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The math frame transforms any web into any shape using Kirigami cuts



  Shapeshifter
Researchers at the Harvard John A. Paulson College of Engineering and Applied Sciences have developed a mathematical framework that can be used to make any material sheet into any prescribed shape with the Paper Craft Kirigami. Picture credits: Harvard SEAS

Researchers at the Harvard John A. Paulson College of Engineering and Applied Sciences (SEAS) have developed a mathematical framework that allows each web to be put into a prescribed shape, meaning cut and kami, which means Paper).

Unlike his more famous cousin origami, which uses paper to form wrinkles, kirigami uses a pattern in a flat sheet of paper to change its flexibility and transform it into 3D shapes. Artists have long used this art form to create everything, from pop-up maps to castles and dragons, number, size and orientation of the cuts in a flat sheet so it can morph into any shape, "said L Mahadevan, de Valpine's Professor of Applied Mathematics, Physics, and Organismic and Evolutionary Biology, the lead author of the paper.

"If we get a general shape in two or three dimensions, how should we design the patterns in a reference shape?" Gary PT Choi, a graduate student at SEAS and first author of the paper, said, "In this work, we solve this problem by identifying the conditions that need to be met in order to be able to get it into shape To achieve this pattern, use a numerical optimization approach to determine the patterns, and then experimentally verify them. "”

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Har The vard John A. Paulson School of Engineering and Applied Sciences has developed a mathematical framework that allows each sheet of material to be put into any prescribed shape with the paper craft kirigami. Picture credits: Harvard SEAS

The study was published in Nature Materials .

This study builds on previous work by the Mahadevan Laboratory, which explored how origami-based patterns can be used as building blocks for the generation of nearly any three-dimensional curve shape.

"With Kirigami, we actually achieved a little more than origami," said Levi Dudte, a doctoral student in the Mahadevan lab and co-author of the paper. "The presence of cuts and holes inside the material gives Kirigami the ability to significantly change its shape."

"Our work is based on the inspiration of art, tempered by the rigor of mathematics and the challenges of the technical form, finding Kirigami tessellations that can turn a square into a circle or a flat sheet into a poncho is just the beginning. We believe this is just the beginning of a series of new ways to construct shapes in the digital age using geometry and topology, and computation, "Mahadevan said.

Next, the researchers want to explore how cuts and folds can be combined to create any shape with a set of properties that bind Origami and Kirigami together.


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Further information:
Form Programming with Kirigami Tessellations, Nature Materials (2019). DOI: 10.1038 / s41563-019-0452-y, https://nature.com/articles/s41563-019-0452-y

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College of Engineering and Applied Sciences Harvard John A. Paulson




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The mathematical framework transforms any material web with Kirigami cuts into any shape (2019, 20 August)
retrieved on August 20, 2019
from https://phys.org/news/2019-08-mathematical-framework-sheet-material-kirigami.html

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