Comparison of peridynamics and lattice dynamics wave dispersion relationships

Peridynamics is a non-local continuum formulation and material points inside an influence domain, named horizon, can interact with each other. Peridynamics also has a capability to represent wave dispersion which is observed in real materials especially at shorter wave lengths. Therefore, wave frequency and wave number have a non-linear relationship in peridynamics. In this study, we present wave dispersion characteristics of peridynamics and compare with lattice dynamics to determine the horizon size for different materials including copper, gold, silver and platinum through an iterative process for the first time in the literature. This study also shows the superiority of peridynamics over classical continuum mechanics by having a length scale parameter, horizon, which allows peridynamics to represent the entire range of dispersion curves for both short and long wave lengths as opposed to limitation of classical mechanics to long wave lengths.