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The mechanics of twining plants: an elastic model
joint work with Alain Goriely
Can a given twining plant climb around supports of different sizes?
This question was first raised by Charles Darwin in his book on The movements and habits of climbing plants. In there he comments: "Most twining plants are adapted to ascend supports of moderate though of different thicknesses. Our English twiners, as far as I have seen, never twine round trees [...]". As an example, Darwin noted that Solanum dulcamara can twine around supports of 3mm but not on supports of 5 or 6mm.
On the left, a twiner succesfully climbs around a support of moderate thickness. On the right the same twiner fails to wind around a thick support.
For a given twiner, what is the critical cylinder radius above which a plant is no longer able to twine?
We model the plant stem as an elastic rod with natural curvature and twist. We start with a 2D version of the model: a naturally curved elastica around a disc. When look for stable equilibrium configurations of such a rod with appropriate boundary conditions:
We focus on the part of the plant near its upper end (apex). The anchoring boundary condition at the start of the rod stands for the constraint applied by the lower part (not shown here) of the plant on the stem apex.
Quite evidently the radius of the support has to be larger than the natural radius of curvature of the plant. On the other hand, we found that the radius of the support should not be too large: not larger than 3.3 times the natural radius of curvature of the plant.
Indeed if the support radius is 3 times the natural radius of the plant, the plants grows:
However if the support radius is 3.5 times the natural radius of the plant, the plant fails to grow:
Our article: here.
Some slides in PDF format.
Wendy Kuhn Silk experiements.
Noel Michele Holbrook lab.