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Wilting experiments carried out with Caladium bicolor 'Candyland' ; habitus of well-watered plants (day 0); habitus of plants without watering for 4 and 7 d, respectively.  

Wilting experiments carried out with Caladium bicolor 'Candyland' ; habitus of well-watered plants (day 0); habitus of plants without watering for 4 and 7 d, respectively.  

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Premise of the study: Cell turgor plays an important role in the mechanical stability of herbaceous plants. This study on petioles of Caladium bicolor 'Candyland' analyzes the correlation between flexural rigidity and cell turgor. The results offer new insights into the underlying form-structure-function relationship and the dependency of mechanic...

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... experiments -To obtain petioles showing a wide turgor range in the parenchymatous cells, we set up the plants to wilt under normal laboratory conditions (20 ° C, 50% relative humidity, 07:00-19:00 hours, additional artifi - cial illumination) by removing residual water from the saucer and discontinuing watering. Watered plants and plants not watered for 4 to 15 d were used for the experiments ( Fig. 3 ). Only petioles showing no visible changes in morphology during wilting were selected for testing. ...

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... Figure 2 illustrates various transverse sections of plant axes with differing cross-sectional geometries and tissue patterns. Based on stained thin sections from previous studies [1,21,[23][24][25], corresponding schematic drawings were created depicting the cross-sectional geometry of the plant axes and the distribution of the tissues involved. These plant examples were selected because their geometric, mechanical and structural properties were available for discussion of the results of the simulations of this study (electronic supplementary material, S1 and table S1.1). ...
... Investigations of C. bicolor petioles (figure 2c,d) have revealed that their mechanical properties exhibit a high value of E/ G ≈ 64, resulting in a twist-to-bend ratio of approximately 40 [1] (electronic supplementary material, S1 and table S1.1). The almost circular petioles have in the periphery a median of 66 individual collenchyma strands, which are elliptical in cross-section [23]. By contrast, figure 7b shows that, according to our calculations, 45 collenchyma strands already merge. ...
Article
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).
... In the peel parenchyma cells, the influence of the water content mainly depends on cell wall properties and turgor pressure. Freeze-drying results in dehydration of the entire cell (and cell wall) by sublimating the frozen water from the vacuole, the protoplast and the cell wall matrix [3,24,[36][37][38]. The pressure loss of the individual cells and the contraction stresses are results of the water loss in the tissue. ...
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This study analyzes the impact behavior of lemon peel (Citrus x limon) and investigates its functional morphology compared with the anatomy of pomelo peel (Citrus maxima). Both fruit peels consist mainly of parenchyma structured by a density gradient. In order to characterize the lemon peel, both energy dissipation and transmitted force are determined by conducting drop weight tests at different impact strengths (0.15–0.74 J). Fresh and freeze-dried samples were used to investigate the influence on the mechanics of peel tissue’s water content. The samples of lemon peel dissipate significantly more kinetic energy in the freeze-dried state than in the fresh state. Fresh lemon samples experience a higher impulse than freeze-dried samples at the same momentum. Drop weight tests results show that fresh lemon samples have a significantly longer impact duration and lower transmitted force than freeze-dried samples. With higher impact energy (0.74 J) the impact behavior becomes more plastic, and a greater fraction of the kinetic energy is dissipated. Lemon peel has pronounced energy dissipation properties, even though the peel is relatively thin and lemon fruits are comparably light. The cell arrangement of citrus peel tissue can serve as a model for bio-inspired, functional graded materials in technical foams with high energy dissipation.
... Petioles possess various tapering modes (Langer et al., 2021a). 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). Because of these significant differences, the tapering mode α will be considered in our calculations of the bending elastic modulus E and the torsional modulus G. ...
... where r l is the radius in lateral direction and r a the radius und adaxial-abaxial direction. According to Caliaro et al. (2013), the tapering mode α was calculated as follows: ...
