Aging and self-organization of shear bands in granular materials

We introduce a simple lattice model for the formation and evolution of shear bands in granular media. We study this model by numerical simulations and find that due to the localization of the shear band and the consequent inhomogeneous aging of the material, the average density shows very unusual system-size-dependent features. We find qualitatively similar features on studying the same model on a hierarchical lattice for which we are able to derive several analytical results.