Revisiting Granular Packing Model Concepts and Evaluation Using Molecular Dynamics (MD)

Over the years, granular packing models have evolved from linear to non-linear models in order to improve their predictive capabilities. Expressed in terms of specific volumes, the paper shows that the models have been structured around three main approaches: a “top-down” approach based on the “worst-case scenario” from a completely segregated mixture and two “bottom-up” approaches, one based on an “ideal scenario” comprising filling and embedment mechanisms and the other based on a “quasi-ideal scenario” given two virtually unavoidable granular interactions: the wall effect and the loosening effect. These three approaches are illustrated by the use of three models (Chang’s, Westman’s, Roquier’s), evaluated on binary packings of spheres generated by Molecular Dynamics (MD). The minimum value of the specific volume is obtained at isostatic equilibrium under isotropic stress in the limit of frictionless rigid particles. Access to the coordination numbers between fine and coarse components leads to the definition of coarse-to-coarse, coarse-to-fine & fine-to-coarse, and fine-to-fine contact proportions, which allow to characterise, respectively, the zone dominated by coarse grains, the mixed zone and the zone dominated by fine grains. The three packing models are evaluated in terms of estimates of specific volumes with reference to these three zones for two size ratios.