The University of Arizona

The role of weak forces in the self-similar buckling of non-Euclidean elastic sheets

The role of weak forces in the self-similar buckling of non-Euclidean elastic sheets

Series: Analysis, Dynamics, and Applications Seminar
Location: Math 402
Presenter: Ken Yamamoto, Program in Applied Mathematics, University of Arizona

The mechanics of thin elastic sheets can exhibit extreme properties, from crumpled paper to lettuce leaves. The former are quite rigid; whereas the latter are floppy. In fact, we argue that non-Euclidean elastic sheets (like lettuce) are easily manipulated by weak forces, which play a role in their intricate wrinkling shapes, e.g, along edges of torn plastic sheets and growing leaves. I will discuss a quantitative measure for the “floppiness” of non-Euclidean sheets. Our investigations suggest that these complex morphologies result from the selection of potentially non-smooth configurations with vanishing in-plane strain (i.e., no stretching) that contain defects influenced by weak forces, i.e., effects other than stretching or bending.

Department of Mathematics, The University of Arizona 617 N. Santa Rita Ave. P.O. Box 210089 Tucson, AZ 85721-0089 USA Voice: (520) 621-6892 Fax: (520) 621-8322 Contact Us © Copyright 2018 Arizona Board of Regents All rights reserved