  Using numerical simulations, we consider an amorphous particle mixture which
exhibits shear banding, and find that the addition of even a small fraction of
chains strongly enhances the material strength, creating pronounced overshoot
features in the stress-strain curves. The strengthening occurs in the case
where the chains are initially perpendicular to the shear direction, leading to
a suppression of the shear band. For large strain, the chains migrate to the
region where a shear band forms, resulting in a stress drop. The alignment of
the chains by the shear bands results in a Bauschinger-like effect for
subsequent reversed shear. Many of these features are captured in a simple
model of a single chain being pulled through a viscous material. Our results
are also useful for providing insights into methods of controlling and
strengthening granular materials against failure.
