Geometry, mechanics, and dynamics of leaves, flowers, and sea slugs

Why are there intricate, self-similar wrinkles along the edges of growing leaves, blooming flowers, torn plastic sheets, and frilly sea slugs? We argue that the mechanics and dynamics of these non-Euclidean elastic sheets are governed by interacting non-smooth geometric defects in the material. I will describe novel ideas stemming from characterizing and analyzing these defects using discrete differential geometry in order to uncover fundamental insights into the elastic behavior and properties of thin hyperbolic bodies. New theories based on the mechanics of non-smooth defects may (i) explain biological phenomena, from the morphogenesis of leaves, flowers, etc. to the biomechanics of sea slugs, as well as (ii) introduce new paradigms for materials design and actuation in a variety of new technologies, e.g., soft robotics.