A finite difference-augmented peridynamics method for reducing wave dispersion

Abstract

A method is presented for the modeling of brittle elastic fracture which combines peridynamics and a finite difference method to mitigate the wave dispersion properties of peridynamics. Essentially, a finite difference method is used in the bulk for wave propagation modeling, while peridynamics is automatically inserted in high strain areas to model crack initiation and growth. The dispersion properties of finite difference methods and discretized peridynamics are reviewed and the interface reflection properties between the two regions are investigated. Results show that the augmented method can improve the modeling of wave propagation and boundary conditions. In addition, the numerical stress intensity factor computed at a crack tip shows reduced oscillations in the augmented method, likely due to the improved dispersion properties of the bulk. Dynamic fracture simulations show a difference in crack paths between the methods.