  We use Shear Transformation Zone (STZ) theory to develop a deformation map
for amorphous solids as a function of the imposed shear rate and initial
material preparation. The STZ formulation incorporates recent simulation
results [Haxton and Liu, PRL 99 195701 (2007)] showing that the steady state
effective temperature is rate dependent. The resulting model predicts a wide
range of deformation behavior as a function of the initial conditions,
including homogeneous deformation, broad shear bands, extremely thin shear
bands, and the onset of material failure. In particular, the STZ model predicts
homogeneous deformation for shorter quench times and lower strain rates, and
inhomogeneous deformation for longer quench times and higher strain rates. The
location of the transition between homogeneous and inhomogeneous flow on the
deformation map is determined in part by the steady state effective
temperature, which is likely material dependent. This model also suggests that
material failure occurs due to a runaway feedback between shear heating and the
local disorder, and provides an explanation for the thickness of shear bands
near the onset of material failure. We find that this model, which resolves
dynamics within a sheared material interface, predicts that the stress weakens
with strain much more rapidly than a similar model which uses a single state
variable to specify internal dynamics on the interface.
