Abstract Ken Yamamoto

Abstract: Optimization and data analysis for non-Euclidean elastic sheets

Non-Euclidean elastic sheets buckle easily (rather than stretch) to create periodic, self-similar wrinkles along the edges of growing leaves/flowers and torn plastic sheets. We argue that the mechanics of these soft structures are governed by non-trivial geometric considerations (i.e., non-smooth defects) which may be explored by new methods based on discrete differential geometry. The shapes we observe appear as an optimization of many topological/geometric degrees of freedom underlying its microstructure. Our investigations further reveal how localized geometric defects are easily manipulated with little energetic cost, making these sheets very floppy. In order to connect our theory with experiments, we have also made some preliminary progress in analyzing noisy profilometric data for real-world sheets. Ultimately, these modeling techniques have the potential to explain hyperbolic sheets in nature and enable the control/design of thin soft structures. This is joint work with Shankar Venkataramani.