Shock Absorption by Small, Scalable, Tapered Granular Chains

Making shock proof layers is an outstanding challenge. Elastic spheres are known to repel softer than springs when gently squeezed but develop strong repulsion upon compression and the forces between adjacent spheres lead to \textit{ballistic-like} energy transfer between them. Here we demonstrate for the first time that a \textit{small alignment} of progressively shrinking spheres of a strong, light-mass material, placed horizontally in an appropriate casing,$^{ }$can absorb $\sim $ 80{\%} ($\sim $90{\%}) of the incident force (energy) pulse. The system can be scaled down in size. Effects of varying the size, radius shrinkage and restitutive losses are shown via computed ``dynamical phase diagrams.''