Corresponding author: Hongping Zhao, Xiqiao Feng E-mail: zhaohp@tsinghua.edu.cn, fengxq@tsinghua.edu.cn

Journal of Bionic Engineering 12 (2015) 634–642

Synergistic Effects of Chiral Morphology and Reconfiguration in Cattail Leaves

Zilong Zhao1,2, Weixi Huang1, Bingwei Li1, Kexing Chen1, Kuifu Chen3, Hongping Zhao1, Xiqiao Feng1,2

1. AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China 2. Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China

3. College of Sciences, China Agricultural University, Beijing 100083, China

Abstract Cattail, a type of herbaceous emergent aquatic macrophyte, has upright-standing leaves with a large slenderness ratio and a

chiral morphology. With the aim of understanding the effect of chiral morphology on their mechanical behavior, we investi-gated, both experimentally and theoretically, the twisting chiral morphologies and wind-adaptive reconfigurations of cattailleaves. Their multiscale structures were observed by using optical microscope and scanning electron microscopy. Their me-chanical properties were measured by uniaxial tension and three-point bending tests. By modeling a chiral leaf as a pre-twisted cantilever-free beam, fluid dynamics simulations were performed to elucidate the synergistic effects of the leaf’s chiral mor-phology and reconfiguration in wind. It was observed that the leaves have evolved multiscale structures and superior mechanical properties, both of which feature functionally gradient variations in the height direction, to improve their ability to resist lodging failure by reducing the maximal stress. The synergistic effect of chiral morphology and reconfiguration can greatly improve the survivability of cattail plants in wind.

Keywords: cattail, chiral morphology, reconfiguration, fluid-structure interaction, lodging resistance Copyright © 2015, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(14)60153-0

1 Introduction

Typha orientalis C. Presl, also named cattail (Fig. 1), is an herbaceous perennial emergent aquatic macrophyte mainly inhabiting streams, lakes, marshes, rivers, reservoirs, ditches, freshwater ponds, canals, and other shallow water areas[1,2]. Owing to their superior mechanical properties, the stems and leaves of cattails can be used as, for example, crude materials for candle wicks[3], paper[4], rope[5,6], and braided fabrics.

The multiple biological functions of plants are closely related to their structures at different length scales[7–9]. The chirality of biological materials has at-tracted the curiosity of many scientists. Over a century ago, von Marilaum and Oliver qualitatively stated that the spirally twisted leaves of bulbous plants, bur-reeds, and grasses could possess a greater resistance to flexion than flat leaves[10]. Silk and Hubbard found that the stems of morning glory placed themselves in tension and that their helical morphology is important for

Fig. 1 Cattail plants in the wild.

Zhao et al.: Synergistic Effects of Chiral Morphology and Reconfiguration in Cattail Leaves 635

maintaining the twining habit[11]. Wang et al. uncovered the mechanism of hierarchical chirality transfer in the growth of Towel Gourd tendrils[12,13]. Cattails have long, narrow, vertical, and porous leaves, which are essential for the plant to accommodate water-level fluctuations and to fulfill their biological functions, e.g., photosyn-thesis. The leaves possess an intrinsic chiral morphology, which is prevalent in many other aquatic plants. The chirality can improve the ability of the slender emergent leaves to maintain an erect posture under severe envi-ronmental loads, e.g., wind and rain[14]. Schulgasser and Witztum noted that the spiral shapes of cattail, Narcissus, and Pancratium can help their leaves to reach a greater height without loss of stability[15]. Recently, the ex-periments of Zhao et al. demonstrated that chiral growth is an optimal biomechanical strategy for aquatic macrophytes to survive in complex environments[16]. However, the effect of fluid–structure interaction has not been taken into account in previous studies.

To accommodate wind loads, the stems and leaves of plants generally reconfigure themselves by stream-lining[17,18], bending, and twisting[19–22]. The curling and folding of monocotyledon leaves have been recognized as a biomechanical strategy for improving their struc-tural stiffness[23]. The rolling of maize leaves has been observed to be strongly dependent on minimal me-chanical energy constraints[24]. Vogel suggested that the reconfigurations of leaves were guided by the twisti-ness-to-bendiness ratio[25]. It should be noted that changes in morphology to adapt to wind have a consid-erable effect on the flow load exerted on plants. The drag applied on a moving flexible object due to deformation is not proportional to the square of the object’s speed[26]. For example, the stem-twisting reconfiguration of daf-fodil flowers can reduce drag by approximately 30%[27]. In addition, much effort has been directed toward un-derstanding the lodging resistance of plants, e.g., cere-als[28], wheat[29], maize[30], and rice[31]. In addition to biological and chemical factors, the lodging resistance of a plant is also related to its slenderness, cross-sectional geometry, hierarchical structures, me-chanical properties, basal constraints, moisture content, and external loads[32,33]. A slender plant is more likely to lodge than a stocky one. Although they exhibit a large slenderness ratio, cattail leaves can stand upright. However, it remains unclear that how the chiral mor-phology and reconfiguration of such aquatic macrophyte

structures as cattail leaves affect their survivability in winds.

