Isostatic Phase Transition and Instability in Stiff Granular Materials

Structural rigidity concepts are used to understand the origin of instabilities in granular aggregates. It is first demonstrated that the contact network of a noncohesive granular aggregate becomes exactly isostatic when $I=k\epsilon /f_l\gg 1$, where $k$ is the stiffness, $\epsilon$ is the typical interparticle gap, and $f_L$ is the typical stress induced by loads. Thus random packings of stiff particles are typically isostatic. Furthermore isostaticity is responsible for the anomalously large susceptibility to perturbation observed in granular aggregates. The load-stress response function of granular piles is critical (power-law distributed) in the isostatic limit, which means that slight overloads will produce internal rearrangements.