Twist-to-Bend Ratios and Safety Factors of Petioles Having Various Geometries, Sizes and Shapes

Abstract

From a mechanical viewpoint, petioles of foliage leaves are subject to contradictory mechanical requirements. High flexural rigidity guarantees support of the lamina and low torsional rigidity ensures streamlining of the leaves in wind. This mechanical trade-off between flexural and torsional rigidity is described by the twist-to-bend ratio. The safety factor describes the maximum load capacity. We selected four herbaceous species with different body plans (monocotyledonous, dicotyledonous) and spatial configurations of petiole and lamina (2-dimensional, 3-dimensional) and carried out morphological-anatomical studies, two-point bending tests and torsional tests on the petioles to analyze the influence of geometry, size and shape on their twist-to-bend ratio and safety factor. The monocotyledons studied had significantly higher twist-to-bend ratios (23.7 and 39.2) than the dicotyledons (11.5 and 13.3). High twist-to-bend ratios can be geometry-based, which is true for the U-profile of Hosta x tardiana with a ratio of axial second moment of area to torsion constant of over 1.0. High twist-to-bend ratios can also be material-based, as found for the petioles of Caladium bicolor with a ratio of bending elastic modulus and torsional modulus of 64. The safety factors range between 1.7 and 2.9, meaning that each petiole can support about double to triple the leaf’s weight.

Acclimation to wind loads and/or contact stimuli? A biomechanical study of peltate leaves of Pilea peperomioides

“…We selected the species P. peperomioides ( Fig. 1 ) as a model for this study because, on the one hand, we already had prior knowledge of the morphology, anatomy, and biomechanics of the petiole and the morphology and anatomy of the transition zone from previous studies ( Langer et al 2021 a , b ), and on the other hand, the different habitats of the plant seem to make it very suitable for studying acclimation effects, as it grows both in forests and on cliffs ( Diels, 1909 –1912; Radcliffe-Smith, 1984 ). In other words, P. peperomioides is native to wind-protected and open sites, which makes it likely that the fleshy leaves acclimate differently in these two habitats.…”

“…The bending elastic modulus of the petioles of P. peperomioides , however, measured in two-point bending tests, ranged between 76 and 165 MPa ( Langer et al , 2021 a ). To investigate this difference between the bending and tensile elastic moduli, verification measurements were made with 10 petioles of P. peperomioides ( Supplementary Dataset S3 ).…”

“…The tapering mode is a dimensionless variable that describes the shape of a slender rod representing a circular cylinder (α=0), a second-order paraboloid of revolution (α=0.5), a circular cone (α=1), or a hyperboloid of revolution (α=1.5). Petioles possess various tapering modes ( Langer et al , 2021 a ). Caliaro et al (2013) , showed highly significant differences ( P <0.01) when calculating the bending elastic modulus of petioles of Caladium bicolor with the equation considering the tapering mode compared with the equation for untapered cylindrical beams with constant circular cross-section using the mean radius of each petiole ( n =54).…”

“…This conclusion is supported by the fact that plant materials are much more rigid in bending than in torsion ( Niklas, 1992 , 1999 ). In this context, we found E / G ratios of 20–60 for the petioles of four herbaceous plant species, namely Hosta × tardiana ‘El Nino’, Caladium bicolor , Hemigraphis alternata , and Pilea peperomioides ( Langer et al , 2021 a ). Nevertheless, plants can only build a very limited number of materials ( Knippers and Speck, 2012 ), while they are less restricted in terms of the geometry, size, and shape of their organs or plant axes or the three-dimensional arrangement of the involved materials.…”

“…With the exception of a perfectly circular cross-section, the torsion constant K is usually smaller than J . In some cases, such as the U-profiled petioles of Hosta × tardiana ‘El Nino’ ( Langer et al , 2021 a ) or Musa textiles ( Ennos et al , 2000 ), this can lead to I / K >1.0 contributing to high twist-to-bend ratios. Flexural rigidity and twist-to-bend ratio can be increased by increasing the absolute magnitude of the axial second moment of area ( Niklas, 1992 ).…”