Twist-to-bend ratio: an important selective factor for many rod-shaped biological structures

Abstract

Mechanical optimisation plays a key role in living beings either as an immediate response of individuals or as an evolutionary adaptation of populations to changing environmental conditions. Since biological structures are the result of multifunctional evolutionary constraints, the dimensionless twist-to-bend ratio is particularly meaningful because it provides information about the ratio of flexural rigidity to torsional rigidity determined by both material properties (bending and shear modulus) and morphometric parameters (axial and polar second moment of area). The determination of the mutual contributions of material properties and structural arrangements (geometry) or their ontogenetic alteration to the overall mechanical functionality of biological structures is difficult. Numerical methods in the form of gradient flows of phase field functionals offer a means of addressing this question and of analysing the influence of the cross-sectional shape of the main load-bearing structures on the mechanical functionality. Three phase field simulations were carried out showing good agreement with the cross-sections found in selected plants: (i) U-shaped cross-sections comparable with those of Musa sp. petioles, (ii) star-shaped cross-sections with deep grooves as can be found in the lianoid wood of Condylocarpon guianense stems, and (iii) flat elliptic cross-sections with one deep groove comparable with the cross-sections of the climbing ribbon-shaped stems of Bauhinia guianensis.

Petiole-Lamina Transition Zone: A Functionally Crucial but Often Overlooked Leaf Trait

“…This is because the U-profiled petiole is “fixed” in the most favorable position in terms of bending, i.e., with the opening of the U against the acting bending force. Wolff-Vorbeck et al [ 34 ] have shown that, with an increasing size of the groove, the twist-to bend ratio increases because of an increase of the flexural rigidity and a simultaneous decrease of the torsional rigidity. Higher torsional flexibility enables lamina attached to their basal margin to reorient, streamline and thus reduce the wind-induced drag [ 23 , 26 ].…”

Peak values of twist‐to‐bend ratio in triangular flower stalks of Carex pendula: a study on biomechanics and functional morphology

“…The above-described structure of the nodes, which differs from the internodes, may explain why the flexural rigidity of the stems consisting of two internodes and three nodes differs highly significantly from the flexural rigidity of the internodal segments. Additionally, the closed ring of sclerenchyma without intervening aerenchym especially increases the torsional rigidity of the nodes in contrast to the internodes with individual sclerenchyma strands alternating with aerenchymatous regions that allows for easier torsional movement (Wolff-Vorbeck et al, 2019).…”

Influence of Structural Reinforcements on the Twist-to-bend Ratio of Plant Stems

“…A plethora of evolutionary adaptations can be observed in aerial stems, especially with regard to bending and torsional loading, which represent the predominant load cases in plants with self-supporting upright stems. In addition to experimental analyses, theoretical considerations including analytical and numerical simulations can help to decipher the complex interplay between form, structure and mechanical properties of the involved plant tissues 16,[24][25][26][27] .…”

“…As in our previous work 16 , in which we assumed a constant elastic modulus E, we use methods from linear elasticity, which we repeat here for the readers convenience. As we are interested in investigating mechanical properties of the long and narrow flower stalk of C. pendula we describe a plant stem as a long thin elastic rod with domain B = Ω × (0, L) of length L and simply connected cross-section Ω remaining constant along the longitudinal axis.…”