Strain compatibility and gradient elasticity in morphing origami metamaterials

TL;DR

This paper develops a unified theory to analyze strain compatibility and gradient elasticity in origami metamaterials, revealing universal properties and providing insights into their morphing behavior and energy characteristics.

Contribution

It introduces a comprehensive framework for understanding strain compatibility and gradient elasticity in various origami tessellations, including Miura-ori and its variants.

Findings

Origami patterns have equal and opposite in-plane and out-of-plane Poisson's ratios.

Bending energy depends on strain gradient, not just in-plane strain.

Universal properties across different origami tessellations.

Abstract

The principles of origami design have proven useful in a number of technological applications. Origami tessellations in particular constitute a class of morphing metamaterials with unusual geometric and elastic properties. Although inextensible in principle, fine creases allow origami metamaterials to effectively deform non-isometrically. Determining the strains that are compatible with coarse-grained origami kinematics as well as the corresponding elasticity functionals is paramount to understanding and controlling the morphing paths of origami metamaterials. Here, within a unified theory, we solve this problem for a wide array of well-known origami tessellations including the Miura-ori as well as its more formidable oblique, non-developable and non-flat-foldable variants. We find that these patterns exhibit two universal properties. On one hand, they all admit equal but opposite in-plane and out-of-plane Poisson's ratios. On the other hand, their bending energy detaches from their in-plane strain and depends instead on the strain gradient. The results are illustrated over a case study of the self-equilibrium geometry of origami pillars.