On local kirigami mechanics I: Isometric conical solutions
On local kirigami mechanics I: Isometric conical solutions
复制标题
DOI：
10.1016/j.jmps.2021.104370
复制
发表时间：
2021-02
影响因子：
5.3
通讯作者：
Souhayl Sadik;M. Dias
中科院分区：
文献类型：
--
作者：
Souhayl Sadik;M. Dias
在过去的十年里，kirigami-日本的剪纸艺术-在新兴的机械超材料领域和无数其他机械应用中发挥着越来越大的作用。尽管如此，对kirigami结构的数学和力学的深入理解尚未实现，以释放其在该领域更先进应用的全部潜力。在这项工作中，我们研究了kirigami最基本的几何构建块：一个单一的削减薄片。本文考虑了一个简化的二维平板模型，即带有径向狭缝的薄圆盘，并研究了它在狭缝张开和唇缘转动后的变形。在等轴测极限中--当圆盘的厚度接近零时--弹性能没有拉伸作用，薄片呈圆锥形，称为e锥。我们解决后屈曲问题的e-锥的几何非线性设置假设圣维南-基尔霍夫本构板模型，我们发现封闭形式的应力场的表达式，并显示的几何形状的e-锥由球形弹性问题。这使我们能够充分映射出的空间的解决方案，并调查的稳定性后屈曲的e-锥问题假设镜像对称的边界条件上的唇上的开口狭缝的旋转。
Over the past decade, kirigami—the Japanese art of paper cutting—has been playing an increasing role in the emerging field of mechanical metamaterials and a myriad of other mechanical applications. Nonetheless, a deep understanding of the mathematics and mechanics of kirigami structures is yet to be achieved in order to unlock their full potential to pioneer more advanced applications in the field. In this work, we study the most fundamental geometric building block of kirigami: a thin sheet with a single cut. We consider a reduced two-dimensional plate model of a circular thin disk with a radial slit and investigate its deformation following the opening of the slit and the rotation of its lips. In the isometric limit—as the thickness of the disk approaches zero—the elastic energy has no stretching contribution and the thin sheet takes a conical shape known as the e-cone. We solve the post-buckling problem for the e-cone in the geometrically nonlinear setting assuming a Saint Venant-Kirchhoff constitutive plate model; we find closed-form expressions for the stress fields and show the geometry of the e-cone to be governed by the spherical elastica problem. This allows us to fully map out the space of solutions and investigate the stability of the post-buckled e-cone problem assuming mirror symmetric boundary conditions on the rotation of the lips on the open slit.