Article
Plants are exposed to various environmental stresses. To mechano-stimulation, such as wind and touch, leaves immediately respond by bending and twisting or acclimate over a longer time period by thigmomorphogenetic changes of mechanical and geometrical properties. We selected the peltate leaves of Pilea peperomioides for a comparative analysis of mechano-induced effects on morphology, anatomy and biomechanics of petiole and transition zone. The plants were cultivated for six weeks in a phytochamber divided into four treatment groups: control (no stimulus), touch stimulus (brushing every 30 s), wind stimulus (constant air flow of 4.6 ms -1), and a combination of touch and wind stimuli. Comparing the treatment groups, neither the petiole nor the transition zone show significant thigmomorphogenetic acclimations. However, comparing the petiole and the transition zone, the elastic modulus (E), the torsional modulus (G), the E/G ratio and the axial rigidity (EA) differed significantly, whereas no significant difference was found for the torsional rigidity (GK). The twist-to-bend ratios (EI/GK) of all petioles ranged between 4.33 and 5.99, and of all transition zones between 0.67 and 0.78. Based on the twist-to-bend ratios, we hypothesise that bending loads are accommodated by the petiole, while torsional loads are shared between the transition zone and petiole.
... The tapering mode α is a dimensionless parameter that describes the shape of a slender structure (Figure 2), which is, in our case, the petiole. Calculations of the tapering mode were based on the formulae published by Caliaro et al. (2013). First, we calculated the equivalent radius to account for non-perfectly circular cross-sections: ...
... We calculated the torsional rigidity GK by using the torsion constant K, which is valid for crosssections of any geometry, unlike the polar second moment of area J, which is valid only for circular cross-sections. Based on Equations (9) and (10) and the approach of Caliaro et al. (2013), we calculated the elastic modulus E and torsional modulus G taking into consideration the tapering mode: ...
... However, in formula (19), the tapering mode α is not taken into account. Since we found tapered petioles in all the species studied, the tapering mode α was included in the flexural rigidity EI, similar to the approach given by Caliaro et al. (2013) for the elastic modulus E in Equation (11). The first term is the conventional equation for calculating the elastic modulus in twopoint bending tests, with the assumption of a constant axial second moment of area I. ...
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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.
... The percentage values inherent to the fibre reinforcements are computed with respect to the optimal number of fibre strands. namely, *49 sclerenchyma strands and **24 collenchyma strands (see Figs. 4,5). This because, as the distance between the fibre strands becomes smaller, the gradient of φ between two fibre strands is increased and, therefore, the value of φ in the inner part of the cross-section is raised. ...
... Together, they form a doubly secured mechanical system that is sensitive to drought stress. The decrease of flexural rigidity and, thus, the wilting of the leaf stalk are the result of a turgor-loss-induced decrease of the elastic moduli of both the collenchyma fibres and the parenchyma cells 5 . As a withered leaf stalk cannot be restored to its healthy positioning, even with sufficient water support, the evolution of a redundant mechanical system to maintain the flexural rigidity of the plant, in particular, is of great advantage for selection. ...
Article
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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.
... Stem mechanical strength is not only determined by vascular tissues (xylem vessels and tracheids), but also by collenchyma (composed of living cells) and sclerenchyma (composed of dead cells), which are crucial for mechanical support in angiosperms [12,13]. Collenchyma provides mechanical support to rapidly growing organs thanks to its low compressibility and relatively high moduli of elasticity [11]. ...
... This confirms that the higher collenchyma area in plant stems exposed to lower soil moisture contents is the result of the formation of additional collenchyma cells. Considering the stem segments were brought to full turgidity before performing the mechanical bending test, and that stem segments of comparable size were used, this difference in stem strength can be attributed to collenchyma formation and not to the loss of turgor in these cells [13]. The flexural strength (σ) and the flexural modulus (Ebend) decreased with an increase in the soil moisture content, which indicates a reduction in the stiffness of the stems. ...
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As plants would benefit from adjusting and optimizing their architecture to changing environmental stimuli, ensuring a strong and healthy plant, it was hypothesized that different soil moisture levels would affect xylem and collenchyma development in basil (Ocimum basilicum L. cv. Marian) stems. Four different irrigation set-points (20, 30, 40 and 50% VWC), corresponding respectively to pF values of 1.95, 1.65, 1.30 and 1.15, were applied. Basil plants grown near the theoretical wilting point (pF 2) had a higher xylem vessel frequency and lower mean vessel diameter, promoting water transport under drought conditions. Cultivation at low soil moisture also impacted the formation of collenchyma in the apical stem segments, providing mechanical and structural support to these fast-growing stems and vascular tissues. The proportion of collenchyma area was significantly lower for the pF1.15 treatment (9.25 ± 3.24%) compared to the pF1.95 and pF1.30 treatments (16.04 ± 1.83% and 13.28 ± 1.38%, respectively). Higher fractions of collenchyma resulted in a higher mechanical stem strength against bending. Additionally, tracheids acted as the major support tissues in the basal stem segments. These results confirm that the available soil moisture impacts mechanical stem strength and overall plant quality of basil plants by impacting xylem and collenchyma development during cultivation, ensuring sufficient mechanical support to the fast-growing stem and to the protection of the vascular tissues. To our knowledge, this study is the first to compare the mechanical and anatomical characteristics of plant stems cultivated at different soil moisture levels.
