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 - 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.]
UR - http://www.scopus.com/inward/record.url?scp=85110281780&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85110281780&partnerID=8YFLogxK
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 -