Geometry of Miura-folded metamaterials

TLDR

The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which depends only on geometry and is therefore scale‑independent. The paper presents two folded metamaterials that employ the Miura‑ori fold pattern. The authors introduce a folded shell with a Miura‑ori pattern that yields a negative in‑plane Poisson’s ratio and a positive out‑of‑plane bending ratio, and a cellular metamaterial formed by stacking compatible folded layers, allowing further design flexibility by varying the fold pattern within each layer.

Abstract

This paper describes two folded metamaterials based on the Miura-ori fold pattern. The structural mechanics of these metamaterials are dominated by the kinematics of the folding, which only depends on the geometry and therefore is scale-independent. First, a folded shell structure is introduced, where the fold pattern provides a negative Poisson's ratio for in-plane deformations and a positive Poisson's ratio for out-of-plane bending. Second, a cellular metamaterial is described based on a stacking of individual folded layers, where the folding kinematics are compatible between layers. Additional freedom in the design of the metamaterial can be achieved by varying the fold pattern within each layer.