Softening the Blow

Given the choice, you'd probably prefer 100 punches from your 4-year-old nephew to one from boxer Mike Tyson. But if you have to take an uppercut from the pugilist, a specially designed layer of ball bearings might save your skull. Arranged appropriately, such spheres can transform a single sharp blow into a sequence of much smaller impacts, a theoretical physicist predicts. Described in the 18 March PRL, the configuration might be used to construct a "granular protector" to shield delicate objects.

From packing sandbags around bunkers to using iron shot to absorb shocks in industrial processes, people have long used granular materials to protect things from impacts. Friction between the grains turns the energy of a blow into heat. But researchers are trying to develop more sophisticated granular materials that provide better protection from blasts--perhaps even for defense against terrorist bombs. Now, Jongbae Hong of Seoul National University in Korea calculates that granular materials can also trap energy and release it slowly over time. The key is to arrange grains of different masses in specific patterns.

Using a computer, Hong analyzed a one-dimensional chain of spherical beads much like ball bearings. When two spheres squeeze together, they push on each other with a force proportional to the change in the distance between their centers raised to the exponent 3/2. This "non-linear" force relation gives the chain peculiar properties: If the beads barely touch, ordinary oscillating sound waves cannot propagate along the chain. But if the end of the chain is struck sharply, a solitary pulse of compression, a bit like a tsunami, passes down the chain.

When the solitary wave passes from heavier beads into lighter ones, it breaks into a train of weaker, slower pulses. On the other hand, when a pulse moves from lighter beads to heavier ones, part of it reflects back through the lighter ones. Hong exploited both phenomena to trap the energy from one large pulse. In his virtual material, he arranged beads of the same size and hardness in several zones. Beads in the first zone were heaviest, those in the next one were lighter, and those in the third zone were lighter still. Midway down the chain, the pattern of masses reversed.

As a solitary wave progressed from one end of the chain, it disintegrated into several smaller pulses, which were then partially reflected. Soon, the chain was filled with small, slow pulses bouncing back and forth. These trickled out the far end of the chain gradually. In fact, the energy in the chain decreased in proportion to time raised to an exponent--a so-called power law. Curiously, the exponent was essentially the same regardless of the details of the chain. Hong envisions stacking chains of ball-bearing-sized particles to make a 3-dimensional material.

"The idea that you can cage a pulse inside this layer is conceptually fascinating," says Vitali Nesterenko of the University of California, San Diego, who in the 1980s predicted the existence of solitary waves in such chains. But turning the idea into a real material may be "a really great challenge," Nesterenko says. Surajit Sen of the State University of New York at Buffalo says the most intriguing finding is the power law describing the rate at which energy leaks out of the chain: "That should be checked" by experimenters.