When you try to compress a spring, it pushes back. Materials scientists call that property positive stiffness. Although it is possible to create materials with negative stiffness, they are unstable. One push and they either fly apart or collapse into something with positive stiffness. Now a researcher reports in the 26 March *PRL* that in theory one can dramatically increase a material’s overall positive stiffness by peppering it with small bubbles of negative stiffness. In other experimental work, he has proven the concept. The surprising advance may one day be used to make more rigid airplane wings, quieter cars, and perhaps even temporary substitute tendons.

Mechanical designs are limited by stiffness. No one wants to fly in a plane equipped with wings that flap around like a wet noodle in turbulent air. One way that engineers increase the stiffness of a material is to mix it with a second material to form a composite. But once the geometry and composition are fixed, a thirty-year-old series of mathematical theorems sets a definitive upper limit on the stiffness. Increasing the upper limit requires heavier or more expensive materials; but there is a catch. “All these theorems make the tacit assumption that the stiffnesses are positive,” says University of Wisconsin materials scientist Roderic Lakes.

Adding negative stiffness turns all those assumptions on their heads. Instead of exerting the usual restoring force that tries to resist deformation, materials with a negative stiffness draw on the energy stored in their unstable equilibrium state to help the deformation proceed faster. Because they are unstable, negative stiffness materials usually break down rapidly. But small bubbles of negative stiffness can be preserved in a background of positive stiffness material. In some cases, the composite would have a lower overall stiffness, but in his *PRL* paper, Lakes shows mathematically that the opposite can also happen.

“The two phases cooperate with each other in some geometries, and you end up with zero effect,” says Lakes. “But it is not a linear addition, and sometimes the stiffnesses add inversely, giving more positive stiffness.” Although his paper presents a mathematical argument for the effect, it isn’t just a theoretical fantasy. In a separate article [1] Lakes shows that when silicone rubber tubes are buckled like partially squished soda cans, they have negative stiffness. When the buckled tubes are mixed with non-buckled tubes, the composite stiffness rises by orders of magnitude, as his theory predicts. The high stiffness composite also tends to damp vibrations quickly, says Lakes, which makes the materials potentially ideal for airplane wings and cars.

“This is quite innovative and exciting,” says Lawrence Katz, a biomedical engineer at Case Western Reserve University in Cleveland, OH. Katz speculates that negative stiffness materials could also be used in medical applications. “If a negative stiffness material could be placed in a tendon under tension, it would expand into a scaffold that leaves room for natural tissue to grow in,” says Katz.

### References

- R. S. Lakes, Philos. Mag. Lett. 81, 95-100 (2001).