Micro-mechanical modelling of granular material. Part 2: Plane wave propagation in infinite media

This paper discusses the propagation of plane body waves through a second-g radient micropolar elastic continuum. In an accompanying paper, this macros copic constitutive law has been derived from the micro-level particle chara cteristics, which are the inter-particle stiffness, the particle size and t he pack-age density. As a result of incorporating the micro-scale effects, the body waves propagate in a dispersive manner, where dispersion becomes m ore prominent when the wavelength of the generated body waves reaches the o rder of magnitude of the particle size. After successively deriving the equ ations of motion and the dispersion relations for plane body wave propagati on, the compressional wave properties for the second-gradient micro-polar m odel are compared to those for the Born-Karman lattice structure. Furthermo re, distinguished features of the second-gradient micro-polar model are exh ibited by comparing the dispersion relations of the coupled propagation of the shear wave and the micro-rotational wave with those of more simple cons titutive models. The paper ends with a parameter study, where the effect by the translational particle contact stiffness and the rotational particle c ontact stiffness is examined.