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Lauren Dreier was looking through a book written by Gottfried Semper in 19th-century Germany when she noticed some exciting patterns made from lace. Dreier is a professional artist and designer who frequently incorporates technology. She also studies at Princeton University’s School of Architecture, where she decided to create printed illustrations in 3D.
She pulled out the ribbon-like plastic material she had been playing with in her studio and bent and connected the semi-rigid pieces. Dreier was surprised to discover that the structure she constructed had a bumpy geometry with four distinct hills and valleys. Dreier stated, “I expected it to make a dome. But it was this strange shape.” She was curious to discover what caused this unusual twist and reached out to Sigrid Adriaenssens (an associate professor in Princeton’s Department of Civil and Environmental Engineering). Adriaenssens could not explain it either but was equally intrigued. She suggested a joint investigation to discover the mysterious structural mechanics.
Dreier’s discovery led to a reconfigurable structure that the researchers called a big ring. The team created geometries from different looping behavior by tweaking the structure’s design. The Journal of the Mechanics and Physics of Solids published a paper describing the results. The mathematical framework can be applied to any general elastic rod network made of thread, bamboo, or plastic. This could lead to new products and technologies capable of changing their shape to improve performance in various conditions, from spacecraft to wearable tech.
Adriaenssens stated, “Taking inspiration from lacing patterns, I believe we can say nobody has done that before.” “Some of this behavior was unexpected, and you can adjust the angle or width to get a completely different behavior.” Dreier collaborated closely with Tian Yu, a postdoctoral researcher at Adriaenssens’ laboratory, to investigate the physics behind these observations. You stated, “This is my first collaboration with an artist, and I didn’t expect to be working on a project-inspired lace.” “I am fascinated by the mechanics of this project.”
The researchers used loose, looping patterns to create their lace, rather than traditional lacemakers who use soft threads that are twisted together. Dreier stated, “It’s about creating excess space between nodes.” The team began by creating closed structures known as bigons. They fixed the ends of two straight strips at an angle to create eye- or almond-like shapes. The bigons were similar to the metal hair clips of the 1990s in that they had bistability. The structures could switch between two stable bodies with slight pressure.
The researchers then made a chain of multiple bigons and connected their ends to create a loop. These bistable bigons created an overall structure that could be used to create many possible geometries. Multistable structures are a collection of forms that can be independently stable. These new big rings were sometimes described as folding similarly to a bandsaw blade. They also looped back on themselves. Their behavior can be adjusted by changing the angle of intersection and aspect ratio of the strips making up the bigons and the number of bigons in the ring.
You developed a numerical model of these structures while Dreier worked on them. You used Kirchhoff rod equations to show how an elastic rod, thin, behaves under displacements and forces. By comparing measurements taken from Dreier’s physical creations, the researchers confirmed the model’s accuracy and comparability. The computational model allowed for identifying different configurations that bigons and big on rings may be capable of taking theoretically. The researchers then tested these mathematical predictions through physical models to determine which equilibriums were stable. Dreier stated that there were a lot of back-and-forths between Tian and Dreier. He said, “If you make six big rings at such-and-such angles, what happens?”
The researchers eventually developed a new numerical model that captured multistable behavior. They believe it can be used in other studies to study general interlaced elastic network mechanics.
The team will continue to investigate the shapes immense on-based structures can form and how best to achieve those shapes. Their findings may lead to new materials that are compacted to take up the least space but can be compressed to create a larger package. Adriaenssens stated that materials and structures intended for space travel must be packed in a bundle and put in a rocket. Then they have to expand to the maximum extent possible. “Some of these combinations do that.”
There are also novel soft robotic arms, toys, and wearable technology that could be used in real life. For example, unique textiles could support a component in a particular position and loosen in other places. Adriaenssens stated that it could either enclose or not, stiffen and not. It can perform many functions.
The project demonstrates the untapped potential of interdisciplinarity between engineers and artists in addition to its practical application. Dreier stated that art is often driven by intuition and feelings, which are not scientifically based. However, it can lead to the discovery of interesting phenomena. “I was very excited to see these worlds come together in a handy way.
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