Development and Growth Form of the Neotropical Liana <Emphasis Type="Italic">Croton nuntians</Emphasis>: The Effect of Light and Mode of Attachment on the Biomechanics of the Stem

The neotropical liana Croton nuntians (Euphorbiaceae) can occur in a variety of different growth habits. Juvenile freestanding plants are mechanically stable without support and resemble morphologically young trees or shrubs, whereas adult plants are climbers. Ontogenetic variation of bending and torsion properties of different growth phases are analyzed by measurements of flexural stiffness, structural bending modulus, torsional stiffness and structural torsional modulus. Mechanical and anatomical data show two fundamentally different patterns for juvenile freestanding and adult climbing plants. In freestanding plants, mechanical properties and the contribution of cortex, wood, and pith to the stem cross-section vary only little during ontogeny as is typical for semi-self-supporting plants. In contrast, climbing plants become significantly more flexible during ontogeny, as is characteristic for lianas. This is accompanied by a transition to the formation of a less dense wood type with large diameter vessels and an increasing contribution of flexible tissues (less dense wood and cortex) to the cross-sectional area and the axial second moment of area of the stems. Depending on the environmental conditions, freestanding plants can differ considerably in their appearance due to differences in branching system or stem taper. Therefore the influence of light quantity, measured as percentage of canopy opening, on the mechanical properties and the stem anatomy was tested. Freestanding plants grown with strong shade are significantly more stiff in bending compared with plants grown with a moderate light environment.     

How to become a tree without wood – biomechanical analysis of the stem of Carica papaya L

Carica papaya L. does not contain wood, according to the botanical definition of wood as lignified secondary xylem. Despite its parenchymatous secondary xylem, these plants are able to grow up to 10‐m high. This is surprising, as wooden structural elements are the ubiquitous strategy for supporting height growth in plants. Proposed possible alternative principles to explain the compensation for lack of wood in C. papaya are turgor pressure of the parenchyma, lignified phloem fibres in the bark, or a combination of the two. Interestingly, lignified tissue comprises only 5–8% of the entire stem mass. Furthermore, the phloem fibres do not form a compact tube enclosing the xylem, but instead form a mesh tubular structure. To investigate the mechanism of papaya's unusually high mechanical strength, a set of mechanical measurements were undertaken on whole stems and tissue sections of secondary phloem and xylem. The structural Young's modulus of mature stems reached 2.5 GPa. Since this is low compared to woody plants, the flexural rigidity of papaya stem construction may mainly be based on a higher second moment of inertia. Additionally, stem turgor pressure was determined indirectly by immersing specimens in sucrose solutions of different osmolalities, followed by mechanical tests; turgor pressure was between 0.82 and 1.25 MPa, indicating that turgor is essential for flexural rigidity of the entire stem.     

Variation in Young's modulus along the length of a rat vibrissa

Rats use specialized tactile hairs on their snout, called vibrissae (whiskers), to explore their surroundings. Vibrissae have no sensors along their length, but instead transmit mechanical information to receptors embedded in the follicle at the vibrissa base. The transmission of mechanical information along the vibrissa, and thus the tactile information ultimately received by the nervous system, depends critically on the mechanical properties of the vibrissa. In particular, transmission depends on the bending stiffness of the vibrissa, defined as the product of the area moment of inertia and Young's modulus. To date, Young's modulus of the rat vibrissa has not been measured in a uniaxial tensile test. We performed tensile tests on 22 vibrissae cut into two halves: a tip-segment and a base-segment. The average Young's modulus across all segments was 3.34±1.48GPa. The average modulus of a tip-segment was 3.96±1.60GPa, and the average modulus of a base-segment was 2.90±1.25GPa. Thus, on average, tip-segments had a higher Young's modulus than base-segments. High-resolution images of vibrissae were taken to seek structural correlates of this trend. The fraction of the cross-sectional area occupied by the vibrissa cuticle was found to increase along the vibrissa length, and may be responsible for the increase in Young's modulus near the tip.     

