Differential-Growth-Induced Center Wave Buckling

Abstract

Morphogenesis is a result of complex biological, chemical, and physical processes in which differential growth in biological systems is a common phenomenon, especially notable in plant organs such as petals and leaves. Mechanisms of these biologic structures have been studied in recent years with a growing focus from the mechanics point of view. However, understanding differential-growth-induced shape formation quantitatively in plant organs remains largely unknown. In this study, we conduct quantitative experimental measurement, theoretical analysis, and sufficient finite element analysis of constrained differential growth of a thin membrane-like structure. By deriving the corresponding strain energy expression of a buckled growing sample, we can calculate the shape function of such membrane structures explicitly. The results of this work demonstrate the effect of growth function, geometry characteristics, and material property. Our research points to potential approaches to novel geometrical design and inspirations on the microscale and the macroscale for items such as soft robotics and flexible electronics.