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 (3)

• Hamiltonians for curves
• Buckling Thin Disks and Ribbons with Non-Euclidean Metrics
• Force and moment balance equations for geometric variational problems on curves

Cited by in corpus (29)

• Origami Multistabilty: From Single Vertices to Metasheets
• Nonlinear conduction via solitons in a topological mechanical insulator
• The mechanical response of a creased sheet
• Lattice Mechanics of Origami Tessellations
• Geometrically controlled snapping transitions in shells with curved creases
• "Wunderlich, meet Kirchhoff": A general and unified description of elastic ribbons and thin rods
• A non-linear rod model for folded elastic strips
• A comparative study of crumpling and folding of thin sheets
• Programming stiff inflatable shells from planar patterned fabrics
• An additive algorithm for origami design
• The shape and mechanics of curved fold origami structures
• Wrapping liquids, solids, and gases in thin sheets
• Origami building blocks: generic and special 4-vertices
• Plasticity and Aging of Folded Elastic Sheets
• Shape programming lines of concentrated Gaussian curvature
• Foldable Cones as a Framework for Nonrigid Origami
• Capillary buckling of a thin film adhering to a sphere
• Evolving, complex topography from combining centers of 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
• A relaxation constant in the folding of thin viscoelastic sheets
• Slender Origami with Complex 3D Folding Shapes
• Finite curved creases in infinite isometric sheets
• Folded Goursat surface and banana-shaped seedpod
• Crumple-Origami Transition for Twisting Cylindrical Shells
• Nonlinear mechanics of rigidifying curves
• Explosive rigidity percolation in origami
• A unified geometric framework for axisymmetric thin sheet buckling