The Mechanics of athermal amorphous solids

Solids may be broadly classifed as crystalline (ordered) and amorphous (disordered). Crystals are characterized by specific spatial symmetries (unlike liquids) and long range order. This regularity renders the mechanics and failure of crystalline solids tractable to theoretical analysis. Amorphous solids on the other hand are structurally disordered by construction. Like liquids, they possess full spatial symmetry but lack long range order. Disorder profoundly changes the mechanical behavior of materials, and challenges our understanding 
of their mechanics. In the absence of periodicity, one cannot explain the microscopic origin of their elastic constants. Additionally, the notion of a topological defect so fundamental to crystalline plasticity is rendered meaningless in amorphous solids. At the fundamental level, 
this problem lies at the frontier of Condensed Matter and Nonequilibrium Statistical Physics. Given a huge fraction of materials employed in daily use (including glasses, plastics, alloys, elastomers, and composites) are amorphous in character, understanding their mechanics 
and failure carries huge significance in Materials Physics applications. In this talk, I will discuss prior work and propose an experimental program to study the mechanical response and failure of amorphous solids with athermal granular solids as the prototypical system.