This paper discusses the propagation of plane body waves through a second-gradient micropolar elastic continuum. In an accompanying paper, this macroscopic constitutive law has been derived from the micro-level particle characteristics, which are the inter-particle stiffness, the particle size and the package density. As a result of incorporating the micro-scale effects, the body waves propagate in a dispersive manner, where dispersion becomes more prominent when the wavelength of the generated body waves reaches the order of magnitude of the particle size. After successively deriving the equations of motion and the dispersion relations for plane body wave propagation, the compressional wave properties for the second-gradient micro-polar model are compared to those for the Born-Karman lattice structure. Furthermore, distinguished features of the second-gradient micro-polar model are exhibited by comparing the dispersion relations of the coupled propagation of the shear wave and the micro-rotational wave with those of more simple constitutive models. The paper ends with a parameter study, where the effect by the translational particle contact stiffness and the rotational particle contact stiffness is examined.
Suiker, A. S. J., Borst, de, R., & Chang, C. S. (2001). Micro-mechanical modelling of granular material. Part 2: Plane wave propagation in infinite media. Acta Mechanica, 149(1-4), 181-200. https://doi.org/10.1007/BF01261671