Gradient-index granular crystals: From boomerang motion to asymmetric transmission of waves

We present a gradient-index crystal that offers extreme tunability in terms of manipulating the propagation of elastic waves. The crystal is a chain made of cylindrical granular particles interacting as per a nonlinear contact law. We show that the stacking angles can be tuned to maintain the desired gradient in stiffness along the system. For small-amplitude excitation, we achieve extreme control over wave transmission depth into the crystal. We numerically and experimentally demonstrate a boomerang-like motion of wave packet injected into the crystal. For large-amplitude excitations on the same crystal, we invoke nonlinear effects, and we numerically and experimentally demonstrate asymmetric wave transmission from two opposite ends of the crystal. Such tunable systems can thus inspire a novel class of designed materials to control linear and nonlinear elastic wave propagation in meso-, micro-, and nano-scales.