The European Physical Journal E ( IF 1.8 ) Pub Date : 2021-07-13 , DOI: 10.1140/epje/s10189-021-00099-6 Kenneth K Yamamoto 1 , Toby L Shearman 2 , Erik J Struckmeyer 2 , John A Gemmer 3 , Shankar C Venkataramani 2
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Abstract
A ubiquitous motif in nature is the self-similar hierarchical buckling of a thin lamina near its margins. This is seen in leaves, flowers, fungi, corals, and marine invertebrates. We investigate this morphology from the perspective of non-Euclidean plate theory. We identify a novel type of defect, a branch-point of the normal map, that allows for the generation of such complex wrinkling patterns in thin elastic hyperbolic surfaces, even in the absence of stretching. We argue that branch points are the natural defects in hyperbolic sheets, they carry a topological charge which gives them a degree of robustness, and they can influence the overall morphology of a hyperbolic surface without concentrating elastic energy. We develop a theory for branch points and investigate their role in determining the mechanical response of hyperbolic sheets to weak external forces.
Graphic Abstract
中文翻译：
自然的形式是褶边、灵活和功能性的
摘要
自然界中一个普遍存在的主题是靠近边缘的薄层的自相似分层屈曲。这可以在叶子、花朵、真菌、珊瑚和海洋无脊椎动物中看到。我们从非欧几里得板块理论的角度研究这种形态。我们确定了一种新型缺陷，即法线贴图的分支点，即使在没有拉伸的情况下，它也允许在薄的弹性双曲线表面上生成这种复杂的皱纹图案。我们认为分支点是双曲片中的自然缺陷，它们带有拓扑电荷，赋予它们一定程度的鲁棒性，并且它们可以影响双曲表面的整体形态而不集中弹性能量。
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