Effects of particle size distribution in a three-dimensional micropolar continuum model of granular media

A particle size distribution is incorporated into a three-dimensional homogenisation scheme, devised on the scale of a particle and its immediate (or first ring) of neighbours. Based on this scheme, micropolar continuum models for polydisperse, dry, and densely packed granular assemblies of spherical particles undergoing quasi-static deformation are developed for various particle size distributions. Three different cases are considered: (1) a monodisperse assembly, (2) a defect particle in an otherwise monodisperse assembly, and (3) an assembly of a given particle size distribution. In Case 1, an additional dependence on particle radius is found in 3D systems, compared with previous 2D constitutive laws. In Case 2, it is found that a small (large) particle in an otherwise monodisperse system increases (decreases) the stress compared to a purely monodisperse assembly, but the couple stress may increase or decrease depending on the relative size of the rolling resistance compared with the tangential stiffness coefficients. On the other hand, if the defect particle is substantially smaller or larger than the monodisperse particle size, the stress and couple stress are always increased. In Case 3, three different distributions are examined, i.e. square, normal and a lognormal distribution. For Cases 2 and 3, both the stress and the couple stress increased with the degree of dispersity, from the lower bound value corresponding to the monodisperse system considered in Case 1. Finally, the paper highlights areas that will need to be addressed to enable the future advancement of micromechanical continuum models.