|Date: Friday, December 07, 2018
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: A geometric theory of wrinkling for confined elastic shells
Abstract: Thin elastic membranes readily take on shapes wildly different from their own. Motivated by recent experiments on wrinkling patterns observed in thin shells floating on a water bath, we obtain a fully rigorous asymptotic expansion of the energy (elastic and otherwise) valid in the highly-wrinkled limit. After renormalizing by the typical energy of wrinkling, we derive a coarse-grained model in which an elastically compatible pattern is assigned energy proportional to the difference between its intrinsic undeformed area and its projected area in the plane. Energetically optimal patterns therefore maximize their projected area. Surprisingly, this limiting model turns out to be explicitly solvable in a large variety of cases, including for shells whose (possibly non-constant) curvature is of a known sign. We demonstrate our methods with concrete examples and offer comparisons with simulations and experiments. What results is an ansatz-free explanation for the geometry of wrinkle patterns seen in confined thin elastic shells.
Speaker: Ian Tobasco
Institution: University of Michigan
Event Organizer: AIM seminar organizers