Nature's forms are frilly, flexible, and functional.
| Autor: | Yamamoto KK; Department of Mathematics, Southern Methodist University, Dallas, TX, 75275, USA., Shearman TL; School of Mathematical Sciences, University of Arizona, Tucson, AZ, 85721, USA., Struckmeyer EJ; School of Mathematical Sciences, University of Arizona, Tucson, AZ, 85721, USA., Gemmer JA; Department of Mathematics and Statistics, Wake Forest University, Winston Salem, NC, 27109, USA., Venkataramani SC; School of Mathematical Sciences, University of Arizona, Tucson, AZ, 85721, USA. shankar@math.arizona.edu. |
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| Jazyk: | angličtina |
| Zdroj: | The European physical journal. E, Soft matter [Eur Phys J E Soft Matter] 2021 Jul 13; Vol. 44 (7), pp. 95. Date of Electronic Publication: 2021 Jul 13. |
| DOI: | 10.1140/epje/s10189-021-00099-6 |
| Abstrakt: | 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. (© 2021. The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.) |
| Databáze: | MEDLINE |
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