I propose an extensive and ambitious program to greatly increase our understanding of the properties of amorphous solids, focusing mainly on the mechanical and magnetic properties of these fascinating materials, including their modes of failure via plastic flow, shear banding and fracture. Amorphous solids are important in many modern engineering applications, including as important examples structural glasses, metallic glasses and polymeric glasses. Our work combines a careful analysis of computer simulations of model-glasses with analytic theory in which we introduce to material science methods from statistical and nonlinear physics, both of which are subjects of expertise in our group. We challenge some present approaches that try to connect linear elasticity with some objects that carry plasticity; we claim that nonlinear elasticity is crucial, as its signature appears much before plastic failure. Similarly, we break away from current theories that assume that plastic events are spatially localized. We show that in athermal conditions the opposite is true, and we discover very interesting sub-extensive scaling phenomena characterized by a host of scaling exponents that need to be understood. The peculiarities of amorphous solids, in particular their memory of past deformation, call for the identification of new 'order parameters' that are sorely missing in present theories. Understanding the dependence on system size, temperature, external loading rates etc. calls for introducing new approaches and methods from statistical and nonlinear physics. In the body of the proposal we present a number of preliminary results that point towards a radically new way of thinking that we propose to develop to a new theory over the next five years.
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