2D numerical modeling of solid materials with virtual boundary particles in ordinary state-based peridynamics

The peridynamic method has become an important theory for predicting crack propagation in solid materials, but due to its non-locality, the boundary material particles will affect the accuracy of the simulation results. For some specimens without a notch or small notch, it is even impossible to simulate the correct path of crack propagation. Therefore, based on the ordinary state-based peridynamic theory, this paper proposes a virtual boundary particles method for simulating solid materials and gives the force formula of virtual particles. The accuracy and precision of the results are improved by arranging virtual particles on the boundary of the model. For quasi-static problems, the simulation results show that the model with virtual boundary particles has higher accuracy. The three-point bending simulation of the long-notch specimen shows that the virtual boundary particles method can reduce the influence of boundary particles on the simulation results. Then, three-point bending simulations are performed on unnotched and small-notched specimens, and the results show that the model with virtual boundary particles could accurately predict crack propagation direction and is more consistent with the experimental results, which verify the validity of the model.