Biomechanical analysis ofPitus dayi: Early seed plant vegetative morphology and its implications on growth habit

A biomechanical method to distinguish self-supporting and non self-supporting growth habits is applied to exceptionally preserved “twigs” ofPitus dayi Gordon. The analysis investigates whether these isolated stem segments are consistent with a self-supporting tree-like habit as suggested by the stumps, trunks and branches of the genusPitus Witham preserved more commonly in the fossil record. Because of difficulties in accurately identifying certain fossil tissues, three centrisymmetrical models were constructed to test a range of possible tissue combinations over five ontogenetic stages. The results suggest a self-supporting habit with trends in mechanical parameters during ontogeny similar to those of extant, self-supporting plants. Less explicitly constrained to the analysis of habit, the investigation also examines the structural significance of specific tissues during ontogeny as observed from contributions of individual tissues to cross-sectional area, axial second moment of area and flexural stiffness.Pitus dayl produced a physiologically “cheap” primary cauline cortex which was rapidly replaced by the development of a rhytidome. A mechanically significant, cauline hypoderm comprising thickwalled sclerenchymatous tissue is absent. This arrangement differs from other tested Palaeozoic pteridosperms interpreted as semi-self-supporting such asLyginopteris oldhamia andCalamopitys sp. in which the primary cortex is mechanically significant and secondary growth of the wood does not reach mechanically significant thresholds within the primary body.     

Mechanical Properties of Black Locust (Robinia pseudoacacia L.) Wood. Size- and Age-dependent Variations in Sap- and Heartwood

Variations in the density and stiffness (Young's elastic modulus)of fresh wood samples drawn from different parts of the threemain trunks of a 32-year-old black locust tree,Robinia pseudoacacia(measuring 19.8 m at its highest point), were studied to determinewhether tree ontogeny can achieve a constant safety factor againstmechanical failure. Based on the properties of isolated woodsamples, the fresh density of sapwood decreased along radialtransects from bark to pith, while that of progressively olderheartwood samples increased, on average, towards the centreof each of the three trunks. Along the same radial transects,the Young's elastic modulus of sap- and heartwood increased.In terms of longitudinal changes in wood properties, mean woodmoduli (averages of sap- and heartwood samples) increased, onaverage, towards the base of each of the three trunks of thetree. However, the mean fresh densities of wood samples increasedtowards the top and the bottom of each trunk and were lowestroughly near trunk mid-length. The mean density-specific stiffness(the quotient of Young's modulus and fresh density) of woodwas thus lower toward the top and the bottom of the trunks andhighest near trunk mid-length. Mean values of fresh wood density-specificstiffness were used to estimate the critical buckling heightsfor sections of the trunks differing in diameter and age. Theseestimates indicated that ontogenetic variation in the physicalproperties and relative amounts of sap- and heartwood in trunkscould maintain a constant factor of safety (approximately equalto 2) as a sapling grows in height and girth into a mature tree.This expectation was supported by data from 16 black locusttrees differing in height and diameter at breast height (DBH). Wood; elastic properties; tree height; biomechanics     

Growth habit and mechanical architecture of the sand dune-adapted climber Clematis flammula var. maritima L

Clematis flammula var. maritima is a woody lianoid plant that grows on coastal sand dunes in the Mediterranean region. Older perennial stems are present as extensive underground axes. These generate surface growth of shorter-lived stems producing monospecific trellises above the surface of the sand. Despite its sand dune habitat and shortage of host support plants, this variety of Clematis shows mechanical characteristics during growth that are closely comparable with those of scandent woody lianas. A significant decrease in the value of structural Young's modulus is observed from the aerial trellis-forming shoots (1.619 +/- 0.492 GN m(-2)) to emergent axes (0.855 +/- 0.253 GN m(-2)) and underground woody stems (0.470 +/- 0.113 GN m(-2)). Biomechanical and developmental observations indicate that most emergent branches are optimized geometrically and mechanically in relation to their points of emergence from the sand, with increases in structural Young's modulus and the second moment of area around the surface of the sand. Lianoid plants, physiologically capable of withstanding sand dune environments, might represent acceptable natural or introduced species for dune stabilization and conservation.     

