Force Network Ensemble: A New Approach to Static Granular Matter

Abstract

For packings of hard but not perfectly rigid particles, the length scales that govern the packing geometry and the contact forces are well separated. This separation of length scales is explored in the force network ensemble, where one studies the space of allowed force configurations for a given, frozen contact geometry. Here we review results of this approach, which yields nontrivial predictions for the effect of packing dimension and anisotropy on the contact force distribution P (f ), the response to overall shear and point forcing, all of which can be studied in great numerical detail. Moreover, there are emerging analytical approaches that very effectively capture, for example, the form of force distributions.

Unjamming of granular packings due to local perturbations: Stability and decay of displacements

“…It is known that, in general case, mechanical equilibrium and Coulomb condition do not determine contact forces uniquely [6,9,12,13]. Consequently there is an ensemble of force networks that satisfy these conditions in the same contact geometry and for the same external load.…”

Force dynamics in weakly vibrated granular packings

“…A weakly driven granular assembly apparently amplifies the local nonlinearities present in the hertzian contacts and the friction law. We propose that force networks "activated" by weak vibrations explore many different configurations consistent with the overall boundary conditions for the stress [4,16]. Such activated force networks could possibly play a role in creep flows, which occur far away from shear zones, and more generally in any granular system in which tiny relative grain motions are excited.…”

“…Weak vibrations thus excite strongly nonlinear and glassy dynamics of the force network. Such force variations are allowed, since for a terrestrial granulate the grain and deformation scales are separated by many orders of magnitude [4]: a 700 µm diameter bronze sphere is compressed only ∼ 100 nm under the weight of 1000 additional identical spheres [5]. Figures 1(b,c) illustrate the main features of F 1 , the first harmonic of and nonlinearly on Γ [e.g.…”

An experimental investigation of the force network ensemble

“…As such, an underdetermined mechanical system, there are many ways in wich force and torque balance on each particle can be statistfied for any given packing geometry and boundary conditions [1,2]. There are both stable configurations, and unstable configurations and initially stable granular systems can evolve into catastrophic failure.…”

“…In this work, we present an experiment to look at the distribution of forces in a loaded granular system, while disentangling the effects of configuration from other influences. This is of interest to compare these distributions to predictions from the Force Network Ensemble theory [1]. Figure 1.…”