Effective Geometries in Elasticity: Wrinkled Shells and Shape-Morphing Kirigami
What do wrinkled shells and shape-morphing kirigami 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 present two recent developments on (i) a hidden duality between the wrinkles of positively and negatively curved confined shells , and (ii) the aggregate deformations of kirigami sheets made by removing a lattice of holes . In both cases, a homogenization-style argument leads to a coarse-grained description of the pattern which is simpler to study, and is even explicitly solvable sometimes. Wrinkle patterns become the subdifferentials of pairs of convex functions; kirigami is shown to deform along a family of non-Euclidean isometries set by the holes. The resulting predictions match the results of simulations and experiments across scales.
 I. Tobasco, Y. Timounay, D. Todorova, G. C. Leggat, J. D. Paulsen, and E. Katifori, “Exact Solutions for the Wrinkle Patterns of Confined Elastic Shells,” Nat. Phys. 18 (2022) 1099-1104
 Y. Zheng, I. Niloy, P. Celli, I. Tobasco, and P. Plucinsky, “Continuum Field Theory for the Deformations of Planar Kirigami,” Phys. Rev. Lett. 128 (2022) 208003