Influence of structural reinforcements on the twist-to-bend ratio of plant axes: a case study on Carex pendula

During biological evolution, plants have developed a wide variety of body plans and concepts that enable them to adapt to changing environmental conditions. The trade-off between flexural and torsional rigidity is an important example of sometimes conflicting mechanical requirements, the adaptation to which can be quantified by the dimensionless twist-to-bend ratio. Our study considers the triangular flower stalk of Carex pendula, which shows the highest twist-to-bend ratios ever measured for herbaceous plant axes. For an in-depth understanding of this peak value, we have developed geometric models reflecting the 2D setting of triangular cross-sections comprised of a parenchymatous matrix with vascular bundles surrounded by an epidermis. We analysed the mathematical models (using finite elements) 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 individual fibre reinforcement strands located in the periphery of the cross-section and embedded in a parenchymatous ground tissue lead to a strong increase of the flexural and a weaker increase of the torsional rigidity and thus resulted 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. Based on our mathematical models, we can thus draw conclusions regarding the influence of mechanical requirements on the development of plant axis geometry, in particular the placement of reinforcements.