1 5 Ja n 20 09 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. 1 INTRODUCTION The mechanical properties of solidlike granular materials are well known to depend on the internal structure of the packing. Classically, one distinguishes between the behaviour of dense and loose materials (Wood 1990; Mitchell 1993). However, some results – see e.g. (Benahmed et al. 2004) – also indicate that other factors than the sole packing fraction (or void index) also determine the quasistatic response to applied load variations. In numerical simulations , it is a common practice to remove friction in the assembling stage in order to prepare dense samples (Makse et al. 1999; Thornton 2000). It is not guaranteed that the correct initial state, as obtained in laboratory experiments, is reproduced. Elastic properties, or sound wave velocities , are now commonly measured in soil mechanics (Chen et al. 1988; Hicher 1996) and condensed matter physics (Jia et al. 1999) laboratories. Their evaluation in numerical calculations can allow for comparisons with experiments. We report here on a numerical study of isotrop-ically assembled and compressed sphere packings, prepared in different initial states. Coordination numbers are found to vary according to the preparation method independently from density, and to determine the elastic moduli and their pressure dependence.