Closed-form dispersion relationships in bond-based peridynamics

Classical continuum mechanics (CCM) has been widely used in structural analysis for the last two centuries. Dispersion curves, which describes the relationship between wave frequency and wave number, are linear according to CCM. This yields constant phase velocities. However, experiments showed that for small wavelengths, dispersion curves are nonlinear. Hence, CCM is not capable to represent such material behaviour for small wavelengths. As an alternative approach, peridynamics can be utilised for this purpose. In this study, closed form dispersion relationships are derived and presented according to the original bond-based peridynamics formulation. According to the evaluated results, it can be concluded that peridynamics can capture non-linear frequency-wave number relationship as also observed in real materials.