  We investigate the effect of annealed disorder on the mechanical properties
and plasticity of a modeled amorphous solid by introducing a small fraction of
heavy impurities into the material which resembles real experimental systems.
The disorder being mobile, the total degrees of freedom and the potential
energy landscape of the pure system are preserved in our model. The mechanical
failure and the shear band formation in the amorphous solid in the presence of
annealed disorder are studied at the microscopic level by employing the finite
shear deformation protocol at nonzero temperature. A significant enhancement in
the shear modulus and yield stress is observed as a function of the heaviness
of the impurity particles. Via the analysis of the non-affine displacement
field and the microscopic strain fluctuations and the nature of their spatial
correlations we find that the shear band formation in the plastic regime is
gradually suppressed with increasing impurity mass. Eventually, a critical mass
of the disordered particles is identified above which the plastic events become
completely localized. This is marked by a transition from a power law to an
exponential decay in the spatial correlations non-affine displacement field.
Likewise, a similar change is observed in the strain correlation function,
transitioning from a slower $1/r$ decay to a more rapid $1/r^3$ decay. Finally,
the effect shear rate on the plastic events in the presence of annealed
disorder is explored.
