Special Colloquium
Ian Tobasco
U Michigan
The cost of crushing: curvature-driven wrinkling of thin elastic shells
Abstract: How much energy does it take to stamp a thin elastic shell flat? Motivated by recent experiments on wrinkling patterns formed by thin floating shells, we develop a rigorous method (via Gamma-convergence) for evaluating the cost of crushing to leading order in the shell’s thickness and other small parameters. The experimentally observed patterns involve regions of well-defined wrinkling alongside totally disordered regions in which no single direction of wrinkling is preferred. Our goal is to explain the appearance of such “wrinkling domains”. Our analysis proves that energy-minimizing wrinkling patterns must maximize their projected area in the plane. This purely geometric variational problem turns out to be explicitly solvable in many cases of interest, and we demonstrate our methods with concrete examples and offer comparisons with simulation and experiment. What results is an ansatz-free explanation for the geometry of wrinkle patterns seen in confined thin elastic shells.
This talk will be mathematically self-contained, not assuming prior background in elasticity.
There will be tea in SEO 300 starting at 4:00.
Thursday November 29, 2018 at 3:00 PM in 636 SEO