ROBERT HOOKE, a contemporary of Isaac Newton, was in his day even more of a polymath than that great natural philosopher. Sic transit gloria mundi. These days Hooke is well known only for his law of elasticity: that the amount a material stretches is proportional to the force applied. Such stretching, inter alia, causes the material to get thinner, of course. Unless the substance in question is what is known as an auxetic material. Then, it gets fatter. And Robert Hooke’s near namesake, Patrick Hook, the boss of Auxetix, a small firm based in south-west England, hopes to exploit this weirdness to make everything from body armour to dental floss.

To understand how an auxetic material works, imagine a rubber bungee cord with a piece of fishing line wrapped around its length in an open spiral. If you pull on the line, the cord’s shape becomes distorted into a spiral, too. That spiral is, in effect, wider than the undistorted cord. But because the line holds it in place, it is no shorter. And if several such line-wrapped bungee cords were laid alongside each other and the fishing lines pulled simultaneously, then they would push each other aside, increasing the area that they covered and the volume they occupied.

The threads from which Auxetix’s materials are made are thinner than bungee cords, obviously. But they are constructed in a similar way, using a technique called weft insertion to wrap a thin line of high-strength material such as Kevlar around a core made of specially processed elastic polyester. These threads are then woven into auxetic cloth that can be cut to shape for the application in mind.

Auxetic materials have two useful properties. One is the shape change per se. The other is that the shape change absorbs and stores energy, and does so rapidly. If a sheet of the material is hit in one place, the energy of the impact is thus spread over the whole sheet. Then, when the material relaxes back into its original shape, that energy is dissipated from the entire surface, rather than just the point of impact.

Auxetix has already tested a bomb-resistant curtain made of such material. It can stop fragments of glass and similar shrapnel, but is thin enough to be translucent and thus let a useful amount of daylight through a window. If hit by a blast, the curtain expands. That creates pores which allow the air of the blast to pass through, so that the cloth is not damaged—but these pores are small enough to stop the passage of solid debris. The kinetic energy of the debris is then absorbed by the material.

The firm also hopes to use its technique to make body armour. The American army’s current kit, known as Interceptor Body Armour, weighs up to 15kg including ceramic-plate inserts. Soldiers are obviously keen to reduce this weight. Dr Hook has tested prototype auxetic armour that is 10% lighter than Interceptor while, he hopes, being just as effective at absorbing impacts.

If the new material works in these military applications, then Dr Hook hopes civilian ones will follow. Auxetic seat belts would dissipate a driver’s kinetic energy in a crash more effectively than existing designs. Auxetic dental floss would expand into the gaps between teeth when it was pulled. And a less obvious application is in an easy-to-clean filter: stretch this filter and its pores grow, allowing stuff stuck in them to be flushed through when the filter is washed.

That line of thinking leads to the idea of smart filters, which maintain a constant pore size by stretching as the gets clogged up, and also to bandages that dispense drugs in response to swelling. In fact, once you get used to the idea of something that stretches thick instead of being stretched thin, the possibilities are enormous. Welcome, then, to the world not of Hooke’s law, but Hook’s.