Geometric Mechanics of Curved Crease Origami

TL;DR

This paper develops a geometric mechanics theory for curved crease origami, analyzing how folding along a circle creates buckled 3D structures influenced by material properties and fold stiffness.

Contribution

It introduces a theoretical framework for understanding the shape and mechanics of curved crease origami structures, including analytical and numerical analysis.

Findings

Stiff folds produce constant curvature creases with oscillatory torsion.

Softer folds exhibit broken symmetry with oscillatory curvature and torsion.

The theory is validated by numerical simulations and extended to multiple folds.

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 which allow us to generalize our analysis to study multiply folded structures.