Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets

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. Copyright (C) EPLA, 2016US-Israel BSF grant [2008432]; NSF [DMS-0807501, PHY11-25915]; NSF-RTG grant [DMS-1148284]Published 10 May 2016. 12 month embargo.This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu