Emergence of spontaneous twist and curvature in non-Euclidean rods: Application to Erodium plant cells

Hillel Aharoni*, Yael Abraham, Rivka Elbaum, Eran Sharon, Raz Kupferman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

53 Scopus citations

Abstract

We present a limiting model for thin non-Euclidean elastic rods. Originating from the three-dimensional (3D) reference metric of the rod, which is determined by its internal material structure, we derive a 1D reduced rod theory. Specifically, we show how the spontaneous twist and curvature of a rod emerge from the reference metric derivatives. Thus, the model allows calculating the unconstrained equilibrium configuration of a thin rod directly from its internal structure. The model is applied to the study of cells from members of the Geraniaceae plant family and their configurational response to dehydration. We show how the geometrical arrangement of cellulose fibrils on the cell walls determines the helical shapes of isolated cells.

Original languageAmerican English
Article number238106
JournalPhysical Review Letters
Volume108
Issue number23
DOIs
StatePublished - 5 Jun 2012

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