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Discrete geometry and mechanics of leaves, flowers, and sea slugs

Analysis, Dynamics, and Applications Seminar

Discrete geometry and mechanics of leaves, flowers, and sea slugs
Series: Analysis, Dynamics, and Applications Seminar
Location: MATH 402
Presenter: Ken Yamamoto, Program in Applied Mathematics, University of Arizona

The edges of growing leaves, blooming flowers, torn plastic sheets, and frilly sea slugs all exhibit intricate wrinkled patterns. Why is this so? We argue that the mechanics of these so-called non-Euclidean elastic sheets are influenced by non-trivial geometric considerations (i.e., non-smooth defects) which may be explored by new methods using discrete differential geometry (DDG). Wrinkled morphologies appear as an optimization of many topological/geometric degrees of freedom underlying its microstructure. I will motivate the need for DDG-inspired methods to study the mechanics of hyperbolic sheets, i.e., soft/thin objects with negative Gauss curvature. And, I will share results obtained from them, including energetic impacts from non-smooth defects, the role of weak external forces, and associated scaling laws. Ultimately, these modeling techniques have the potential to explain rippled shapes in leaves, flowers, etc. and to enable the control/design of slender elastic materials, e.g., for soft robotics. This is joint work with Shankar Venkataramani.