Scientists discover a new shape using rubber bands

While setting out to fabricate new springs to support a cephalopod-inspired imaging project, a group of Harvard researchers stumbled upon a surprising discovery: the hemihelix, a shape rarely seen in nature.

This made the researchers wonder: Were the three-dimensional structures they observed randomly occurring, or are there specific factors that control their formation? The scientists answered that question by performing experiments in which they stretched, joined, and then released rubber strips. Complemented by numerical simulations and analysis of the process, the results appear in a paper published in the journal PLOS ONE.

Knowing precisely how to make the structures, predictably and consistently, may enable scientists to mimic the geometrical features in new molecules that could lead to possible advances in modern nanodevices, including sensors, resonators, and electromagnetic wave absorbers.

“Once you are able to fabricate these complex shapes and control them, the next step will be to see if they have unusual properties; for example, to look at their effect on the propagation of light,” says Katia Bertoldi, associate professor of applied mechanics at theHarvard School of Engineering and Applied Sciences (SEAS).

The shape that Bertoldi and colleagues at SEAS unexpectedly encountered is a hemihelix with multiple “perversions.” Helices are three-dimensional structures; think of a corkscrew or a Slinky toy. Hemihelices form when the direction in which the spiral turns—known as the chirality—changes periodically along the length. The reversal in chirality is called a perversion.

The team was trying to make two-dimensional springs by taking two strips of rubber material of different lengths and stretching the shorter one to reach the same length as the longer one and then sticking them together, explains David R. Clarke, Extended Tarr Family Professor of Materials at SEAS. “We expected that these strips of material would just bend—maybe into a scroll. But what we discovered is that when we did that experiment we got a hemihelix and that it has a chirality that changes, constantly alternating from one side to another.”

Jia Liu, a graduate student in Bertoldi’s group, tested differences in the aspect ratio—the width-to-height ratio of the rubber strips—and discovered that when a strip is very wide relative to its height, it produces a helix. Further measurements revealed that there is a critical value of the aspect ratio at which the resulting shape transitions from a helix to a hemihelix with periodic reversals of chirality.

Other classes of materials would simply break when stretched to the mismatched strains that the polymers endured—likely the reason this behavior had never been observed before.

“We see deterministic growth from a two-dimensional state—two strips bonded together—to a three-dimensional state,” Liu says. “The actual number of perversions, the diameter, everything else about it is entirely prescribed. There is no randomness; it’s fully deterministic. So if you make one hundred of these, they’ll always perform exactly the same way.”

Bertoldi adds: “From a mechanical point of view you can look at these as different springs with very different behavior. Some of them are very soft and then they stiffen up. Some are more linear. Simply by changing geometry, you can design this whole family of springs with very different behavior with predictable results.”

Bertoldi and Clarke believe that their findings provide important clues for how to fabricate a variety of three-dimensional shapes from flat parts.

“Intellectually, it’s interesting—and we believe it is significant too,” Clarke says. “There are a variety of complex shapes in nature that arise as a result of different growth rates. We stumbled quite by accident on a way to achieve fully deterministic manufacture of some three-dimensional objects.” Other contributors to the paper were Jiangshui Huang, a postdoctoral research associate in Clarke’s group and Tianxiang Su, a former postdoc in Bertoldi’s group.


  1. The discovery of the hemihelix, I think, is not by chance as mentioned previously and it will definitely lead to greater discoveries in nature. The phenomena lies in the fact that rubber is the only known material with these characteristics. Other materials will not be able to withstand the applied force.
    It is also remarkable that the pattern of perversions can be predicted, based on the structure of the two rubber bands used in the experiment.
    These unique qualities will contribute to new discoveries and assist in answering questions arising about the appearance of these newly discovered shapes.

  2. Now that the scientists know how to make these structures, it could probably lead to possible advances in the future. I agree with Maritza that nothing in the world is random and that the best explanation for the rubber bands to perform exactly the same is that they are fully deterministic.
    The phenomenon is very interesting and now scientists can achieve fully deterministic manufacture of three-dimensional objects.

  3. The discovery of the hemihelix by the team, along with its fully deterministic occurrence, is further proof that nature compiles to ‘laws of nature’ which ensures the necessary uniformability of molecules, proteins and other naturally occurring structures that allows for life on earth.
    I strongly believe that the discovery of such shapes will eliminate boundaries and allow for advances in the scientific field where new materials with new and useful properties can be synthesised.

  4. I believe that the finding of a hemihelix in the rubber bands and the conclusion that if you make a hundred or a thousand of these rubber bands you will always find the same results and they always perform exactly the the same, proof that nothing in this world and especially in nature is random. Everything happens for a reason. I hope with these experiments they can find significant uses and results for them.

  5. Yes I agree that rubber bands can actually help us find new shapes,due to the property of their molecules which are held together in such a way that their ‘alignment’ is altered only when force is applied.Otherwise they return back to their normal lattice when no force is implemented.
    Therefore i think such a property can allow the formation of many shapes from two dimensional to three,depending on how you apply your force and of course not exceeding limit of elasticity.


Please enter your comment!
Please enter your name here