Abstract

A study is presented of numerical assemblies of spheres created with the help of different preparation procedures: their elastic moduli crucially depend on how the samples are created. All samples match the density of assemblies used during a series of wave propagation experiments, but differ in coordination number, that is not accessible during experiments. Samples with a low coordination number show close mechanical properties to the experimental ones, thus proving that the role of coordination number dominates on that of density, contrary to the general belief. The shear modulus of those samples shows the 1/4-exponent power law dependence on pressure also observed during experiments, in contrast with the 1/6-exponent of the average strain assumption.

Such exponent is related to the displacement fluctuations from the average strain that grains undergo in order to attain equilibrium. These are the more relevant the smaller the coordination number. They can be decomposed into two distinct contributions, that we call “structural” and “residual” fluctuations, respectively. The structural fluctuations depend on the average structure of the assembly and determine the macroscopic behavior: we will test some of the approaches suitable to capture them in the frame of continuum mechanics. On the contrary, the residual fluctuations, often dominant in value, originate in the local deviations from the average geometry and contact stiffness, but have no influence at the macro-scale.