Eur. Phys. J. E (2016) 39: 85
https://doi.org/10.1140/epje/i2016-16085-6

Regular Article

Abrupt out-of-plane edge folding of a circular thin plate: Implication for a mature Victoria regia leaf

¹ International Center for Applied Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, 710049, Xi’an, China
² State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi’an Jiaotong University, 710049, Xi’an, China
³ Columbia Nanomechanics Research Center, Department of Earth and Environmental Engineering, Columbia University, 10027, New York, NY, USA

^* e-mail: yilunliu@mail.xjtu.edu.cn
^** e-mail: xichen@columbia.edu

Received: 4 May 2016
Accepted: 30 August 2016
Published online: 16 September 2016

Abstract

Inspired by the observation of the configurations of Victoria regia leaves, we establish a phenomenological buckling model for the abrupt out-of-plane edge folding of a circular thin sheet. A reduced model is first developed, and further refined by a more sophisticated growth strain field so that the resulting buckling morphology resembles that of a mature Victoria regia leaf. Parametric studies are carried out to investigate the effects of geometric, material, and strain field parameters on the buckling morphology. Several main characteristics discovered through numerical studies are verified by theoretical analysis of a simple geometry-based model. Besides, the roles of the thickness variation and cracks are examined. This work may not only shed some light on the morphogenesis of certain plants, but also provide some useful insights on three-dimensional fabrications using mechanical self-assembly.