The helix is a complex shape found in many natural settings. It is commonly illustrated by the shape of DNA molecules. The roots of some plants also burrow as helices, like corkscrews winding downward in search of richer soil. But during an experiment at Harvard University, mechanical engineers were surprised when a pair of rubber ribbons expected to form a helix did not, buckling into a shape rarely observed in nature.

Every helix winds in a left or right direction. The engineers observed what they called a hemihelix: a helix that changes its direction midway. The region along which it changes its direction is called a perversion. Charles Darwin observed plant tendrils forming hemihelices in 1888. Thanks to the Harvard team, we know why they form: "as a result of elastic instabilities", according to Katia Bertoldi, a professor of applied mechanics at the university and a participant in the study.

Starting with two strips of an elastic polymer of different lengths, the engineers stretched the shorter one to be the same length as the other. Then, while maintaining the stretching force, they joined the strips side-by-side. As the force was dwindled, the bi-strip twisted and bent to create either a helix or a hemihelix.

As energy due to stretching flows through the strip, the strip twists to reduce the load it bears. However, imperfections in the material could cause the strip to buckle at certain places, where perversions form and the chirality reverses.

“The geometry and pre-stretch parameters assign different competition power to these two categories,” explained Dr. Bertoldi in an email. Specifically, they found that which shape forms depends on the strips’ aspect ratio: the ratio of its length to width. With fixed stretching force for a given polymer, hemihelices were preferred for lower aspect ratios, when the buckling load increased. For ratios around or under 1, the number of perversions increased quickly. For ratios over 3, helices were preferred.

A paper detailing the study has been published today (April 24) in PLoS ONE, and presents another interesting conclusion. Though different elastic materials will have different aspect ratios at which the transition from helix to hemihelix occurs, the engineers found the formation of these shapes is independent of the material’s preferred mode of deformation.

Thus, by tweaking the make-up of certain elastic ribbons, Dr. Bertoldi’s work shows we can deterministically manufacture complex 3D shapes from flat structures. This is already a ubiquitous enterprise — e.g. beating sheet metal into the chassis of a car.

But what makes this study different is that, according to Michael Demkowicz, a materials scientist at the Massachusetts Institute of Technology not involved in the study, it describes how 2D objects could spontaneously change into interesting 3D ones by applying simple forces.

“The potential applications involve 3D electromagnetic wave-guides, and mechanical, thermal and chemical sensors,” Prof. Bertoldi added.

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