Kirigami Mechanics as Stress Relief by Elastic Charges

Michael Moshe, Edward Esposito, Suraj Shankar, Baris Bircan, Itai Cohen, David R. Nelson, Mark J. Bowick

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


We develop a geometric approach to understand the mechanics of perforated thin elastic sheets, using the method of strain-dependent image elastic charges. This technique recognizes the buckling response of a hole under an external load as a geometrically tuned mechanism of stress relief. We use a diagonally pulled square paper frame as a model system to quantitatively test and validate our approach. Specifically, we compare nonlinear force-extension curves and global displacement fields in theory and experiment. We find a strong softening of the force response accompanied by curvature localization at the inner corners of the buckled frame. Counterintuitively, though in complete agreement with our theory, for a range of intermediate hole sizes, wider frames are found to buckle more easily than narrower ones. Upon extending these ideas to many holes, we demonstrate that interacting elastic image charges can provide a useful kirigami design principle to selectively relax stresses in elastic materials.

Original languageAmerican English
Article number048001
JournalPhysical Review Letters
Issue number4
StatePublished - 2019

Bibliographical note

Funding Information:
We thank James Pikul, Marc Miskin, and Winston Lee, for their valuable insights and help with guiding the initial experiments. We thank Paul McEuen, Kyle Dorsey, Tanner Pearson, and Zeb Rocklin for very useful conversations throughout the project. Work by I. C. was supported by a grant from the NSF DMREF program under Grant No. DMR-1435829. Work by M. J. B. was supported by the KITP Grant No. PHY-1125915, KITP NSF Grant No. PHY-1748958, and the NSF DMREF program, via Grant No. DMREF-1435794. 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.

Publisher Copyright:
© 2019 American Physical Society.


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