Yin-Yang spiraling transition of a confined buckled elastic sheet

Stéphanie Deboeuf, Suzie Protière, Eytan Katzav

Research output: Contribution to journalArticlepeer-review

Abstract

DNA in viral capsids, plant leaves in buds, and geological folds are examples in nature of tightly packed low-dimensional objects. However, the general equations describing their deformations and stresses are challenging. We report experimental and theoretical results of a model configuration of compression of a confined elastic sheet, which can be conceptualized as a one-dimensional (1D) line inside a 2D rectangular box. In this configuration, the two opposite ends of a planar sheet are pushed closer, while being confined in the orthogonal direction by two rigid walls separated by a given gap. Similar compaction of sheets has been previously studied and was shown to buckle into quasiperiodic motifs. In our experiments, we observed a different phenomenon, namely the spontaneous instability of the sheet, leading to localization into a single Yin-Yang pattern. The linearized Euler Elastica theory of elastic rods, together with global energy considerations, allow us to predict the symmetry breaking of the sheet in terms of the number of motifs, compression distance, and tangential force. Surprisingly, the appearance of the Yin-Yang pattern does not require friction.

Original languageAmerican English
Article number013100
JournalPhysical Review Research
Volume6
Issue number1
DOIs
StatePublished - Jan 2024

Bibliographical note

Publisher Copyright:
© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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