Wave dispersion relations in peridynamics: Influence of kernels and similarities to nonlocal elasticity theories

We investigate the wave dispersion relations of an infinite elastic bar within the framework of linear bond-based peridynamics. This nonlocal integral-type model accounts for long-range interactions, which become significant at small scales and in cases of damage and fracture. Since a key element of this material model is the kernel function, we derive dispersion curves for several kernel choices. Notably, for non-singular kernels, we observe negative group velocities, indicating that peridynamics can describe materials with anomalous dispersion. By comparing one-dimensional (1D) peridynamics with the 1D nonlocal elasticity of Eringen's type, we highlight similarities between the two models in terms of dispersion behavior.