The mechanical role of bark

The ability of stem bark to resist bending forces was examined by testing in bending segments of Acer saccharum, Fraxinus americana, and Quercus robur branches with and without their bark. For each species, the bark contributed significantly to the ability of stem segments differing in age to resist bending forces, but its contribution was age-dependent and differed among the three species. The importance of the mechanical role of the bark decreased basipetally with increasing age of F. americana and Q. robur stem segments and was superceded by that of the wood for segments ≥ 6 yr old. A. saccharum bark was as mechanically important as the wood for stem segments 7 yr old but was not a significant stiffening agent for younger or older portions of stems. On average, the stiffness of the bark from all three species was 50% that of the wood. However, the geometric contribution to the flexural rigidity of stems made by the bark (i.e., the bark's second moment of area) was sufficiently large to offset its lower stiffness (Young's modulus) relative to that of the wood. A simple model is presented that shows that the bark must be as mechanically important as the wood when its radial thickness equals 32% that of the wood and its stiffness is 50% that of the wood. Based on this model, which is shown to comply with the data from three species purported to have stiff woods, it is evident that the role of the bark cannot be neglected when considering the mechanical behavior of juvenile woody stems subjected to externally applied bending forces.     

Leaf support biomechanics of neotropical understory herbs

Plants in light-limited tropical rainforest understories face an important carbon allocation trade-off: investment of available carbon into photosynthetic tissue should be advantageous, while risk of damage and mortality from falling debris favors investment into nonphotosynthetic structural tissue. We examined the modulus of rupture (σ(max)), Young's modulus of elasticity (E), and flexural stiffness (F) of stems and petioles in 14 monocot species from six families. These biomechanical properties were evaluated with respect to habitat, rates of leaf production, clonality, and growth form. Species with higher E and σ(max), indicating greater resistance per unit area to bending and breaking, respectively, tended to be shade-tolerant, slow growing, and nonclonal. This result is consistent with an increase in carbon allocation to structural tissue in shade-tolerant species at the expense of photosynthetic tissue and growth. Forest- edge species were weaker per unit area (had a lower E), but had higher flexural stiffness due to increases in stem and petiole diameter. While this is inefficient in requiring more carbon per unit of structural support, it may enable forest-edge species to support larger and heavier leaves. Our results emphasize the degree to which biomechanical traits vary with ecological niche and illustrate suites of characteristics associated with different carbon allocation strategies.     

Shade induced changes in biomechanical petiole properties in the stoloniferous herb <Emphasis Type="Italic">Trifolium repens</Emphasis>

Increased cell number and cell length both contribute to shade induced elongation of petioles which enables stoloniferous plants to place their leaf lamina higher up in the canopy. Although petiole elongation is assumed to be beneficial, it may also imply costs in terms of decreased biomechanical stability. We test the hypothesis that shade induced elongation changes the biomechanical properties of petioles and that the underlying mechanisms, cell division and cell elongation, differentially affect biomechanical properties. This was done by subjecting 14 genotypes differing in the relative contribution of cell size and cell number to shade induced elongation responses to high light conditions and to simulated canopy shade. Developmental traits (cell size and cell number), morphological traits characterizing the petioles, as well as biomechanical characteristics were measured. Our results show that, comparable to stems of non-clonal plants, the rigidity of a petiole’s tissue (the Young’s modulus) increases, leading to increased flexural stiffness of petioles subjected to shading. Increased flexural stiffness proved to be associated with increased performance under shaded conditions. Our results also indicate that cell number affected the material properties and the flexural stiffness of petioles. However, the degree and pattern of the effects differed between light environments. Shade induced increase in cell number translated into shade induced increase of Young’s modulus and flexural stiffness. Genotypes producing relatively larger cells under shaded conditions experienced a decrease in tissue rigidity. In concert our results indicate that the pattern of selection on flexural stiffness, and thereby also on shade induced changes of cell number and cell size differs among light environments. An erratum to this article can be found at     

