Nutations in growing plant shoots: The role of elastic deformations due to gravity loading

TitleNutations in growing plant shoots: The role of elastic deformations due to gravity loading
Publication TypeJournal Article
Year of Publication2020
AuthorsAgostinelli D, Lucantonio A, Noselli G, DeSimone A
JournalJournal of the Mechanics and Physics of Solids
KeywordsCircumnutations, Flutter instability, Gravitropism, Hopf bifurcation

The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin’s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.