Rigidity phase transition in granular packings

We numerically model two-dimensional systems of granular aggregates confine d between two rough walls and demonstrate that at a critical grain volume f raction nu(c) an abrupt rigidity transition occurs. The transition has firs t-order characteristics, although the elastic constants undergo a second-or der transition. Densely packed grains, with a volume fraction nu>nu(c), dis play an elastic-plastic rheology. Loose packings, with nu>nu(c), display ga slike characteristics. It is shown that when the volume fraction is allowed to change freely (applying a constant normal stress to the walls), it evol ves spontaneously to nu(c) under a wide range of boundary stress values, de monstrating that the phase boundary is an attractive critical state. [S1063 -651X(99)01911-X].