Variations of the mechanical properties of Acer saccharum roots

Longitudinal and transverse variations in the compressive strength c and stiffness measured in bending and torsion (E and G, respectively) were determined for wood samples removed from three old lateral roots of a large sugar maple Acer saccharum L. whose canopy had been heavily pruned on one side such that the three roots had loading conditions assumed to be dominated by different stresses: tensile stresses along the axis of root I, compressive stresses along root III, and torsional shear stresses in root II.Values of c, E and G tended to decrease from the base toward the tip of each root, but maximized at approximately 1 m from the base (perhaps as a consequence of fibre fatigue near the base of the root system). Comparisons between the mechanical properties of wood sampled from the upper and lower root surfaces showed that the wood along the lower surface of roots I and II was stiffer and stronger; the reverse was found to root III.Longitudinal variations in the geometry and size of root transactions resulted in a curvilinear pattern of root taper; maximum taper occurred at 1 m from each root base. These variations, which resulted in longitudinal changes in the second moment of area I and the polar second moment of area J, were sufficient to mask the effects of longitudinal variations in E and G on the flexural and torsional rigidity of roots (El and GJ, respectively) both of which decreased exponentially away from the base of the tree.Based on the correlations observed between the stresses presumed to dominate the loading conditions of each of the three roots and the mechanical properties of wood samples, it appears that the 'biomechanical plasticity' of woody roots holds the potential to maximize the individual ability of roots to cope with the dominant stresses attending their growth and development.     

Mechanical properties of the axial skeleton in gorgonians

Axial skeletons of thirteen species representing a wide range of genera of Gorgonians were investigated using Young's modulus as a measure of stiffness and Torsion modulus as a measure of resistance to shear or twist. Atomic absorption spectroscopic determination of magnesium and calcium content as measures of mineralization were done. Relative quantities of calcareous material in the axial skeletons showed a strong linear correlation with Young's modulus and suggests an important role for calcareous material in the modulation of the mechanical properties of axoskeleton. Torsion moduli also showed a mathematical but non-linear relationship to calcareous content. Axis stiffness correlated well with zonation-related water movement. Stiffest axes occur in deeper water with no wave surge, most flexible in shallower water with moderate surge and intermediate stiffness in shallow, high energy habitats. An extremely high MgCO₃ containing carbonate that may be a previously unreported biological structural material was found in the Plexauridae.     

Axial-shear interaction effects on microdamage in bovine tibial trabecular bone

Because many osteoporotic fractures occur during a fall, understanding the effect of off-axis loads on initiation and propagation of microdamage in trabecular bone should provide further insight into the biomechanics of age-related fractures. Fourteen on-axis cylindrical specimens were prepared from 12 bovine tibiae. Fluorescent stains were used to label the microdamage due to a sequence of compressive and torsional damaging loads. The mean decrease in Young's modulus was over four times greater than that in the shear modulus after the compressive overload, while there was no difference between the decrease in the axial and torsional stiffnesses after the torsional overload. The total microcrack density due to compression was uniform across the radius of the cylindrical specimens, while the mean density of microcracks due to torsional overloading increased from the axis of the cylindrical specimen to the circumference. The high density of microcracks near the axis of the specimen following torsional overloading was unexpected because of the low strains. Nearly 40% of the microcracks due to torsion propagated from pre-existing microcracks caused by axial compression, indicating that existing microcracks may extend at relatively low strain if the loading mode changes. The propagating microcracks were, on average, longer than the initiating microcracks due to either compressive or torsional loading. Damage due to axial compression appears to increase the susceptibility of trabecular bone to damage propagation during subsequent torsional loads, but it has little effect on the elastic properties in shear.     

Incidence and mechanical significance of pneumatization in the long bones of birds

The incidence of pneumatization in avian long bones was studied, by direct observation, in a large sample of species. Only proximal bones (humerus and femur) presented pneumatization in the sample studied. The incidence obtained was related to the variation of the maximum cortical thickness and mechanical properties, such as bending strength and flexural Young's modulus. Cortical thickness, bending strength and flexural Young's modulus were significantly lower in pneumatized bones than in marrow-filled bones. Furthermore, some congruence was found between pneumatization and systematic groups when compared. In this sense, Charadriformes was the only order studied with total absence of long bone pneumatization. Results on cortical thickness appear to be in agreement with modelling predictions previously made and with results obtained on other groups of flying vertebrates. The possible selective advantage of reduction in cortical thickness in relation to flying is suggested.     

