Manufacturers of camping tents or installers of bouncy castles would dream of it: spreading out a canvas, pulling on its corners and, in one fell swoop, popping up the protective dome or the crenellated cylindrical towers. This dream is distant, but physicists from the Laboratory of Physics and Mechanics of Heterogeneous Environments, in Paris, have succeeded in generating a shape by simply pulling on an elastic ribbon that should have remained banally flat. A tower did not grow, but the slender elastomer – 8 inches long, 3 cm wide and 2 mm thick – “tubified”, turning into a large straw.
It is not entirely by chance that these researchers came across the recipe for going from flat to curved. Nature does it very well, with flattened leaves like water lilies, or curled like lettuce. The roots of this idea lie in the “remarkable theorem” of the mathematician Carl Gauss, which lays down rules for the curvatures of objects. These explain, for example, that covering a sphere with a leaf is impossible without tearing or wrinkling it. “If the intensity of the growth of matter is not the same everywhere, then local curvatures appear, therefore forms”, summarizes José Bico (teacher-researcher at ESPCI), co-author of the study published in Physical Review Letters October 14.
In 2018, already with elastomers, this team had invented the “baromorphs”, pancakes traversed inside thin furrows cleverly designed so that the air pressure induces different swelling, to the point of revealing domes, saddles, and even a mask with eyes, nose and mouth.
“By chance, by pulling on one of these elastic cakes, we also noticed that it bends”, explains Etienne Reyssat (CNRS), another co-author, by joining the action to the word, a baromorph leftover in his hand. The secret is there. To “tubify” the tape, it is necessary to engrave on one of its surfaces parallel grooves over the entire length, perpendicular to its largest dimension. By pulling, the ribbon contracts a little over its width, but the grooves oppose this contraction. To resolve this tension, the object bends into a tube, the inside of which is the smooth part, and the outside the grooved part.
Better yet, if the grooves are no longer parallel but offset by a certain angle, the tube can “reverse”: the grooves on the inside and the smooth side on the outside. For an angle of 30 degrees, the tape remains flat. “It was a colleague, during a presentation at the lab, who suggested varying this angle. We hadn’t expected the curvature to reverse at all! “ remembers Emmanuel Siéfert, then in his thesis.
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