  A two dimensional amorphous material is modeled as an assembly of mesoscopic
elemental pieces coupled together to form an elastically coherent structure.
Plasticity is introduced as the existence of different minima in the energy
landscape of the elemental constituents. Upon the application of an external
strain rate, the material shears through the appearance of elemental slip
events with quadrupolar symmetry. When the energy landscape of the elemental
constituents is kept fixed, the slip events distribute uniformly throughout the
sample, producing on average a uniform deformation. However, when the energy
landscape at different spatial positions can be rearranged dynamically to
account for structural relaxation, the system develops inhomogeneous
deformation in the form of shear bands at low shear rates, and stick-slip-like
motion at the shear bands for the lowest shear rates. The origin of strain
localization is traced back to a region of negative correlation between strain
rate and stress, which appears only if structural relaxation is present. The
model also reproduces other well known effects in the rheology of amorphous
materials, as a stress peak in a strain rate controlled experiment staring from
rest, and the increase of the maximum of this peak with sample age.
