Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates
Experimental Study of Shape Transitions and Energy Scaling in Thin Non-Euclidean Plates
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DOI：
10.1103/physrevlett.106.118303
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发表时间：
2011-03-14
影响因子：
8.6
通讯作者：
Sharon, Eran
中科院分区：
文献类型：
--
作者：
Klein, Yael;Venkataramani, Shankar;Sharon, Eran
我们提出了非欧几里得板的形状和能量变化的第一个定量测量。使用环境反应凝胶，我们构建了恒定施加高斯曲率K-tar的非欧几里得圆盘。我们改变圆盘的厚度t(0)，并测量构型、表面曲率和能量含量对t(0)的依赖性。对于K-tar < 0，构型为单一波浪模式，并经历一系列分岔，导致它们随着厚度的减少而细化。这导致表面弯曲量在t(0) -> 0时急剧增加，并且弯曲和拉伸能量都缓慢衰减。两者的变化都是t(0)(2)，与K-tar > 0的圆盘的弯曲能t(0)(3)相比。
We present the first quantitative measurements of shape and energy variation in non-Euclidean plates. Using environmentally responsive gel, we construct non-Euclidean disks of constant imposed Gaussian curvature, K-tar. We vary the disks' thickness t(0) and measure the dependence of configurations, surface curvature, and energy content on t(0). For K-tar < 0, configurations are of a single wavy mode and undergo a set of bifurcations that leads to their refinement with decreasing thickness. This leads to sharp increase in the amount of surface bending as t(0) -> 0, and to a slow decay of both bending and stretching energies. Both vary like t(0)(2), compared with t(0)(3) of the bending energy in disks with K-tar > 0.