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From sea slugs to robots: Soft mechanics, discrete geometry, and computation of hyperbolic elastic sheets

Modeling, Computation, Nonlinearity, Randomness and Waves Seminar

From sea slugs to robots: Soft mechanics, discrete geometry, and computation of hyperbolic elastic sheets
Series: Modeling, Computation, Nonlinearity, Randomness and Waves Seminar
Location: MATH 402
Presenter: Ken Yamamoto, Program in Applied Mathematics, University of Arizona

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 soft 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 modeling 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. This is joint work with Shankar Venkataramani.