Curved-crease origami differs from prismatic, or straight-crease origami, in that the folded surface of the pattern is bent during the folding process. They are developable, but with regions of non-zero principal curvature, a combination of attributes have seen them adopted for numerous novel engineering applications. They are also extremely beautiful and so are widely used in fine art, industrial design,and architecture.

Rigid-Foldable Curved-Crease Approximations

To reduce the difficulty in parameterising and modelling the pattern geometry, the curved-crease surface can be approximated as a planar quadrangle (PQ) mesh. Miura-type patterns can be used as a ‘base’ geometry from which to build such curved-crease approximations. The generated curved-crease pattern corresponds to piecewise assembly of self-similar straight-crease patterns and so can be used to simulate a rigid single-DOF folding motion. Further information: DOI: 10.1115/1.4028532.

Elastica Curved-Crease Origami

The analytical geometric construction method was developed for curved-crease origami, that combines a 1D elastica solution for large elastic bending deformation with a straight-crease origami projection and reflection process. This avoids the need for surface discretisation and can thus concisely and accurately capture the principal surface curvature and developability characteristics of elastically-bent curved-crease origami. Further information: DOI: 10.1016/j.ijsolstr.2017.11.029.

Elastic Buckling Shape Control

Curved-crease origami can be control the shape of elatically-buckled tubes. By using pre-embedded curved-crease origami patterns in thin-walled cylinders, the failure mode can be pre-determined as a stabilized high-order elastica surface, which manifests via a diamond buckling mode. Measurements of the deformed surface show the buckled shapes to have a near-exact correspondence to the analytical curved-crease origami description. DOI: 10.1016/j.ijmecsci.2018.11.005.