On Phase Transition and Self-Organized Critical State in Granular Packings

We model two-dimensional systems of granular aggregates confined between two planes and demonstrate that at a critical grain volume fraction an abrupt rigidity transition occurs. This transition is observed both in static and shear tests. The grain volume fraction at which the transition occurs, νc, decreases with increasing friction between the grains. Densely packed grains, with a volume fraction ν > νc, display an elastic-plastic rheology. Dilute packings, with ν < νc, display gas-like characteristics. It is shown that when volume fraction is allowed to change freely (using constant normal stress boundary condition), it evolves spontaneously to νc under a wide range of boundary conditions, exhibiting ’self-organized criticality’. Granular media is a fundamental, yet not well understood, complex system with wide ranging applications to technological and natural systems. In recent years there has been much work on granular dynamics, with emphasis on how behavior of grain aggregates may resemble solids, liquids or gases [1]. Already Reynolds in 1885 [2] noted that loosely packed sands deform easily as fluids while dense packings resist shear as solids. The two phases