变形折纸超材料中的应变相容性和梯度弹性
Strain compatibility and gradient elasticity in morphing origami metamaterials
摘要：
折纸设计的原则已被证明在许多技术应用中是有用的。特别是折纸镶嵌构成了一类具有不寻常的几何和弹性特性的变形超材料。虽然原则上不可伸展，但精细的折痕允许折纸超材料有效地非等距变形。确定与粗粒度折纸运动学兼容的应变以及相应的弹性泛函对于理解和控制折纸超材料的变形路径至关重要。在这里，在一个统一的理论，我们解决了这个问题的广泛的知名折纸镶嵌，包括三浦ori以及其更强大的倾斜，非可开发和非平面折叠的变种。我们发现，这些模式表现出两个普遍的属性。一方面，它们都承认相等但相反的面内和面外泊松比。另一方面，它们的弯曲能与它们的面内应变分离，而是取决于应变梯度。结果说明了折纸柱的自平衡几何的案例研究。
英文摘要：
The principles of origami design have proven useful in a number of technological applications. Origami tessellations in particular constitute a class of morphing metamaterials with unusual geometric and elastic properties. Although inextensible in principle, fine creases allow origami metamaterials to effectively deform non-isometrically. Determining the strains that are compatible with coarse-grained origami kinematics as well as the corresponding elasticity functionals is paramount to understanding and controlling the morphing paths of origami metamaterials. Here, within a unified theory, we solve this problem for a wide array of well-known origami tessellations including the Miura-ori as well as its more formidable oblique, non-developable and non-flat-foldable variants. We find that these patterns exhibit two universal properties. On one hand, they all admit equal but opposite in-plane and out-of-plane Poisson's ratios. On the other hand, their bending energy detaches from their in-plane strain and depends instead on the strain gradient. The results are illustrated over a case study of the self-equilibrium geometry of origami pillars.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
