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The fact that a disordered material is not constrained in its properties inthe same way as a crystal presents significant and yet largely untappedpotential for novel material design. However, unlike their crystallinecounterparts, disordered solids are not well understood. One of the primaryobstacles is the lack of a theoretical framework for thinking about disorderand its relation to mechanical properties. To this end, we study an idealizedsystem of frictionless athermal soft spheres that, when compressed, undergoes ajamming phase transition with diverging length scales and clean power-lawsignatures. This critical point is the cornerstone of a much larger "jammingscenario" that has the potential to provide the essential theoreticalfoundation necessary for a unified understanding of the mechanics of disorderedsolids. We begin by showing that jammed sphere packings have a valid linearregime despite the presence of "contact nonlinearities." We then investigatethe critical nature of the transition, focusing on diverging length scales andfinite-size effects. Next, we argue that jamming plays the same role fordisordered solids as the perfect crystal plays for crystalline solids. Not onlycan it be considered an idealized starting point for understanding disorderedmaterials, but it can even influence systems that have a relatively high amountof crystalline order. The behavior of solids can thus be thought of as existingon a spectrum, with the perfect crystal and the jamming transition at opposingends. Finally, we introduce a new principle wherein the contribution of anindividual bond to one global property is independent of its contribution toanother. This principle allows the different global responses of a disorderedsystem to be manipulated independently and provides a great deal of flexibilityin designing materials with unique, textured and tunable properties.

Unearthing the anticrystal: criticality in the linear response of disordered solids