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Geodesics and Isometric Immersions in Kirigami

Banff International Research Station for Mathematical Innovation and Discovery

Kirigami is the art of cutting paper to make it articulated and deployable, allowing for it to be shaped into complex two and three-dimensional geometries. The mechanical response of a kirigami sheet when it is pulled at its ends is enabled and limited by the presence of cuts that serve to guide the possible non-planar deformations. Inspired by the geometry of this art form, we ask two questions: (i) What is the shortest path between points at which forces are applied (ii) What is the nature of the ultimate shape of the sheet when it is strongly stretched Mathematically, these questions are related to the nature and form of geodesics in the Euclidean plane with linear obstructions (cuts), and the nature and form of isometric immersions of the sheet with cuts when it can be folded on itself. The talk is based on joint works with M. Lewicka and L. Mahadevan.

Mathematics; Partial Differential Equations; Differential Geometry; Global Analysis

video/mp4

Author affiliation: University of Notre Dame

2023-10-21

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/86240

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/