Connecting the Branches of Multistable Non-Euclidean Origami by Crease Stretching

TL;DR

This paper introduces crease stretching as a method to connect disconnected solution branches in non-Euclidean origami, enabling multistability and passive deployment for advanced structural applications.

Contribution

It demonstrates that crease stretching can unify solution branches, create additional stable states, and serve as an energy storage mechanism in non-Euclidean origami systems.

Findings

Crease stretching connects disconnected solution branches.

A third stable state is enabled by crease stretching.

The model allows inverse design of multistable origami.

Abstract

Non-Euclidean origami is a promising technique for designing multistable deployable structures folded from nonplanar developable surfaces. The impossibility of flat foldability inherent to non-Euclidean origami results in two disconnected solution branches each with the same angular deficiency but opposite handedness. We show that these regions can be connected via "crease stretching" wherein the creases exhibit extensibility in addition to torsional stiffness. We further reveal that crease stretching acts as an energy storage method capable of passive deployment and control. Specifically, we show that in a Miura-Ori system with a single stretchable crease, this is achieved via two unique, easy to realize, equilibrium folding pathways for a certain wide set of parameters. In particular, we demonstrate that this connection mostly preserves the stable states of the non-Euclidean system, while resulting a third stable state enabled only by the interaction of crease torsion and stretching. Finally, we show that this simplified model can be used as an efficient and robust tool for inverse design of multistable origami based on closed-form predictions that yield the system parameters required to attain multiple, desired stable shapes. This facilitates the implementation of multistable origami for applications in architecture materials, robotics, and deployable structures.