Stem biomechanics of the giant moss Dendroligotrichum dendroides s.l. and its significance for growth form diversity in mosses

Abstract

The giant moss Dendroligotrichum dendroides s.l. grows as self-supporting plants up to 40 cm in height in forest habitats in Chile and New Zealand. This moss represents one of the tallest self-supporting bryophytes. Biomechanical tests indicate that the stems can develop a high degree of stiffness (Young’s modulus) via a dense hypodermal sterome that is comparable with that of woody stems of vascular plants. A comparison with mechanical properties of other terrestrial and aquatic mosses indicates that different moss growth and life forms can produce very different mechanical architectures. Values of stem stiffness can vary between different growth forms of mosses to a comparable extent to that observed among diverse growth forms of vascular plants. Plants varying profoundly in overall size, development, and phylogenetic position nevertheless appear to develop comparable mechanical adaptations and growth forms in response to certain environmental conditions.     

Length-dependence of flexural rigidity as a result of anisotropic elastic properties of microtubules

Unexplained length-dependence of flexural rigidity and Young's modulus of microtubules is studied using an orthotropic elastic shell model. It is showed that vibration frequencies and buckling load predicted by the accurate orthotropic shell model are much lower than that given by the approximate isotropic beam model for shorter microtubules, although the two models give almost identical results for sufficiently long microtubules. It is this inaccuracy of the isotropic beam model used by all previous researchers that leads to reported lower flexural rigidity and Young's modulus for shorter microtubules. In particular, much lower shear modulus and circumferential Young's modulus, which only weaken flexural rigidity of shorter microtubules, are responsible for the observed length-dependence of the flexural rigidity. These results confirm that longitudinal Young's modulus of microtubules is length-independent, and the observed length-dependence of the flexural rigidity and Young's modulus is a result of strongly anisotropic elastic properties of microtubules which have a length-dependent weakening effect on flexural rigidity of shorter microtubules.     

Mechanical properties and chemical composition of avian long bones

We have studied the mechanical behaviour of avian long bones as whole structures, by calculating mechanical parameters such as maximum load, stiffness, bending strength and flexural Young's modulus; bones were always tested in three-point bending. Furthermore composition in several chemical elements and amino acids related to collagen content was also analysed. Correlations were established between body mass, mechanical parameters and chemical contents. Both bending strength and Young's modulus were negatively correlated to body mass. Significant correlations were found between nitrogen content and both strength and Young's modulus, with negative slopes in both cases. Magnesium and phosphorus appear to be the most important inorganic elements to the understanding of the mechanical behaviour of avian long bones.     

Mechanical properties of the lateral cortex of mammalian auditory outer hair cells.

Mammalian auditory outer hair cells generate high-frequency mechanical forces that enhance sound-induced displacements of the basilar membrane within the inner ear. It has been proposed that the resulting cell deformation is directed along the longitudinal axis of the cell by the cortical cytoskeleton. We have tested this proposal by making direct mechanical measurements on outer hair cells. The resultant stiffness modulus along the axis of whole dissociated cells was 3 x 10(-3) N/m, consistent with previously published values. The resultant axial and circumferential stiffness moduli for the cortical lattice were 5 x 10(-4) N/m and 3 x 10(-3) N/m, respectively. Thus the cortical lattice is a highly orthotropic structure. Its axial stiffness is small compared with that of the intact cell, but its circumferential stiffness is within the same order of magnitude. These measurements support the theory that the cortical cytoskeleton directs electrically driven length changes along the longitudinal axis of the cell. The Young's modulus of the circumferential filamentous components of the lattice were calculated to be 1 x 10(7) N/m2. The axial cross-links, believed to be a form of spectrin, were calculated to have a Young's modulus of 3 x 10(6) N/m2. Based on the measured values for the lattice and intact cell cortex, an estimate for the resultant stiffness modulus of the plasma membrane was estimated to be on the order of 10(-3) N/m. Thus, the plasma membrane appears to be relatively stiff and may be the dominant contributor to the axial stiffness of the intact cell.     