In this study, an attempt was made to reveal the synergistic effects of intrinsic chiral morphology and reconfiguration on the ability of emergent cattail leaves to withstand winds. We systemically observed the mul-tiscale structures of cattail leaves. Uniaxial tension tests and three-point bending tests were carried out to meas-ure their mechanical properties. By modeling an emer-gent leaf as a pre-twisted cantilever beam, the synergis-tic effects were investigated through fluid dynamics simulations. The results demonstrate that the chiral morphology and reconfiguration can significantly im-prove the survivability of cattails in wind.

2 Materials and methods

We collected 85 intact emergent leaves from 16 cattail plants in a freshwater area at Olympic Forest Park, Beijing, China. To ensure the reliability and repeatability of the experiments, the samples were wrapped in pre-servative films and stored in a refrigerator at 4 ˚C. Ob-servations and measurements were performed not more than three days after the collection. 2.1 Structure observations

The macroscopic chiral morphologies, cross-sectional geometry, and interior microstructures of the emergent leaves were first observed. For each sam-ple, the cross-sectional sizes, chiral parameters, and their gradient variations along the longitudinal direction were investigated. Using an optical microscope (OM, Olym-pus IX71, China), we observed the cross-sections of an emergent leaf. The leaf, which measured 2.17 m in length and 1.5 turns in twist, was cut into six 90˚-twisted segments from the base to the apex. The bottom surfaces of the segments are shown in Fig. 2. The inner micro-structures of the emergent leaves were then observed using Scanning Electron Microscopy (SEM, SS-550, Shimadzu Corporation, Japan). Distilled water was used to clean the sample surfaces, and a glutaraldehyde solu-tion with a volume fraction of 4% was used to fix the inner tissues. The samples were successively cleaned with ionized water, dehydrated, dried, and gold sputtered before observation. By removing the epidermis, we observed the longitudinal sectional microstructures of an emergent leaf, as shown in Fig. 3. The geometric pa-rameters of the inner structures of freshly collected

Journal of Bionic Engineering (2015) Vol.12 No.4 636

5 mm

Fig. 2 Cross-sections of an emergent leaf from the base to the apex.

500 m

50 m

50 m

(a)

(b)

(c)

Fig. 3 Microstructures of an emergent leaf observed using SEM, including (a) the longitudinal sectional microstructures, (b) foam tissues, and (c) diaphragm.

emergent leaves were measured using an Environmental Scanning Electron Microscope (ESEM, FEI Quanta 200, Czech Republic). 2.2 Mechanical tests

The mechanical properties of the emergent leaves were examined by uniaxial tension and three-point bending tests. Quasi-static uniaxial tension tests were performed using a universal testing machine (AG-G, Shimadzu Corporation, Japan) with a crosshead speed of 2.0 mm·min−1 at room temperature. To directly measure the strength and longitudinal elastic modulus of their main load-bearing structure (i.e., epidermis), the emer-gent leaves were hollowed by removing their inner structures, e.g., diaphragm, mediastinum, fiber cables, and foam tissues. Three hollowed emergent leaves were prepared as samples. Each sample was cut along the axial direction into a certain number of segments meas-uring 10 cm in length. The ventral and dorsal parts of a leaf segment, excluding those prepared from the subapical part of the leaf, were separated and tested, respectively. The elastic modulus of a leaf segment was calculated by averaging the moduli of its ventral and dorsal parts. Tensile force–displacement curves were automatically recorded by computer. The nominal ten-sile stress of the specimen was calculated from the ex-ternally applied force divided by the cross-sectional area of the thin-walled epidermis. Three typical stress–strain relations are shown in Fig. 4a, and the longitudinal elastic moduli at representative positions of the speci-mens are plotted in Fig. 4b.

Both the intact and hollowed emergent leaves were submitted to quasi-static three-point bending tests using a universal testing machine (Z005 series, Zwick/Roll Corporation, Ulm, Germany) with a crosshead speed of 2.0 mm·min−1 at room temperature. The measured bending resistances of the emergent leaves with and without inner tissues were compared. The intact and hollowed samples were prepared from an emergent leaf and its opposite phyllotaxis, respectively. Each sample was cut equidistantly along the height direction into seven specimens of approximately 5 cm in length. The force–displacement curves are shown in Fig. 5. 2.3 Fluid dynamics simulation

Fluid dynamics simulations were performed to evaluate the synergistic effects of the intrinsic chiral

Zhao et al.: Synergistic Effects of Chiral Morphology and Reconfiguration in Cattail Leaves 637

morphology and wind-adaptive reconfiguration of an emergent leaf on its survivability to bear wind loads, i.e.,

Stre

ss (M

Pa)

Elas

tic m

odul

us (G

Pa)

Fig. 4 (a) Typical stress–strain curves in the uniaxial tension tests and (b) the variation in the longitudinal elastic modulus of three leaves from the base to the apex.

