Granular matter instability: A structural rigidity point of view

TL;DR

This paper links the instability in granular matter to the isostatic nature of contact networks, showing that large stiffness leads to a phase transition with heightened susceptibility to perturbations.

Contribution

It demonstrates that granular systems become isostatic at high stiffness, causing a phase transition with power-law stress response and increased instability susceptibility.

Findings

Contact network becomes isostatic at high stiffness

Stress response function exhibits power-law distribution

System shows large susceptibility to perturbations

Abstract

Stress paths in granular matter often suffer sudden large-scale rearrangements when the system is slightly perturbed, i.e. granular systems are unstable. We show in this paper that the observed instability is due to the minimally rigid, or isostatic, character of the system's contact network. It is first demonstrated that the contact network of a granular packing becomes isostatic (minimally rigid) in any dimension in the limit of large stiffness-to-load ratio. We next show that, in this isostatic limit, the load-stress response function becomes power-law distributed and takes exponentially large (growing as exp(H) where H is the system's height) positive and negative values. Large negative values of the load-stress response function imply instability, since only positive (compressive) stresses are allowed in non-cohesive granular packings. Thus there is an isostatic phase transition in the limit of large stiffness (or small load), and the resulting isostatic phase has an anomalously large susceptibility to perturbation.