TY - JOUR
T1 - Nature’s forms are frilly, flexible, and functional
AU - Yamamoto, Kenneth K.
AU - Shearman, Toby L.
AU - Struckmeyer, Erik J.
AU - Gemmer, John A.
AU - Venkataramani, Shankar C.
N1 - Funding Information:
We warmly acknowledge the many insightful conversations we’ve had with Benny Davidovitch, Eran Sharon, and Ian Tobasco on these topics. We are grateful to Ido Levin who helped make the PVS gel samples and to Eran Sharon for providing the lab space and equipment for the force-measurement experiments. KY and SV gratefully acknowledge the hospitality of the Racah Institute of Physics at the Hebrew University, where portions of this work were carried out. KY also acknowledges funding from the U.S.-Israel Binational Science Foundation Prof. Rahamimoff Travel Grant for the research visit in Israel. TS was partially supported by a Michael Tabor fellowship from the Graduate Interdisciplinary Program in Applied Mathematics at the University of Arizona. SV was partially supported by the Simons Foundation through awards 524875 and 560103. KY, ES and SV were partially supported by the NSF award DMR-1923922. KY was also partially supported by the 2018-19 Michael Tabor fellowship from the Graduate Interdisciplinary Program in Applied Mathematics at the University of Arizona, the 2020 Marshall Foundation Dissertation Fellowship from the Graduate College at the University of Arizona, and the NSF RTG Grant DMS-184026.
Funding Information:
We warmly acknowledge the many insightful conversations we’ve had with Benny Davidovitch, Eran Sharon, and Ian Tobasco on these topics. We are grateful to Ido Levin who helped make the PVS gel samples and to Eran Sharon for providing the lab space and equipment for the force-measurement experiments. KY and SV gratefully acknowledge the hospitality of the Racah Institute of Physics at the Hebrew University, where portions of this work were carried out. KY also acknowledges funding from the U.S.-Israel Binational Science Foundation Prof. Rahamimoff Travel Grant for the research visit in Israel. TS was partially supported by a Michael Tabor fellowship from the Graduate Interdisciplinary Program in Applied Mathematics at the University of Arizona. SV was partially supported by the Simons Foundation through awards 524875 and 560103. KY, ES and SV were partially supported by the NSF award DMR-1923922. KY was also partially supported by the 2018-19 Michael Tabor fellowship from the Graduate Interdisciplinary Program in Applied Mathematics at the University of Arizona, the 2020 Marshall Foundation Dissertation Fellowship from the Graduate College at the University of Arizona, and the NSF RTG Grant DMS-184026.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/7
Y1 - 2021/7
N2 - 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: [Figure not available: see fulltext.]
AB - 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: [Figure not available: see fulltext.]
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U2 - 10.1140/epje/s10189-021-00099-6
DO - 10.1140/epje/s10189-021-00099-6
M3 - Article
C2 - 34255210
AN - SCOPUS:85110281780
SN - 1292-8941
VL - 44
JO - European Physical Journal E
JF - European Physical Journal E
IS - 7
M1 - 95
ER -