From sea slugs to robots: Computation, discrete geometry, and soft mechanics in non-Euclidean elasticity

The intricate, self-similar wrinkles along the edges of growing leaves, blooming flowers, torn plastic sheets, and frilly sea slugs are striking manifestations of the extreme mechanics of hyperbolic elastic sheets. These complex and exquisite patterns are governed by interacting non-smooth geometric defects in the material. Characterizing and analyzing these defects uncover insights into elastic behavior and properties underlying the morphogenesis of leaves and flowers, the biomechanics of sea slugs, and how one might design and actuate soft robots. We have developed novel and powerful techniques based on discrete differential geometry for modeling these defects to predict the mechanics and dynamics of thin hyperbolic bodies and enable new biomimetic technologies.