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On the relationship between the modulus of particulate media and the surface energy of the constituent particles

Considers the mathematical formulation for the macroscopic elastic properties of particulate media in terms of the distribution of the stiffnesses at the contacts between the constituent particles. Both random and regular arrays are considered. If the particles are sufficiently small the analysis leads to a relationship between the ensemble modulus and the surface energy of the solid particles. It has been previously suggested that, for random isotropic assemblies of spheres, this relationship could be predicted by a simple density scaling rule based on the solution for a simple cubic packing. The paper re-examines this analysis and identifies an inconsistency in the definition of the contact stiffness. An alternative analysis is also presented which is based on the solution for a body centred cubic packing. The new analysis suggests that the original theory overestimates the ensemble modulus and underpredicts the surface energy of the solid particles.