Buckling of geometrically confined shells
Buckling of geometrically confined shells
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DOI：
10.1039/c8sm02035c
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发表时间：
2019-02-14
期刊：
影响因子：
3.4
通讯作者：
Holmes, Douglas P.
中科院分区：
文献类型：
--
作者：
Stein-Montalvo, Lucia;Costa, Paul;Holmes, Douglas P.
我们研究了当弹性壳受到几何约束时出现的周期性屈曲模式。残余膨胀提供了各种形状（鞍座、轧制板、圆柱体和球形截面）的访问范围，这些形状在其外在和内在曲率上变化。我们的实验和数值数据表明，当这些中等厚度的结构受到径向约束时，一个单一的几何参数——总壳半径与未受约束材料的数量之比——可以预测形成的叶的数量。我们提出了一个模型，将这种缩放解释为径向和周向弯曲之间的竞争。接下来，我们用类似的标度分析表明，减小鞍的横向约束会导致瓣数减少。因此，一个几何参数通过广泛的径向和横向约束来捕获波数，将壳的形状与限制它的边界的形状联系起来。我们期望这些结果与外壳形状的扩展有关，从而适用于变形材料的设计和软结构的膨胀和生长。
We study the periodic buckling patterns that emerge when elastic shells are subjected to geometric confinement. Residual swelling provides access to range of shapes (saddles, rolled sheets, cylinders, and spherical sections) which vary in their extrinsic and intrinsic curvatures. Our experimental and numerical data show that when these moderately thick structures are radially confined, a single geometric parameter - the ratio of the total shell radius to the amount of unconstrained material - predicts the number of lobes formed. We present a model that interprets this scaling as the competition between radial and circumferential bending. Next, we show that reducing the transverse confinement of saddles causes the lobe number to decrease with a similar scaling analysis. Hence, one geometric parameter captures the wave number through a wide range of radial and transverse confinement, connecting the shell shape to the shape of the boundary that confines it. We expect these results to be relevant for an expanse of shell shapes, and thus applicable to the design of shape- shifting materials and the swelling and growth of soft structures.