Nature’s forms are frilly, flexible, and functional

Kenneth K. Yamamoto, Toby L. Shearman, Erik J. Struckmeyer, John A. Gemmer, Shankar C. Venkataramani

Research output: Contribution to journalArticlepeer-review

Abstract

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.]

Original languageEnglish (US)
Article number95
JournalEuropean Physical Journal E
Volume44
Issue number7
DOIs
StatePublished - Jul 2021

ASJC Scopus subject areas

  • Biotechnology
  • Biophysics
  • Chemistry(all)
  • Materials Science(all)
  • Surfaces and Interfaces

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