Volume 114, Number 2, April 2016
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||10 May 2016|
Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets
1 Division of Applied Mathematics, Brown University - Providence, RI 02906, USA
2 Racah Institute of Physics, The Hebrew University - Jerusalem, 91904, Israel
3 Program in Applied Mathematics, University of Arizona - Tucson, AZ 85721, USA
4 Mathematics Department, University of Arizona - Tucson, AZ 85721, USA
5 Kavli Institute of Theoretical Physics, University of California - Santa Barbara, CA 93106, USA
Received: 1 February 2016
Accepted: 27 April 2016
The edges of torn plastic sheets and growing leaves often display hierarchical buckling patterns. We show that this complex morphology i) emerges even in zero strain configurations, and ii) is driven by a competition between the two principal curvatures, rather than between bending and stretching. We identify the key role of branch point (or “monkey saddle”) singularities in generating complex wrinkling patterns in isometric immersions, and show how they arise naturally from minimizing the elastic energy.
PACS: 46.70.Hg – Membranes, rods, and strings / 46.32.+x – Static buckling and instability / 02.40.Hw – Classical differential geometry
© EPLA, 2016
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