Deployable Structures in Plants

The deployment of leaves with plane surface and straight parallel folds, as observed in leaves of hornbeam and beech, was investigated by using numerical methods. In both species the veins are angled at 30° to 50° from the midrib, when the leaves are outstretched. Although a higher angle allows the leaf to be folded more compactly within the bud, it has very small leaf area in the early stage of unfolding. The midrib of leaf grows very slowly at first and then it does with an almost constant speed. From the numerical simulation, it was found that the midrib grows with the minimum unfolding energy. The deployment of flowers was also investigated from mechanical point of view. A potato flower has five or six petals with triangle gussets between petals. The bud volume becomes largest when the number of petals, N, is five. However, the energy for unfolding of the model with N = 5 or 6 is smaller than those of other models, if the energy can be represented by the total kinetic energy during unfolding.