  All solids yield under sufficiently high mechanical loads. Below yield, the
mechanical responses of all disordered solids are nearly alike, but above yield
every different disordered solid responds in its own way. Brittle systems can
shatter without warning, like ordinary window glass, or exhibit strain
localization prior to fracture, like metallic or polymeric glasses. Ductile
systems, e.g. foams like shaving cream or emulsions like mayonnaise, can flow
indefinitely with no strain localization. While there are empirical strategies
for tuning the degree of strain localization, there is no framework that
explains their effectiveness or limitations. We show that
Structuro-Elastoplastic (StEP) models provide microscopic understanding of how
strain localization depends on the interplay of structure, plasticity and
elasticity.
