Geometric Mechanics of Periodic Pleated Origami
Abstract
Origami structures are mechanical metamaterials with properties that arise almost exclusively from the geometry of the constituent folds and the constraint of piecewise isometric deformations. Here we characterize the geometry and planar and nonplanar effective elastic response of a simple periodically folded Miuraori structure, which is composed of identical unit cells of mountain and valley folds with fourcoordinated ridges, defined completely by two angles and two lengths. We show that the inplane and outofplane 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 twodimensional deformation of a plate in terms of a onedimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.
 Publication:

Physical Review Letters
 Pub Date:
 May 2013
 DOI:
 10.1103/PhysRevLett.110.215501
 arXiv:
 arXiv:1211.6396
 Bibcode:
 2013PhRvL.110u5501W
 Keywords:

 81.05.Xj;
 46.70.De;
 Beams plates and shells;
 Physics  Classical Physics
 EPrint:
 doi:10.1103/PhysRevLett.110.215501