Safety and streamlining of woody shoots in wind: an empirical study across 39 species in tropical Australia

? Wind is a key mechanical stress for woody plants, so how do shoot traits affect performance in wind? ? We used a vehicle mounted apparatus to measure drag, streamlining and mechanical safety in 127 vertical lead-shoots, 1.2 m long, across 39 species in tropical Australia. ? Shoot dimensions and stem tissue properties were closely coupled so that shoots with low stem specific gravity or larger projected area had thicker stems. Thicker stems provide larger second moment of area (I), which increased shoot safety and bending stiffness but impeded shoot reconfiguration in strong winds, including frontal area reduction. Nonetheless, increasing I also improved streamlining. Streamlining was unrelated to traits except I. Stem tissue material properties only had small effects. Higher modulus of rupture increased shoot safety and higher Young's modulus impeded shoot reconfiguration. ? We found no conflict between bending stiffness and streamlining for woody shoots. Stiffness might help streamlining by increasing damping and stability, thereby reducing flagging in wind. Tissue-level traits did influence shoot-level mechanical safety and behaviour, but shoot geometry was much more important. Variable shoot and stem traits, which all influenced shoot biomechanics, were integrated in shoots to yield a relatively narrow range of outcomes in wind.     

Tensile properties of the in vivo human gastrocnemius tendon

In the present experiment we obtained the tensile properties of the human gastrocnemius tendon, a high-stressed tendon suitable for spring-like action during locomotion. Measurements were taken in vivo in six men. The gastrocnemius tendon elongation during tendon loading−unloading induced by muscle contraction−relaxation was measured using real-time ultrasonography. Tendon forces were calculated from the moment generated during isometric plantarflexion contraction, using tendon moment arm length data obtained in vivo with the tendon travel method. Tendon stiffness data were calculated from the slope of the tendon force−elongation curve, and were then normalized to the tendon's original dimensions, obtained from morphometric analysis of sonographs, to estimate the tendon Young's modulus. Mechanical hysteresis values were obtained from area calculations by numerical integration. The elongation of the tendon increased curvilinearly with the force acting upon it, from 1.7±1 mm (0.8±0.3% strain) at 87.5±8.5 N to 11.1±3.1 mm (4.9±1% strain) at 875±85 N. The tendon Young's modulus and mechanical hysteresis were 1.16±0.15 GPa and 18±3%, respectively. These values fall within the range of values obtained from in vitro experiments and are very similar to the respective values recently obtained from in vivo measurements in the less highly stressed human tibialis anterior tendon (1.2 GPa and 19%), thus indicating that the material properties of tendon are independent of physiological loading and function. Combining the present tendon force−elongation data with previously reported Achilles tendon force data recorded during walking indicates that the gastrocnemius tendon would provide 6% of the total external work produced by the locomotor system. This estimate illustrates the contribution of passive elastic mechanisms on the economy and efficiency of walking. The contributions would be greater in more active exercise such as running.     

The functional morphology of penile erection: tissue designs for increasing and maintaining stiffness

Inflatable penises have evolved independently at least fourtimes in amniotes, specifically in mammals, turtles, squamates,and the archosaurs. Males in these lineages therefore sharethe functional problem of building a penis out of soft and flexibletissues that can increase its flexural stiffness and resistbending during copulation. Research on penile erectile tissuesin mammals and turtles shows that these two taxa have convergentlyevolved an axial orthogonal array of collagen fibers to reinforcethe penis during erection and copulation; in both lineages,the collagen fibers in the array are crimped and folded in theflaccid penis. Collagen fiber straightening during erectionincreases the stiffness of the tissue and allows changes inpenile radius that increase its second moment of area: bothof these changes increase the flexural stiffness of the penisas a whole. And once erect, axial orthogonal arrays have thehighest flexural stiffness of any fiber arrangement. The highdegree of anatomical convergence (to the level of microanatomicalfeatures) within mammals and turtles suggests that the stiffnessrequirements for copulation produce an extremely restrictiveselective regime in organisms that evolve inflatable penises.