... In addition, the tapering mode α petiole was calculated for the 25 petioles per species by using the method described by Caliaro et al. [36]. The tapering mode describes whether the shape of the petiole resembles more 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). ...
Article
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Although both the petiole and lamina of foliage leaves have been thoroughly studied, the transition zone between them has often been overlooked. We aimed to identify objectively measurable morphological and anatomical criteria for a generally valid definition of the petiole–lamina transition zone by comparing foliage leaves with various body plans (monocotyledons vs. dicotyledons) and spatial arrangements of petiole and lamina (two-dimensional vs. three-dimensional configurations). Cross-sectional geometry and tissue arrangement of petioles and transition zones were investigated via serial thin-sections and µCT. The changes in the cross-sectional geometries from the petiole to the transition zone and the course of the vascular bundles in the transition zone apparently depend on the spatial arrangement, while the arrangement of the vascular bundles in the petioles depends on the body plan. We found an exponential acropetal increase in the cross-sectional area and axial and polar second moments of area to be the defining characteristic of all transition zones studied, regardless of body plan or spatial arrangement. In conclusion, a variety of terms is used in the literature for describing the region between petiole and lamina. We prefer the term “petiole–lamina transition zone” to underline its three-dimensional nature and the integration of multiple gradients of geometry, shape, and size.
... Collection of anoline setal morphometric data allowed the effective bending stiffness of anoline setae to be estimated. We found these setae to be noticeably tapered, requiring the modification of the traditional equation used to estimate bending stiffness of cylinders with fixed radius because the moment of inertia varies along the length of the fiber (Caliaro et al., 2013). This modification is simply the multiplication of the bending stiffness of a fixed radius cylinder (k) by what we call the tapering ratio (t), which is the ratio of the apex radius (R a ) to the base radius (R b ). ...
Article
The functional morphology of squamate fibrillar adhesive systems has been extensively investigated and has indirectly and directly influenced the design of synthetic counter- parts. Not surprisingly, the structure and geometry of exemplar fibrils (setae) have been the subject of the bulk of the attention in such research, although variation in setal mor- phology along the length of subdigital adhesive pads has been implicated to be impor- tant in the effective functioning of these systems. Adhesive setal field configuration has been described for several geckos, but that of the convergent Anolis lizards, comprised of morphologically simpler fibrils, remains largely unexplored. Here, we examine setal morphology along the proximodistal axis of the digits of Anolis equestris and compare our findings to those for a model gecko, Gekko gecko. Consistent with previous work, we found that the setae of A. equestris are generally thinner, shorter, and present at higher densities than those of G. gecko and terminate in a single spatulate tip. Contrastingly, the setae of G. gecko are hierarchically branched in structure and carry hundreds of spatulate tips. Although the splitting of contacts into multiple smaller tips is predicted to increase the adhesive performance of a fiber compared to an unbranched one, we posited that the adhesive performance of G. gecko and A. equestris would be relatively similar when the configuration of the setal fields of each was accounted for. We found that, as in geckos, setal morphology of A. equestris follows a predictable pattern along the proximodistal axis of the pad, although there are several critical differences in the configuration of the setal fields of these two groups. Most notably, the pattern of vari- ation in setal length of A. equestris is effectively opposite to that exhibited by G. gecko. This difference in clinal variation mirrors the difference in the direction in which the setal fields of anoles and geckos are peeled from the substrate, consistent with the hypothesis that biomechanical factors are the chief determinants of these patterns of variation. Future empirical work, however, is needed to validate this. Our findings set the stage for future comparative studies investigating the functional morphology of these convergent adhesive apparatuses. Such investigations will lead to an enhanced understanding of the interactions between form, function, and environment of fibril- based biological adhesive systems.
... Directly after the bending tests, segments T 1 and T 2 were prepared for torsional tests. radius at distance x from the base, r b is the equivalent radius at the base and r a is the equivalent radius at the apex of the stem (Caliaro et al., 2013). The bending elastic modulus E alpha considering the tapering mode was calculated according to Eq. 6, where L is the length of the stem between the support point and the attached mass, k is the slope in the displacement-force diagram and I b is the axial second moment of area at the base (Caliaro et al., 2013): ...
