Rigidity phase transition in granular packings

We numerically model two-dimensional systems of granular aggregates confined between two rough walls and demonstrate that at a critical grain volume fraction ${\nu }_c$ an abrupt rigidity transition occurs. The transition has first-order characteristics, although the elastic constants undergo a second-order transition. Densely packed grains, with a volume fraction $\nu >{\nu }_c,$ display an elastic-plastic rheology. Loose packings, with $\nu <{\nu }_c,$ display gaslike characteristics. It is shown that when the volume fraction is allowed to change freely (applying a constant normal stress to the walls), it evolves spontaneously to ${\nu }_c$ under a wide range of boundary stress values, demonstrating that the phase boundary is an attractive critical state.