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.
- Received 7 February 2012
DOI:https://doi.org/10.1103/PhysRevLett.108.238106
© 2012 American Physical Society
Synopsis
Catapults for Seeds
Published 4 June 2012
Changes in plant tissue geometry with humidity explain how some species bend and turn to disperse their seeds.
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