Granular materials, including sand and soil, have long been used to absorb impacts, but if the grains are all the same size, the shock waves are not always dispersed effectively. Instead, Sen’s team simulated a shock wave travelling along a chain of several hundred spherical elastic beads of ever-decreasing size. The beads at one end of the chain were around ten centimetres in diameter, and became progressively smaller.

After the shock wave has passed through the large sphere at the beginning of the chain, it proceeds to the next – slightly smaller – sphere. But the wave cannot be transmitted symmetrically into this sphere. To ensure that its energy is conserved, the wave is forced to stretch out. Its leading edge accelerates away from its trailing edge and this effect occurs every time the wave moves from one bead to the next. As the beads get smaller, the energy of the impulse is distributed and successive beads carry less and less kinetic energy.

Sen’s group found that the smallest bead at the other end of the chain feels the initial large impact as a long series of very small shocks. The amplitudes of these mini-shocks are less than 10% of the original impulse. “This very simple system demonstrates that theoretically, any size shock can be absorbed with assemblies of appropriately tapered chains”, explains Sen.

This kind of nonlinear wave propagation is still poorly understood, according to Sen. But he is optimistic that his team’s demonstration could one day be exploited to reuse the energy from unwanted man-made mechanical vibrations and even natural shocks from geological activity.