Influence of Structural Reinforcements on the Twist-to-bend Ratio of Plant Stems
During biological evolution, plants have developed a wide variety of body plans and concepts that enable them to react or adapt to changing environmental conditions. Their morphological-anatomical and mechanical adaptations to conflicting conditions are especially interesting. A good example is the trade-off between flexural and torsional rigidity, as represented by the dimensionless twist-to-bend ratio. We have developed geometric models of a plant tissue reflecting the 2D situation of
... ituation of triangular cross-sections comprising of a parenchymatous matrix with vascular bundles surrounded by an epidermis and analysed them by using mathematical models (finite element analysis) to measure the effect of either reinforcements of the epidermal tissue or fibre reinforcements such as collenchyma and sclerenchyma on the twist-to-bend ratio. The change from an epidermis to a covering tissue of corky periderm increases both the flexural and the torsional rigidity and decreases the twist-to-bend ratio. Furthermore, additional fibre reinforcement strands in a parenchymatous ground tissue lead to a strong increase of the flexural and a weaker increase of the torsional rigidity and thus resulting in a marked increase of the twist-to-bend ratio. Within the developed model, a reinforcement by 49 sclerenchyma fibre strands or 24 collenchyma fibre strands is optimal in order to achieve high twist-to-bend ratios. Dependent on the mechanical quality of the fibres, the twist-to-bend ratio of collenchyma-reinforced axes is noticeably smaller, with collenchyma having an elastic modulus that is approximately 20 times smaller than that of sclerenchyma.