Ian Tobasco
Assistant Professor
Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago

What do wrinkles and shape-morphing architectural sheets have in common? The answer is fine scale buckling — a patterned response driven by mechanical instabilities enabling macroscopic shape change beyond bulk elasticity. This talk will highlight two recent developments in the mathematics of materials leading to new predictions for (i) the zoo of wrinkle patterns that form when a shell is incompatibly confined, and (ii) the emergent deformations of kirigami sheets made by removing a lattice of holes. Behind both advances is the concept of an “effective geometrical description” in which the underlying patterns are “averaged out”. Systematic energy minimization leads to a limiting description in which the effective geometry can be found, sometimes even by hand. Our story reminds of the classical homogenization of composites, but with fine scale buckling patterns in place of a rapidly oscillating material law. Finding effective geometries is the first step towards an effective mechanical theory of shape change.

About the speaker...
Ian Tobasco is an Assistant Professor at the University of Illinois at Chicago Department of Mathematics, Statistics, and Computer Science. He holds a Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences at New York University, and a B.S.E. in Aerospace Engineering from the University of Michigan. Tobasco works at the interface of mathematics, physics, and engineering, where advances in analysis can lead to scientific breakthroughs in the lab and vice versa. Besides elasticity, Tobasco’s current interests include the search for optimal transport mechanisms in fluid dynamics, and their comparison with naturally turbulent flows.