Abstract
Origami, the ancient art of folding thin sheets, has attracted increasing attention for its practical value in diverse fields: Architectural design, therapeutics, deployable space structures, medical stent design, antenna design and robotics. In this survey article, we highlight its suggestive value for the design of materials. At continuum level, the rules for constructing origami have direct analogues in the analysis of the microstructure of materials. At atomistic level, the structure of crystals, nanostructures, viruses and quasi-crystals all link to simplified methods of constructing origami. Underlying these linkages are basic physical scaling laws, the role of isometries, and the simplifying role of group theory. Non-discrete isometry groups suggest an unexpected framework for the design of novel materials. This article is part of the theme issue 'Topics in mathematical design of complex materials'.
| Original language | English (US) |
|---|---|
| Article number | 20200113 |
| Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 379 |
| Issue number | 2201 |
| DOIs | |
| State | Published - Jul 12 2021 |
Bibliographical note
Funding Information:Funding. The authors thank the Isaac Newton Institute for Mathematical Sciences for support during the program ‘The mathematical design of new materials’ supported by EPSRC grant no. EP/R014604/1. The residence of R.D.J. there was supported by a Simons Fellowship. R.D.J. and H.L. also benefited from the support of ONR (N00014-18-1-2766), MURI (FA9550-18-1-0095), and a Vannevar Bush Faculty Fellowship, and all authors acknowledge the support of the MURI project FA9550-16-1-0566. Acknowledgements. The authors thank Reidun Twarock for helpful comments.
Publisher Copyright:
© 2021 The Authors.
Keywords
- Design of materials
- Isometry groups
- Origami
- Phase transformations
- Quasi-crystals
- Viruses
PubMed: MeSH publication types
- Journal Article