few cycles. Aiming to further enhance the computation efficiency for three-dimensional problems, the number of elements is decreased by introducing the effective fracture toughness. Several representative two- and three-dimensional numerical examples are presented to demonstrate the robustness, efficiency, and accuracy of the proposed framework.