The dramatic effect kirigami, such as hole cutting, has on the elastic properties of thin sheets invites a study of the mechanics of thin elastic frames under an external load. Such frames can be thought of as modular elements needed to build any kirigami pattern. Here we develop the technique of elastic charges to address a variety of elastic problems involving thin sheets with perforations, focusing on frames with sharp corners. We find that holes generate elastic defects (partial disclinations), which act as sources of geometric incompatibility. Numerical and analytic studies are made of three different aspects of loaded frames - the deformed configuration itself, the effective mechanical properties in the form of force-extension curves, and the buckling transition triggered by defects. This allows us to understand generic kirigami mechanics in terms of a set of force-dependent elastic charges with long-range interactions.
Bibliographical noteFunding Information:
We thank Paul McEuen for insightful discussions. Work by M.J.B. was supported by the KITP Grant No. PHY-1125915, KITP NSF Grant No. PHY-1748958, and by the NSF DMREF program, via Grant No. DMREF-1435794. Work by I.C. was supported by a grant from the NSF DMREF program under Grant No. DMR-1435829. Work by D.R.N. was primarily supported through the NSF DMREF program, via Grant No. DMREF-1435999, as well as in part through the Harvard Materials Research and Engineering Center, via NSF Grant No. DMR-1420570. M.M. acknowledges the USIEF Fulbright program. M.M., S.S., and M.J.B. thank the Syracuse Soft & Living Matter Program for support and the KITP for hospitality during completion of some of this work.
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