School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA.
Phys Rev Lett. 2013 May 24;110(21):215501. doi: 10.1103/PhysRevLett.110.215501. Epub 2013 May 21.
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 Miura-ori structure, which is composed of identical unit cells of mountain and valley folds with four-coordinated ridges, defined completely by two angles and two 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 two-dimensional deformation of a plate in terms of a one-dimensional theory. Finally, we solve the inverse design problem of determining the geometric parameters for the optimal geometric and mechanical response of these extreme structures.
折纸结构是具有机械超材料特性的结构，其特性几乎完全来自组成褶皱的几何形状和分段等距变形的约束。在这里，我们描述了一种简单的周期性折叠型三原折纸结构的几何形状以及平面和非平面有效弹性响应，该结构由具有四配位脊的相同的山峰和山谷褶皱单元组成，完全由两个角度和两个长度定义。我们表明，平面内和平面外泊松比的大小相等，但符号相反，与材料特性无关。此外，我们表明单元的有效弯曲刚度是奇异的，这使得我们可以根据一维理论来描述板的二维变形。最后，我们解决了确定这些极端结构的最佳几何和机械响应的几何参数的逆向设计问题。
