  A two-dimensional lattice model for the formation and evolution of shear
bands in granular media is proposed. Each lattice site is assigned a random
variable which reflects the local density. At every time step, the strain is
localized along a single shear-band which is a spanning path on the lattice
chosen through an extremum condition. The dynamics consists of randomly
changing the `density' of the sites only along the shear band, and then
repeating the procedure of locating the extremal path and changing it. Starting
from an initially uncorrelated density field, it is found that this dynamics
leads to a slow compaction along with a non-trivial patterning of the system,
with high density regions forming which shelter long-lived low-density valleys.
Further, as a result of these large density fluctuations, the shear band which
was initially equally likely to be found anywhere on the lattice, gets
progressively trapped for longer and longer periods of time. This state is
however meta-stable, and the system continues to evolve slowly in a manner
reminiscent of glassy dynamics. Several quantities have been studied
numerically which support this picture and elucidate the unusual system-size
effects at play.

Statistical Mechanics