Simulation of emergent rippling on growing thin-shells

Abstract

Many thin tissues, such as leaves and flower petals, exhibit rippling and buckling patterns along their edge as they grow (Figure 1). Experiments with plastic materials have replicated the rippling patterns found in nature and shown that such patterns exhibit a fractal quality of ripples upon ripples --- a so called "buckling cascade" [Eran et al. 2004]. Such patterns are influenced by many physical mechanisms, including stress forces, physical properties of materials (e.g., stiffness), and space constraints [Prusinkiewicz and Barbier de Reuille 2010]. Physics-based computer animation that produces emergent rippling patterns on thin surface can improve the realism of virtual flowers and leaves, and also help to explain which physical mechanisms are most important for controlling the morphology of tissues with buckling cascades.