Journal
NATURE COMMUNICATIONS
Volume 8, Issue -, Pages -Publisher
NATURE PUBLISHING GROUP
DOI: 10.1038/ncomms15477
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Funding
- NSF MSPRF [DMS-1204686]
- American Australian Association
- NSF-MRSEC [1420709]
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Programmable stiff sheets with a single low-energy folding motion have been sought in fields ranging from the ancient art of origami to modern meta-materials research. Despite such attention, only two extreme classes of crease patterns are usually studied; special Miura-Ori-based zero-energy patterns, in which crease folding requires no sheet bending, and random patterns with high-energy folding, in which the sheet bends as much as creases fold. We present a physical approach that allows systematic exploration of the entire space of crease patterns as a function of the folding energy. Consequently, we uncover statistical results in origami, finding the entropy of crease patterns of given folding energy. Notably, we identify three classes of Mountain-Valley choices that have widely varying 'typical' folding energies. Our work opens up a wealth of experimentally relevant self-folding origami designs not reliant on Miura-Ori, the Kawasaki condition or any special symmetry in space.
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