Strain versus stress in a model granular material: A Devil's staircase
The series of equilibrium states reached by disordered packings of rigid, frictionless disks in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration space are found to be independent of specific assumptions ruling granular dynamics, and determined by geometry only. A monotonic increase in some macroscopic loading parameter causes a discrete sequence of rearrangements. For a biaxial compression, we show that, due to the statistical importance of such events of large magnitude, the dependence of the resulting strain on stress direction is a Levy flight in the thermodynamic limit.
Combe
G
Laboratoire Central des Ponts et Chaussees, 58 Boulevard Lefebvre, 75732 Paris Cedex 15, France.
Roux
JN