Elasticity of sphere packings: pressure and initial state dependence

Elastic properties and internal states of isotropic sphere packings are studied by numerical simulations. Several numerical protocols to assemble dense configurations are compared. One, which imitates experiments with lubricated contacts, produces well coordinated states, while another, mimicking the effect of vibrations, results, for the same density, in a much smaller coordination number z, as small as in much looser systems. Upon varying the confining pressure P, simulations show a very nearly reversible variation of density, while z is irreversibly changed in a pressure cycle. Elastic moduli are shown to be mainly related to the coordination number. Their P dependence notably departs from predictions of simple homogenization approaches in the case of the shear moduli of poorly coordinated systems.