Geometric mechanics of curved crease origami

Marcelo A. Dias, Levi H. Dudte, L. Mahadevan, Christian D. Santangelo

Research output: Contribution to journalArticle

63 Scopus citations

Abstract

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihedral angle of the fold, and the mechanical properties of the sheet of paper and the fold itself. When the sheet is isometrically deformed everywhere except along the fold itself, stiff folds result in creases with constant curvature and oscillatory torsion. However, relatively softer folds inherit the broken symmetry of the buckled shape with oscillatory curvature and torsion. Our asymptotic analysis of the isometrically deformed state is corroborated by numerical simulations that allow us to generalize our analysis to study structures with multiple curved creases.

Original languageEnglish (US)
Article number114301
JournalPhysical Review Letters
Volume109
Issue number11
DOIs
StatePublished - Sep 13 2012

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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