Geometry and mechanics of inextensible curvilinear balloons
Geometry and mechanics of inextensible curvilinear balloons
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不可伸展曲线气球的几何和力学
DOI：
10.1016/j.jmps.2020.104068
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发表时间：
2020
影响因子：
5.3
通讯作者：
B. Roman
中科院分区：
文献类型：
--
作者：
E. Siéfert;J. Bico;E. Reyssat;B. Roman
Mylar气球在游乐场或生日派对上很受欢迎。他们的概念非常简单：将两块扁平的薄片沿着边缘切割并密封在一起，形成一个扁平的信封。通货膨胀往往会使这个包络变形，以使其内部体积最大化。然而，尽管薄板很容易弯曲，很难抵抗压缩载荷，但它们几乎不会拉伸，这施加了不平凡的几何约束。这种薄板一般在“张力场理论”的框架下描述，其中它们的刚度在拉伸时被认为是无限的，而在压缩或弯曲下则为零。在这项研究中，我们关注的是等宽度的平面和曲面模板膨胀后的形状。与直觉相反的是，路径的曲率在膨胀时趋于增加，这导致无约束闭合结构的平面外屈曲。在确定了轴对称环空的最佳截面后，我们预测了开放路径中局部曲率的变化。最后，我们描述了在充气结构中观察到的皱纹和光滑区的位置，分别对应于压缩和拉伸。
Mylar balloons are popular in funfairs or birthday parties. Their conception is very simple: two pieces of flat thin sheets are cut and sealed together along their edges to form a flat envelope. Inflation tends to deform this envelope in order to maximize its inner volume. However, although thin sheets are easy to bend and hardly resist compressive loads, they barely stretch, which imposes non-trivial geometrical constraints. Such thin sheets are generally described under the framework of “tension field theory” where their stiffness is considered as infinite under stretching and vanishes under compression or bending. In this study, we focus on the shape after inflation of flat, curved templates of constant width. Counter-intuitively, the curvatures of the paths tend to increase upon inflation, which leads to out of plane buckling of non-confined closed structures. After determining the optimal cross section of axisymmetric annuli, we predict the change in local curvature induced in open paths. We finally describe the location of wrinkled and smooth areas observed in inflated structures that correspond to compression and tension, respectively.
影响因子：
25
作者：
Hawkes, Elliot W.;Blumenschein, Laura H.;Okamura, Allison M.
通讯作者：
Okamura, Allison M.