Influence of kernel functions on dynamic fracture in the bond-based peridynamics

Peridynamics is a nonlocal extension of classical continuum mechanics and is increasingly used to solve fracture mechanics problems. However, some issues remain, such as its dispersion characteristics and the use of the constant micromodulus. The introduction of the weighted or kernel functions can effectively address these issues. In this work, several micromodulus functions in the bond-based peridynamics approach are used to explore the influence of the kernel functions on wave dispersion, as well as on the evaluation of dynamic stress intensity factors (DSIFs) and crack propagation. First, a wave dispersion analysis for a 1D problem is performed for different kernel functions. Then, Mode-I and Mode-II DSIFs are computed. The DSIFs are calculated from the displacement field in the vicinity of the crack tip using the displacement extrapolation method. Finally, the Kalthoff–Winkler benchmark is simulated to assess the effect of the kernel functions on dynamic crack propagation.