Buckling transition and boundary layer in non-Euclidean plates
Buckling transition and boundary layer in non-Euclidean plates
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DOI：
10.1103/physreve.80.016602
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发表时间：
2009-07-01
影响因子：
2.4
通讯作者：
Kupferman, Raz
中科院分区：
文献类型：
--
作者：
Efrati, Efi;Sharon, Eran;Kupferman, Raz
非欧几里德板是薄的弹性体，没有无应力的配置，因此在没有外部约束的情况下表现出残余应力。这些物体被赋予三维参考度量，其不一定浸入物理空间中。在这里，基于最近开发的理论，这样的机构，我们的特点从平面到屈曲平衡配置在板厚度的临界值的过渡。根据参考度量，屈曲过渡可以是连续的或不连续的。在无限薄板极限，假设存在一个限制配置，我们表明，极限是一个配置，最大限度地减少弯曲内容，在所有配置中，零拉伸内容（等距浸入的中表面）。对于小的，但有限的板厚度，我们显示的边界层的形成，其尺寸尺度与板厚度的平方根，其形状是由拉伸和弯曲能量之间的平衡。
Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled equilibrium configurations at a critical value of the plate thickness. Depending on the reference metric, the buckling transition may be either continuous or discontinuous. In the infinitely thin plate limit, under the assumption that a limiting configuration exists, we show that the limit is a configuration that minimizes the bending content, among all configurations with zero stretching content (isometric immersions of the midsurface). For small but finite plate thickness, we show the formation of a boundary layer, whose size scales with the square root of the plate thickness and whose shape is determined by a balance between stretching and bending energies.