The Role of Weak Forces in the Self-Similar Buckling of Non-Euclidean Elastic Sheets

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.