Direct micromechanics derivation and DEM confirmation of the elastic moduli of isotropic particulate materials:: Part II Particle rotation

In Part I, Fleischmann et al. (2013), we performed theoretical analyses of three cubic packings of uniform spheres (simple, body-centered, and face-centered) assuming no particle rotation, employed these results to derive the effective elastic moduli for a statistically isotropic particulate material, and assessed these results by performing numerical discrete element method (DEM) simulations with particle rotations prohibited. In this second part, we explore the effect that particle rotation has on the overall elastic moduli of a statistically isotropic particulate material. We do this both theoretically, by re-analyzing the elementary cells of the three cubic packings with particle rotation allowed, which leads to the introduction of an internal parameter to measure zero-energy rotations at the local level, and numerically via DEM simulations in which particle rotation is unrestrained. We find that the effects of particle rotation cannot be neglected. For unrestrained particle rotation, we find that the self-consistent homogenization assumption applied to the locally body-centered cubic packing incorporating particle rotation effects most accurately predicts the measured values of the overall elastic moduli obtained from the DEM simulations, in particular Poisson's ratio. Our new self-consistent results and theoretical modeling of particle rotation effects together lead to significantly better theoretical predictions of Poisson's ratio than all prior published results. Moreover, our results are based on a direct micromechanics analysis of specific geometrical packings of uniform spheres, in contrast to prior theoretical analyses based on hypotheses involving overall inter-particle contact distributions. Thus, our results permit a direct assessment of the reasons for the theory–experiment discrepancies noted in the literature with regard to previous theoretical derivations of the macroscopic elastic moduli for particulate materials, and our new theoretical results greatly narrow such discrepancies.