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The mathematical framework converts each sheet of material into any shape using kirigami cuts



  Shift Sheets
Researchers at the John A. Paulson Harvard School of Engineering and Applied Sciences have developed a mathematical framework that can transform any sheet of material into any prescribed form using paper-making jigsaws. Credit: Harvard SEAS

Researchers at the John A. Paulson Harvard School of Engineering and Applied Sciences (SEAS) have developed a mathematical framework that can transform any piece of material into any prescribed form, inspired by a paper craft called kirigami (Japanese, kiri which means to cut daggers, which means paper).


Unlike his better-known original cousin, who uses folds to form paper, kirigami relies on a model of cuts in a flat sheet of paper to change its flexibility and allow it to be converted to 3-D forms. Artists have long used this art form to create everything from pop-up cards to castles and dragons.

"We asked if it was possible to discover the basic mathematical principles underlying the circuits and to use them to create algorithms that would allow us to design the number, size and orientation of sections in a flat sheet so that we could to transform into any form, "said L. Mahadevan, professor of applied mathematics, physics and organismal and evolutionary biology de Valpin, senior author of the article.

"In particular, if we are given a two- or three-dimensional overall shape, how do we design cut patterns in a reference shape so that we can make it expand to the final shape in one go?" said Gary P. T. Choi, a graduate student at SEAS and the first author of the article. "In this work, we solve this problem by identifying the constraints that must be satisfied in order to achieve this cutting model, using a digital optimization approach to identify the models, and then test this experimentally."

  Shift Sheets
Researchers at the John A. Paulson Harvard School of Engineering and Applied Sciences have developed a mathematical framework that can transform any sheet of material into any prescribed shape using kyigami to produce x artery. Credit: Harvard SEAS

The study was published in Nature Conservation Materials .

This study follows the previous work of Mahadevan's laboratory, which characterizes how origami-based models can be used as building blocks to create almost any three-dimensional curved shape.

"In fact, we were able to do a little more with jigsaws than we did with origami," says Levi Dudte, a graduate student at Mahadevan's laboratory and co-author of the article. "The presence of cuts and holes inside the material gives the kirigami the ability to significantly change its shape."

"Our work draws inspiration from the art, tempered by the rigor of mathematics and the challenges of engineering form. Finding tessellation kirigami that can transform a square into a circle or a flat sheet into a poncho is just the beginning. "We think this is just the beginning of a class of new ways of engineering in the digital age, using geometry, topology, and calculation," says Mahadevan.

Researchers are then looking to explore how to combine cuts and folds to achieve each shape with a given set of properties, thus linking origami and kyrigami.


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More information:
Programming form using tessellation circuits, Natural materials (2019). DOI: 10.1038 / s41563-019-0452-y, https://nature.com/articles/s41563-019-0452-y

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Harvard John A. Paulson School of Engineering and Applied Sciences
Reference :
The mathematical framework converts each sheet of material into any shape using kirigami sections (2019, August 20)
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from https://phys.org/news/2019-08-mathematical-framework-sheet-material-kirigami.html

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