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

• Main Authors: Gemmer, John, Sharon, Eran, Shearman, Toby, Venkataramani, Shankar C.
• Other Authors: Univ Arizona, Program Appl Math
• Language: en
• Published: EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY 2016
• Online Access: http://hdl.handle.net/10150/617197; http://arizona.openrepository.com/arizona/handle/10150/617197

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, 2016