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 [Formula Presented] 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 [Formula Presented] display an elastic-plastic rheology. Loose packings, with [Formula Presented] 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 [Formula Presented] under a wide range of boundary stress values, demonstrating that the phase boundary is an attractive critical state.