Issue |
EPL
Volume 114, Number 2, April 2016
|
|
---|---|---|
Article Number | 24003 | |
Number of page(s) | 6 | |
Section | Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics | |
DOI | https://doi.org/10.1209/0295-5075/114/24003 | |
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.