... radius at distance x from the base, r b is the equivalent radius at the base and r a is the equivalent radius at the apex of the stem (Caliaro et al., 2013). The bending elastic modulus E alpha considering the tapering mode was calculated according to Eq. 6, where L is the length of the stem between the support point and the attached mass, k is the slope in the displacement-force diagram and I b is the axial second moment of area at the base (Caliaro et al., 2013): ...
... Another aspect we considered is the influence of the taper of the stems on the bending elastic modulus. The tapering mode describes whether the shape resembles more 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) (Caliaro et al., 2013). Depending on the respective taper, the difference of the elastic bending modulus can be more or less pronounced, if taking into account the mean values of the axial second moment of area or adue to the tapering-apically decreasing axial second moment of area. ...
Article
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Premise Because of their own weight and additional wind forces, plants are exposed to various bending and torsional loads that sometimes require contradictory structural characteristics and mechanical properties. The resulting trade‐off between flexural and torsional rigidity can be quantified and compared using the dimensionless twist‐to‐bend ratio. Methods The flexural rigidity of the stems of Carex pendula was determined by 2‐point bending tests. Additionally, 4‐point bending tests and torsional tests were carried out on segments of two internodes directly below the inflorescences to measure flexural and torsional rigidity. Anatomical investigations were performed to quantify the cross‐sectional distribution of their tissues. Results The flexural rigidity of the stems, segments of the apical internode 1, and the more basal internode 2 differed significantly from each other, whereas the bending elastic moduli were not significantly different. The torsional rigidity of segments of internode 2 was a factor of 3.3 higher than that of internode 1, whereas the torsional moduli did not differ significantly. The twist‐to‐bend ratios of segments of internode 1 and 2 reached values between 85 and 403. Light microscopic investigations revealed a triangular stem possessing individual sclerenchyma strands, with internode 2 having significantly more strands than internode 1. Conclusions In the case of Carex pendula, flexural and torsional rigidity are adapted to the given mechanical constraints by significant changes in morphometric variables (axial and polar second moment of area, number of sclerenchyma strands), whereas the material properties (bending and torsional modulus) do not change markedly along the stem.
... All stresses were set to zero and a pressure of 0.07 MPa was applied to the surface of the cell walls of the bulliform cells to imitate increasing turgor, which should lead to a leaf opening. The magnitude of the applied pressure was thereby based on the turgor difference measured for the parenchyma of Caladium bicolor 'Candyland' petioles in the fully turgescent state (0.45 ± 0.04 MPa) and under drought stress (0.38 ± 0.08 MPa) [27]. To represent this turgor variation, pressure was applied to the inside of the bulliform cells by hydrostatic fluid elements (HSFLD242), requiring a nonlinear calculation. ...
... The opening angles of fresh (turgescent) leaves were significantly higher than those of dehydrated leaves after a drying period of 24 h (electronic supplementary material, table S1 in S2). As no turgor values were available for the bulliform cells in various turgescent states, value changes of 0.07 MPa measured for petioles of Caladium bicolor 'Candyland' with a sufficient water supply and under drought stress were used [27]. Figure 5 shows a calculated and almost linear relationship between the turgor increase in the bulliform cells and angular change resulting in a rotary motion of the leaf lamina with respect to the calculated pivot point. ...
... This relation is also reflected in the comparably high internal cell pressure (turgor pressure of approx. 0.45 MPa [27]) of the small plant cells. The material used has to possess the envisaged flexibility and further combine a low density and high stiffness, in addition to having stable long-term behaviour. ...
Article
Within the framework of a biomimetic top-down approach, our study started with the technical question of the development of a hinge-free and compliant actuator inspired by plant movements. One meaningful biological concept generator was the opening and closing movements of the leaf halves of grasses. Functional morphological investigations were carried out on the selected model plant Sesleria nitida . The results formed the basis for further clarifying the functional movement principle with a particular focus on the role of turgor changes in bulliform cells on kinetic amplification. All findings gained from the investigations of the biological model were incorporated into a finite-element analysis, as a prerequisite for the development of a pneumatic cellular actuator. The first prototype consisted of a row of single cells positioned on a plate. The cells were designed in such a way that the entire structure bent when the pneumatic pressure applied to each individual cell was increased. The pneumatic cellular actuator thus has the potential for applications on an architectural scale. It has subsequently been integrated into the midrib of the facade shading system Flectofold in which the bending of its midrib controls the hoisting of its wings.