A generalized stress-driven approach to anomalous dispersion in peridynamics

The manuscript investigates the dispersive behavior of one-dimensional nonlocal continua within the frameworks of peridynamics and stress-driven nonlocal elasticity. The peridynamic model is first analyzed, showing that the choice of the kernel function significantly affects the dispersion relation and may lead to anomalous dispersion phenomena characterized by non-monotonic trends and negative group velocity. The classical stress-driven model with Helmholtz kernel is then considered, highlighting its limitations in reproducing such effects due to its purely monotonic response and strictly positive group velocity. A three-parameter local/nonlocal stress-gradient model is also introduced, allowing for a more flexible description of the dispersive behavior through the variation of the nonlocal parameter, gradient length parameter and mixture parameter. However, despite this increased flexibility, anomalous dispersion cannot be captured within this framework. Finally, a generalized stress-driven model is proposed, in which the spectral representation of the nonlocal constitutive operator is not prescribed a priori but is determined so as to reproduce the peridynamic dispersion relation. The resulting model is shown to reproduce the same dispersive behavior as the peridynamic one, including anomalous dispersion phenomena. The results highlight that the capability of describing complex dispersive effects is strongly governed by the spectral structure of the adopted nonlocal kernel. The main results are presented and discussed by varying the governing parameters of the models.