Kirigami Mechanics as Stress Relief by Elastic Charges

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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 languageEnglish (US)
Article number048001
JournalPhysical Review Letters
Volume122
Issue number4
DOIs
StatePublished - Jan 1 2019

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elastic sheets
buckling
softening
curvature
curves

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Moshe, M., Esposito, E., Shankar, S., Bircan, B., Cohen, I., Nelson, D. R., & Bowick, M. J. (2019). Kirigami Mechanics as Stress Relief by Elastic Charges. Physical Review Letters, 122(4), [048001]. https://doi.org/10.1103/PhysRevLett.122.048001

Kirigami Mechanics as Stress Relief by Elastic Charges. / Moshe, Michael; Esposito, Edward; Shankar, Suraj; Bircan, Baris; Cohen, Itai; Nelson, David R.; Bowick, Mark John.

In: Physical Review Letters, Vol. 122, No. 4, 048001, 01.01.2019.

Research output: Contribution to journalArticle

Moshe, M, Esposito, E, Shankar, S, Bircan, B, Cohen, I, Nelson, DR & Bowick, MJ 2019, 'Kirigami Mechanics as Stress Relief by Elastic Charges', Physical Review Letters, vol. 122, no. 4, 048001. https://doi.org/10.1103/PhysRevLett.122.048001
Moshe M, Esposito E, Shankar S, Bircan B, Cohen I, Nelson DR et al. Kirigami Mechanics as Stress Relief by Elastic Charges. Physical Review Letters. 2019 Jan 1;122(4). 048001. https://doi.org/10.1103/PhysRevLett.122.048001
Moshe, Michael ; Esposito, Edward ; Shankar, Suraj ; Bircan, Baris ; Cohen, Itai ; Nelson, David R. ; Bowick, Mark John. / Kirigami Mechanics as Stress Relief by Elastic Charges. In: Physical Review Letters. 2019 ; Vol. 122, No. 4.
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