Closed-Form Wave Dispersion Relationships for Ordinary State-Based Peridynamics

Abstract

Peridynamics (PD) is a new continuum mechanics formulation introduced to overcome limitations of classical continuum mechanics (CCM). This is mainly achieved by using integro-differential equations rather than partial differential equations. Another important difference of PD is its nonlocal nature with respect to local characteristic of CCM. Moreover, it has a length scale parameter, horizon, defining the range of nonlocal interactions between material points. This nonclassical behaviour also shows itself for dispersion relationships. As opposed to linear dispersion relationships for CCM, PD dispersion relationships are non-linear similar to the observed in experiments. In this study, closed-form dispersion relationships are provided for ordinary state-based peridynamics which is one of the most common PD formulations. Finally, derived closed-form solutions are used to demonstrate the dispersion relationships for various material systems including copper, gold, silver and platinum.