Charting the twist-to-bend ratio of plant axes

Abstract

During the evolution of land plants many body plans have been developed. Differences in the cross-sectional geometry and tissue pattern of plant axes influence their flexural rigidity, torsional rigidity and the ratio of both of these rigidities, the so-called twist-to-bend ratio. For comparison, we have designed artificial cross-sections with various cross-sectional geometries and patterns of vascular bundles, collenchyma or sclerenchyma strands, but fixed percentages for these tissues. Our mathematical model allows the calculation of the twist-to-bend ratio by taking both cross-sectional geometry and tissue pattern into account. Each artificial cross-section was placed into a rigidity chart to provide information about its twist-to-bend ratio. In these charts, artificial cross-sections with the same geometry did not form clusters, whereas those with similar tissue patterns formed clusters characterized by vascular bundles, collenchyma or sclerenchyma arranged as one central strand, as a peripheral closed ring or as distributed individual strands. Generally, flexural rigidity increased the more the bundles or fibre strands were placed at the periphery. Torsional rigidity decreased the more the bundles or strands were separated and the less that they were arranged along a peripheral ring. The calculated twist-to-bend ratios ranged between 0.85 (ellipse with central vascular bundles) and 196 (triangle with individual peripheral sclerenchyma strands).

Conjoining Trees for the Provision of Living Architecture in Future Cities: A Long-Term Inosculation Study

“…With regard to the practice of Baubotanik, inosculations and branch junctions can be deduced to be anatomically comparable to a high degree if the common growth rings dominate the structure. Wolff–Vorbeck et al [ 45 ] have shown that the flexural rigidity and the torsional rigidity, both mechanical properties in the linear-elastic range, are largely determined by the cross-sectional patterns of the involved tissues. Since the tissue distributions are remarkably similar for inosculation and branch junction, we can assume that the flexural rigidity and the torsional rigidity are also comparable.…”

Progression toward maximum leaf surface storage during the rainfall interception process

“…The high correlations between LIA i and ΔLIA max may be due to the relative stiffness of the petiole (Filartiga et al, 2022; Niklas, 1999; Wolff‐Vorbeck et al, 2022). A less stiff petiole would result in a larger LIA i as well as a larger maximum change.…”

“…Leaf vibration may cause leaf surface storage to vary depending on individual rainfall characteristics, such as raindrop‐size distribution, acceleration and velocity of falling raindrops, and raindrop impact frequency (Konrad et al, 2021; Lauderbaugh & Holder, 2022). The degree to which leaves move following impact from the momentum of a falling raindrop is primarily influenced by species‐specific, biomechanical properties of the leaf, such as material composition, morphology, and stiffness (Lauderbaugh & Holder, 2022; Roth‐Nebelsick et al, 2022; Wolff‐Vorbeck et al, 2022). Hydrophobic properties of the leaf surface may also influence the degree to which water drops shed from the leaf surface (Holder, 2007).…”

A 2D model to study how secondary growth affects the self-supporting behaviour of climbing plants

“…These measurements associated with the anatomical study of the tissues could allow a better understanding of the mechanism at the origin of the rigidification dynamics at all points of the searcher shoots. The anatomical organizations in the mechanical and postural life-histories of plants are potentially embracing ecology, biomechanics and robotics [ 36 ].…”