2021/03/31 by Kenneth K. Yamamoto, Toby Shearman, Toby L. Shearman +3 · 10 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Buckling #Combinatorics #Computer science #Engineering #Euclidean geometry #Geometry #Liquid Crystal Research Advancements #Mathematics #Non-Euclidean geometry #Physics #Pure mathematics #Structural Analysis and Optimization #Structural engineering #Topological quantum number #Topology (electrical circuits) #cond-mat.soft #math.DG #nlin.PS
paper · pdf · doi:10.1140/epje/s10189-021-00099-6
published in The European Physical Journal E 44(7), 95 (Springer Science+Business Media) · 23 pages, 19 figures
openalex publication_date 2021/07/01 · arxiv created 2021/08/02 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.