Self-assembly of granular crystals

Acoustic meta-materials are engineered materials with the ability to control, direct, and manipulate sound waves. Since the 1990s, several groups have developed acoustic meta-materials with novel capabilities including negative index materials for acoustic super-lenses, phononic crystals with acoustic band gaps for wave guides and mirrors, and acoustic cloaking device. Most previous work on acoustic meta-materials has focused on continuum solids and fluids. In contrast, we report on coordinated computational and experimental studies to use macro-self-assembly of granular materials to produce acoustic meta-materials. The advantages of {\it granular} acoustic materials are three-fold: 1) {\it Microscopic control:} The discrete nature of granular media allows us to optimize acoustic properties on both the grain and network scales. 2) {\it Tunability:} The speed of sound in granular media depends strongly on pressure due to non-linear contact interactions and contact breaking. 3) {\it Direct visualization:} The macro-scale size of the grains enables visualization of the structure and stress propagation within granular assemblies. We report simulations and experiments of vibrated particles that form a variety of self-assembled ordered structures in two- and three-dimensions. In the simplest case of mono-disperse spheres, using a combination of pressure and vibration we produce crystals with long-range order on the scale of 100's of particles. Using special particle shapes that form ``lock and key'' structures we are able to make binary crystals with prescribed stoichiometries. We discuss the mechanical properties of these structures and methods to create more complicated structures.