Wave dispersion relations in peridynamics: Influence of kernels and similarities to nonlocal elasticity theories
Victor A. Eremeyev, Konstantin Naumenko
Abstract
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.