Isostatic phase transition and instability in stiff granular materials

TL;DR

This paper explores how granular materials become critically stable and highly susceptible to perturbations as their contact network reaches an isostatic state at high stiffness, revealing a phase transition with significant instability implications.

Contribution

It demonstrates that granular aggregates become exactly isostatic at high stiffness, linking this to critical response behavior and phase transition phenomena.

Findings

Contact network becomes exactly isostatic at high stiffness

Isostaticity causes large susceptibility to perturbations

Stress response follows a power-law distribution at the isostatic limit

Abstract

In this letter, structural rigidity concepts are used to understand the origin of instabilities in granular aggregates. It is shown that: a) The contact network of a noncohesive granular aggregate becomes exactly isostatic in the limit of large stiffness-to-load ratio. b) Isostaticity is responsible for the anomalously large susceptibility to perturbation of these systems, and c) The load-stress response function of granular materials is critical (power-law distributed) in the isostatic limit. Thus there is a phase transition in the limit of intinitely large stiffness, and the resulting isostatic phase is characterized by huge instability to perturbation.