Nutations in growing plant shoots as a morphoelastic flutter instability

Abstract

Growing plant shoots exhibit spontaneous oscillations that Darwin observed, and termed ‘circumnutations’. Recently, they have received renewed attention for the design and optimal actuation of bioinspired robotic devices. We discuss a possible interpretation of these spontaneous oscillations as a Hopf-type bifurcation in a growing morphoelastic rod. Using a three-dimensional model and numerical simulations, we analyse the salient features of this flutter-like phenomenon (e.g. the characteristic period of the oscillations) and their dependence on the model details (in particular, the impact of choosing different growth models) finding that, overall, these features are robust with respect to changes in the details of the growth model adopted. This article is part of the theme issue ‘Topics in mathematical design of complex materials’.

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

“…According to a prevailing theory for the interpretation of circumnutations, such oscillatory movements are of exogenous nature and arise from the over-compensatory response of the plant to the changing orientation of its gravisensory apparatus relative to the Earth's gravity [120][121][122][123][124]. Recently, mechanical models based on morphoelastic rods theory [125] have been proposed and tested to support this hypothesis [126][127][128]. Specifically, it was shown that nutations in growing plant shoots may be interpreted as spontaneous oscillations caused by a flutter instability (a Hopf bifurcation) in a growing elastic system subject to gravity loading, while sensing and actively responding to external stimuli.…”