Robust Folding of Elastic Origami

TL;DR

This paper introduces a model for elastic origami that accounts for finite stretching rigidity, revealing how elasticity influences folding pathways and reduces misfolding in complex self-folding origami structures.

Contribution

The study develops a new energy landscape model for elastic origami, demonstrating how elasticity can be tuned to improve folding accuracy and resilience against misfolding.

Findings

Elasticity regulates the proliferation of misfolded states.

Small errors induce metastability in rigid origami, but elasticity enhances robustness.

Stiffer folds and faces improve self-folding accuracy.

Abstract

Self-folding origami, structures that are engineered flat to fold into targeted, three-dimensional shapes, have many potential engineering applications. Though significant effort in recent years has been devoted to designing fold patterns that can achieve a variety of target shapes, recent work has also made clear that many origami structures exhibit multiple folding pathways, with a proliferation of geometric folding pathways as the origami structure becomes complex. The competition between these pathways can lead to structures that are programmed for one shape, yet fold incorrectly. To disentangle the features that lead to misfolding, we introduce a model of self-folding origami that accounts for the finite stretching rigidity of the origami faces and allows the computation of energy landscapes that lead to misfolding. We find that, in addition to the geometrical features of the origami, the finite elasticity of the nearly-flat origami configurations regulates the proliferation of potential misfolded states through a series of saddle-node bifurcations. We apply our model to one of the most common origami motifs, the symmetric "bird's foot," a single vertex with four folds. We show that though even a small error in programmed fold angles induces metastability in rigid origami, elasticity allows one to tune resilience to misfolding. In a more complex design, the "Randlett flapping bird," which has thousands of potential competing states, we further show that the number of actual observed minima is strongly determined by the structure's elasticity. In general, we show that elastic origami with both stiffer folds and stiffer faces self-folds better.