Lauren Dreier was paging by a nineteenth century e book by the German architect Gottfried Semper when she noticed some intriguing patterns impressed by lace. An expert artist and designer who typically incorporates expertise into her work, Dreier, who can also be a doctoral scholar on the Faculty of Structure at Princeton College, determined to recreate the printed illustrations in 3D.
She grabbed ribbon-like plastic materials she had been experimenting with in her studio, bending and connecting the semi-rigid strips. To Dreier’s shock, the construction she constructed assumed a bumpy geometry, with 4 distinct hills and valleys. “I assumed it might make a dome, nevertheless it was this uncommon form,” Dreier stated. Curious to know what precipitated this surprising twist, she reached out to Sigrid Adriaenssens, an affiliate professor in Princeton’s Division of Civil and Environmental Engineering. Adriaenssens couldn’t clarify it, both, however she, too, was intrigued. She proposed a joint investigation to seek out out what was behind the unusual structural mechanics.
Dreier’s discovery wound up resulting in the creation of a reconfigurable construction the researchers termed a bigon ring. By tweaking the precise design of the construction’s patterns, the staff was capable of produce a number of geometries that come up from totally different looping behaviors. Based on a paper describing the findings within the Journal of the Mechanics and Physics of Solids, the numerical framework behind the invention may be utilized to any normal elastic rod community, whether or not fabricated from thread, bamboo or plastic. It might additionally result in the creation of latest merchandise and applied sciences which might be able to altering form to enhance efficiency below variable situations from spacecraft to wearable expertise.
“Drawing inspiration from patterns in lacing, I feel we will say no person’s completed that earlier than,” Adriaenssens stated. “A few of these behaviors have been very surprising, and simply by adjusting the angle or the width, you get a very totally different conduct.”
To analyze the physics behind these observations, Dreier labored carefully with a number of collaborators, together with Tian Yu, a postdoctoral researcher in Adriaenssens’ lab. “That is my first time working with an artist, and I by no means anticipated to work on a undertaking impressed by lace,” Yu stated. “I’m fascinated by the mechanics a part of this undertaking.”
Not like conventional lace makers who use tender threads twisted collectively, the researchers organized their creations into unfastened, looping formations. “It’s all about creating extra house between the nodes,” Dreier stated. The staff began by making closed buildings known as bigons by fixing the ends of two initially straight strips at a sure angle, creating eye- or almond-like kinds. Much like metallic hair clips from the Nineteen Nineties, the bigons exhibited bistability, or two totally different secure shapes that the buildings might toggle between when slight stress was utilized.
From there, the researchers organized a number of bigons into a series, after which a loop by connecting their ends. The bistable bigons collectively created an total construction that might type quite a few potential geometries. The buildings have been multistable, which means they have been made up of a set kinds every of which might be secure impartial of the others. Bigon rings, as they known as these new kinds, generally exhibited an analogous folding conduct as a bandsaw blade, looping again on themselves. However their conduct is also tuned by adjusting the intersection angle and the side ratio of the strips that composed the bigons, and by altering the variety of bigons that made up the ring.
As Dreier labored on constructing these buildings, Yu created a numerical mannequin particular to them utilizing Kirchhoff rod equations for the way a skinny, elastic rod behaves when loaded with forces and displacements. The researchers have been capable of affirm the accuracy of the mannequin by taking measurements from Dreier’s bodily creations and evaluating the outcomes. The computational mannequin additionally made it potential to establish totally different configurations that the bigons or bigon rings would possibly be capable of take theoretically. The researchers then examined these mathematical predictions by the bodily fashions to see which equilibria have been secure and which weren’t. “Quite a lot of forwards and backwards got here from Tian going deep into the information and saying, ‘For those who make a six-bigon ring at such-and-such an angle, what occurs?’” Dreier stated.
The staff finally produced a brand new numerical mannequin that captures multistable conduct, and that the researchers say may be utilized to different research that look at the mechanics of normal interlaced elastic networks.
In future work, the staff plans to conduct a extra intensive investigation of the various shapes that bigon-based buildings are able to forming, and how you can greatest obtain particular goal shapes. Ultimately, their findings might result in new designs for supplies that have to be packed to take up as little room as potential, however that assume a a lot bigger type when unpacked. “For instance, supplies and buildings that go into house should be folded right into a bundle, put in a rocket after which should increase into as giant a measurement as potential,” Adriaenssens stated. “A few of these combos of parameters do this.”
Different potential real-world functions embrace novel tender robotic arms, toys and wearable expertise. The latter, for instance, might embrace particular textiles that stiffen to assist somebody’s arm in a sure place, and loosen in others. “It may possibly envelop issues or not, stiffen or not,” Adriaenssens stated. “It may possibly have many capabilities.”
Along with the sensible functions of the work, the undertaking additionally demonstrates the largely untapped worth of interdisciplinary collaboration between artists and engineers. Whereas artwork tends to be pushed by instinct and emotions that function outdoors of the realm of scientific pondering, “it will probably result in discoveries of some fascinating phenomena,” Dreier stated. “I used to be actually excited that these totally different worlds might come collectively in a really related method.”
Reference: “Numerical modeling of static equilibria and bifurcations in bigons and bigon rings” by Tian Yu, Lauren Dreier, Francesco Marmo, Stefano Gabriele, Stefana Parascho and SigridAdriaenssens, 24 April 2021, Journal of Mechanics and Physics of Solids.
Moreover Adriaenssens, Dreier and Yu, co-authors embrace Stefana Parascho, of the Princeton Faculty of Structure; Stefano Gabriele, of Roma Tre College; Francesco Marmo, of the College of Naples Federico II. Help for the undertaking was offered partially by the Princeton Faculty of Engineering and Utilized Science Undertaking X Fund, the Princeton College Magic Grants for Innovation and The Council for Worldwide Instructing and Analysis.