Geometric Mechanics of Curved Crease Origami

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.

References in corpus (1)

• Force and moment balance equations for geometric variational problems on curves

Cited by in corpus (12)

• Nonlinear conduction via solitons in a topological mechanical insulator
• The mechanical response of a creased sheet
• Programming stiff inflatable shells from planar patterned fabrics
• The shape and mechanics of curved fold origami structures
• Plasticity and Aging of Folded Elastic Sheets
• Shape programming lines of concentrated Gaussian curvature
• Cutting holes in bistable folds
• Interfacial metric mechanics: stitching patterns of shape change in active sheets
• Bistability and equilibria of creased annular sheets and strips
• Finite curved creases in infinite isometric sheets
• Explosive rigidity percolation in origami
• A unified geometric framework for axisymmetric thin sheet buckling