Internal states of model isotropic granular packings. II. Compression and pressure cycles

Abstract

This is the second paper of a series of three investigating, by numerical means, the geometric and mechanical properties of spherical bead packings under isotropic stresses. We study the effects of varying the applied pressure P (from 1 or 10 kPa up to 100 MPa in the case of glass beads) on several types of configurations assembled by different procedures, as reported in the preceding paper [1]. As functions of P , we monitor changes in solid fraction Φ, coordination number z, proportion of rattlers (grains carrying no force) x0, the distribution of normal forces, the level of friction mobilization, and the distribution of near neighbor distances. Assuming that the contact law does not involve material plasticity or damage, Φ is found to vary very nearly reversibly with P in an isotropic compression cycle, but all other quantities, due to the frictional hysteresis of contact forces, change irreversibly. In particular, initial low P states with high coordination numbers lose many contacts in a compression cycle, and end up with values of z and x0 close to those of the most poorly coordinated initial configurations. Proportional load variations which do not entail notable configuration changes can therefore nevertheless significantly affect contact networks of granular packings in quasistatic conditions.

Goddard rattler-jamming mechanism for quantifying pressure dependence of elastic moduli of grain packs

“…Although Goddard's ideas [10] have certainly received some attention [9,14,[17][18][19][20][21] in the granular packing literature, the present authors feel more attention to the details is appropriate, and this is the main contribution that is being made here. Goddard [10] was motivated to demonstrate that the elastic moduli increase with pressure as P 1/2 , instead of P 1/3 (which is again the result due to Hertz).…”

“…For random loose packing of grains, as many as 10% of the grains may be experiencing no stress whatsoever at low strain levels [9]. Such grains are called "rattlers," because there remains a certain degree of rattling room between themselves and their immediate neighbors.…”

Internal states of model isotropic granular packings. I. Assembling process, geometry, and contact networks

“…It is the first one of a series of three, and deals with the geometric characterization of low pressure isotropic states assembled by different procedures, both without and with intergranular friction. The other two, hereafter referred to as papers II [37] and III [38], respectively investigate the effects of compressions and pressure cycles, and the elastic response of the different numerical packings, with comparisons to experimental results. Although mechanical aspects are hardly dealt with in the present paper, we insist that geometry and mechanics are strongly and mutually related.…”

“…Although many geometric features of particle packings do not depend on the details of the model for contact elasticity, and could be observed as well with a simpler, linear unilateral elastic model, it is necessary to implement suitable non-linear contact models to deal with the mechanical properties in papers II and III [37,38]. Tangential elasticity and friction in contacts are appropriately described by the Cattaneo-Mindlin-Deresiewicz laws [39], which we implement in a simplified form, as used e.g., in refs.…”

“…Such values, as we shall check, are high enough for some characteristic properties of rigid sphere packings to be approached with good accuracy. Upon increasing P , the entire experimental pressure range will be explored in the two companion papers [37,38].…”