Meeting Abstract

90.6  Wednesday, Jan. 7  The undulating shape of growing surfaces LIANG, Haiyi*; MAHADEVAN, L; Harvard University; Harvard University hyliang@seas.harvard.edu

The undulating morphology of leaves and petals is now accepted as a consequence of differential growth of the underlying tissue. Various qualitative and quantitative aspects of the buckling patterns seen in both vascular and avascular leaves may thus be ascribed to the distribution of non-uniform growth in the lamina, and have been demonstrated in normal and mutant leaves, as well as in physical models thereof. To understand the different modalities that arise quantitatively, we construct a mathematical model for the stability of an initially flat elastic ribbon with excess growth along its edges, directly motivated by observations of kelp that are capable of phenotypic plasticity in different environments. Using a combination of analysis and numerical simulation, we map out the phase space of possible shapes for these growing ribbons. We find that are two generic buckling modes that arise: a global catenoid-like structure and a more localized periodically-rippled structure. In general, we find that as the relative growth strain is increased, the flat ribbon-like structure switches to a catenoidal shape before developing undulating edges that can develop on the catenoid’s edges. Our theoretical and numerical framework allows us to delineate the few macroscopic parameters that control the morphology of leaves and captures a large variety of observed shapes in elongated blade-like leaves.