Hierarchy of geometrical frustration in elastic ribbons: Shape-transitions and energy scaling obtained from a general asymptotic theory

Ido Levin*, Emmanuel Siéfert, Eran Sharon, Cy Maor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Geometrically frustrated elastic ribbons exhibit, in many cases, significant changes in configuration depending on the relation between their width and thickness. We show that the existence of such a transition, and the scaling at which it occurs, strongly depend on the system considered. Using an asymptotic approach, treating the width as a small parameter, we find the leading energy terms resulting from the frustration and predict the existence and scaling of the shape transition. We study in detail 5 different types of frustrated ribbons with a different morphological dependence on ribbon's width: a sharp shape-transition at a critical width, a moderate transition with an intermediate regime, and no transition at all. We show that the predictions of our approach match experimental results from two different experimental systems: prestressed rubber bilayers and 4D printed thermoplastics, in a wide variety of geometric settings.

Original languageAmerican English
Article number104579
JournalJournal of the Mechanics and Physics of Solids
Volume156
DOIs
StatePublished - Nov 2021

Bibliographical note

Funding Information:
This research was supported by the USA?Israel binational science foundation, Israel, Grant No. 2014310. I. L. is grateful to the Azrieli Foundation, Canada for the award of an Azrieli Fellowship. E. S. acknowledges support from the Lady Davis Fellowship Trust, Israel. C. M. was partially supported by ISF-grant, Israel1269/19.

Funding Information:
This research was supported by the USA–Israel binational science foundation, Israel , Grant No. 2014310 . I. L. is grateful to the Azrieli Foundation, Canada for the award of an Azrieli Fellowship. E. S. acknowledges support from the Lady Davis Fellowship Trust, Israel . C. M. was partially supported by ISF-grant, Israel 1269/19 .

Publisher Copyright:
© 2021 Elsevier Ltd

Keywords

  • Differential geometry
  • Geometrical frustration
  • Ribbons
  • Scaling laws
  • Shape transition
  • Thin sheets

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