Towards a relevant set of state variables to describe static granular packings

Abstract

We analyze, experimentally and numerically, the steady states, obtained by tapping, of a two-dimensional granular layer. Contrary to the usual assumption, we show that the reversible ͑steady state branch͒ of the density-acceleration curve is nonmonotonous. Accordingly, steady states with the same mean volume can be reached by tapping the system with very different intensities. Simulations of dissipative frictional disks show that equal volume steady states have different values of the force moment tensor. Additionally, we find that steady states of equal stress can be obtained by changing the duration of the taps; however, these states present distinct mean volumes. These results confirm previous speculations that the volume and the force moment tensor are both needed to describe univocally equilibrium states in static granular assemblies.

The effect of the packing fraction on the jamming of granular flow through small apertures

“…The sharp drop of φ is associated to a discontinuous order-disorder transition previously reported for this model [18] and also observed in granular dynamics of polygonal grains [27]. The appearance of the minimum packing fraction as a function of tap intensity has been reported for several models (including a frustrated lattice gas model [28], a Monte Carlo type deposition [21] and a realistic discrete element method simulation [21]) and in experiments of tapping with a quasi-2D system [29,30]. For the model we use in this paper, the minimum φ has been shown to exist even if bidisperse systems are considered [31].…”

“…This has been pointed out in Refs. [29,30] where steady states with the same φ but bearing different stresses were obtained through tapping. In our simulations, forces are not calculated and therefore the stress tensor cannot be obtained.…”

Relevance of system size to the steady-state properties of tapped granular systems

“…Stationary states of static granular packs subjected to pulsed excitations have been considered by a number of workers [1][2][3][4][5][6][7][8][9][10][11][12][13]. In recent years, the granular community has been focused on finding the correct variables to describe the macroscopic stationary states of static granular packs.…”

Topological analysis of tapped granular media using persistent homology

“…Thus, it has also been widely studied experimentally [32][33][34][35][36] and by means of simulations [28,37,38]. In [28,38] it was shown that the packing fraction φ of the bed is not a monotonous function of the tapping intensity . This raises the question of whether states with the same density are equivalent or not, in the sense of the statistical mechanical theory.…”

“…This question was addressed in [27] where the topology of 2D granular samples in mechanical equilibrium, in the sense of Edwards' theory, was studied. It was already known [28] that samples with the same density and number of particles may not be in the same state of equilibrium since the average force moment tensor can be different. In [27] it was shown that the topology of the contact network (without information on the forces) was enough to distinguish these mechanically different states.…”