Strain versus stress in a model granular material: A devil's staircase

The series of equilibrium states reached by disordered packings of rigid, f rictionless disks in two dimensions, under gradually varying stress, are st udied by numerical simulations. Statistical properties of trajectories in c onfiguration space are found to be independent of specific assumptions ruli ng granular dynamics, and determined by geometry only. A monotonic increase in some macroscopic loading parameter causes a discrete sequence of rearra ngements. For a biaxial compression, we show that, due to the statistical i mportance of such events of large magnitude, the dependence of the resultin g strain on stress direction is a Levy flight in the thermodynamic limit.