Non-uniform discretization bond-based peridynamics with constant horizon and a novel volume correction for the cracking behaviors

•Non-uniform discretization peridynamic method is proposed to investigate cracking behavior.•A novel volume correction method is proposed to eliminate unbalance force.•The force loading condition is modified to replace the displacement loading.•The relationship between the material points discretization form and cracking behavior is defined. The proposed non-uniform discretization peridynamics reduces computational costs. Cracking behavior investigation is very important in solid mechanics. In this study, a non-uniform discretization bond-based peridynamic (NUD-BBPD) method is proposed to investigate the cracking behavior, in which the new volume correction method for regenerative family material points is proposed based on Monte Carlo statistical approach. When computational domain non-uniform discretization (NUD) is employed, the proposed method eliminates the need to use the variational horizon, and naturally solves the issue of unbalanced force in NUD. Additionally, the force loading condition is revised based on the energy conservation in the proposed method. This revision eliminates the need for fictitious material points when the displacement loading condition is used in simulation, and the drawback of the conventional force loading condition, in which the force is constrained, is also solved. The proposed method is then used to analyze the static and dynamic fractures of solids. The effects of the material points arrangement on the cracking behavior are obtained via a comprehensive comparison, and the numerical results obtained by the proposed method are in good agreement with those obtained by the conventional uniform discretizational peridynamics. Moreover, NUD peridynamics with constant horizon has higher computational efficiency than traditional peridynamics.