Folding and Bending
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.
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.
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.
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.