Geometric Mechanics of Periodic Pleated Origami

TL;DR

This paper analyzes the geometric mechanics of Miura-ori origami, revealing its elastic properties and Poisson's ratios, and provides a method for inverse design to optimize its mechanical response.

Contribution

It introduces a geometric framework for understanding and designing the mechanical behavior of Miura-ori origami structures.

Findings

In-plane and out-of-plane Poisson's ratios are equal in magnitude but opposite in sign.

The geometric approach enables inverse design of optimal structural parameters.

Calculated the elastic response of Miura-ori sheets to various deformations.

Abstract

Origami is the archetype of a structural material with unusual mechanical properties that arise almost exclusively from the geometry of its constituent folds and forms the basis for mechanical metamaterials with an extreme deformation response. Here we consider a simple periodically folded structure Miura-ori, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by 2 angles and 2 lengths. We use the geometrical properties of a Miura-ori plate to characterize its elastic response to planar and non-planar piece- wise isometric deformations and calculate the two-dimensional stretching and bending response of a Miura-ori sheet, and show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign. Our geometric approach also allows us to solve the inverse design problem of determining the geometric parameters that achieve the optimal geometric and mechanical response of such structures.