The micromorphic constitutive parameters and dispersion behaviors in different granular crystals

Abstract This study considers granular crystals respectively with different three-dimensional microstructures categorized into a medium dense microstructure and two dense microstructures in one-sized and two-sized particles. Macroscopic micromorphic constitutive parameters are obtained for different granular crystals based on the micromechanics-based micromorphic model. Furthermore, two micromorphic wave modes are predicted for a plane strain problem, including coupled transverse-rotational and longitudinal waves. This study predicts obvious dispersions of micromorphic waves in different granular crystals. The widest frequency band gap is predicted for granular crystals with medium dense microstructure, and granular crystals with two dense microstructures have the same frequency band gap. The correlations are respectively obtained between frequency band gaps and void ratios, coordination numbers, characteristic lengths and micromorphic parameters. According to dispersion behaviors, correspondences between micromorphic and Cosserat waves are obtained. The simulations of dispersion curves based on the discrete element model are obtained to compare with the theoretical mircomorphic dispersion ones.