Geometric mechanics of periodic pleated origami
Z. Y. Wei, Z. V. Guo, L. Dudte, H. Y. Liang, and L. Mahadevan
Accepted
Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piece-wise isometric deformations. Here we characterize the geometry and planar and non-planar effective elastic response of 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 show that the in-plane and out-of-plane Poisson's ratios are equal in magnitude, but opposite in sign, independent of material properties. Furthermore, we show that effective bending stiffness of the unit cell is singular, allowing us to characterize the 2-dimensional deformation of a plate in terms of a 1-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters that achieve the optimal geometric and mechanical response of these extreme structures.