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 [1], and (ii) the aggregate deformations of kirigami sheets made by removing a lattice of holes [2]. 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.

[1] 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
[2] 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



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