Forc

e (N

)

Fig. 5 Force–displacement curves of both the intact and hollow specimens.

ability against lodging failure. The leaf was modeled as a linear elastic cantilever beam subjected to an incoming flow. The deflection of the beam in a viscous flow was calculated by using an improved immersed boundary method[34]. We established an Eulerian coordinate sys-tem to describe the fluid flow and a separate Lagrangian coordinate system to describe the structure. In the im-mersed boundary method, the governing equations of fluid flow and the deflection of the beam were solved in each coordinate system using finite difference method, and the fluid-structure interactions were realized using a feedback law.

To examine the effect of chiral morphology, we compare two cases in which the beams exhibit or do not exhibit twisting chirality. The twist angle from bottom to top was denoted as θ. A deformed flat beam (θ = 0˚) and twisted beam (θ = 360˚) are sketched in Fig. 6.

For simplicity, the mechanical properties of the beam were assumed to be uniform in the length direction. The length-width ratio of the beam was set to 16. The Reynolds number, Re = ρ0VLμ−1, was used to investigate different flow conditions, where ρ0 is the fluid density, V the far-field flow velocity, L the beam length, and μ the fluid dynamic viscosity. The dimensionless bending

z

yx

z

z

z

yx

(b)

(a)

Fig. 6 (a) Flat and (b) twisting beam models in the velocity fields with the same far-field flow.

Journal of Bionic Engineering (2015) Vol.12 No.4 638

rigidity of the beam was defined as γ = EIρ0−1V−2L−3,

where E is the Young’s modulus of the material and I the minimal principal moment of inertia of the cross-section. The parameters for the fluid dynamics simulation were set as follows: beam length L = 1 m, beam width b = 0.0625 m, beam thickness h = 0.001 m, Poisson’s ratio υ = 0, fluid density ρ0 = 1.29 kg·m−3, wind speed V = 0.141 m·s−1, and fluid dynamic viscosity μ = 1.82×10−3 Pa·s. The dimensionless bending rigidity γ was tuned by varying the Young’s modulus E from 0.33 GPa to 3.3 GPa in the following simulations, corresponding to γ values ranging from 0.067 to 0.67. Note that the fluid dynamic viscosity was set to a value approximately two orders of magnitude higher than that of real air, resulting in the Reynolds number Re = 100, primarily due to numerical accuracy and stability considerations. Be-cause the main wind load on the beam was the pressure force, the effect of fluid viscosity was assumed to be insignificant in this problem.

The computational domain for the fluid flow, normalized by the beam length L, was established within a box with dimensions of −0.5 ≤ x ≤ 0.5, −1 ≤ y ≤ 3, and 0≤ z ≤ 2, where the x, y, and z axes lay along the span-wise, streamwise, and wall-normal directions, respec-tively. Before deformation, the centerline of the beam was aligned along the z axis, its centroid at the bottom wall (z = 0) was located at the origin of the horizontal (x, y) plane, and the width direction was aligned with the x axis. The beam was clamped at the bottom wall. During computation, the fluid domain was discretized uniformly by 64×256×128 grids in the x, y, and z directions, re-spectively, and a 64×4 mesh was used for the beam. The inflow velocity was given by the Blasius solution of the boundary layer flow, with the boundary layer thickness equal to the beam length.

3 Results and discussion

3.1 Chiral morphology

For cattail leaves living in water with fluctuating levels, a vertical configuration with a great height is crucial to guarantee the biological functions of the leaves, e.g., respiration and photosynthesis. However, it is well known that with an increase in height, plant stalks and leaves will have a higher risk of lodging in strong winds. A reduced cross-sectional size leads to a smaller windward area and reduces the risk of lodging. The

heights of the collected cattail leaves were measured to range from 2.15 m to 2.73 m, and the leaves possessed a large slenderness ratio. All cattail leaves used in our experiments were found to be left-handed, which may hold a genetic significance. The intrinsic chiral mor-phologies of the leaves featured a total twist angle of 580˚±110˚ (or 1.6±0.3 turns). In addition, our meas-urements showed that for each leaf, the twisting angle per unit length increased along the height direction.

As shown in Fig. 2, the cross-section of a cattail leaf has a crescent moon-like shape. The inner paren-chyma forms partition structures (i.e., mediastinum) normal to the epidermis, which separate the cavum of the leaf into approximately 11–18 compartments filled with foam tissues. The leaf structure is analogous to the wings of planes. Through the chambers, oxygen is transported from the aerial part to the submerged part, whereas carbon dioxide flows in the inverse direc-tion[35,36]. According to our measurements, both the cross-sectional width and thickness decrease gradually along the growth direction of the plant. The maximal width and maximal thickness of the cross-section of a leaf are in the vicinity of this bottom end. For different leaves, the maximal widths and thicknesses are in the ranges of 14.7 mm – 16.3 mm and 2.5 mm – 4.0 mm, respectively. Because the thickness exhibits a more dis-tinct reduction than the width, the cross-sectional aspect ratio of the leaf increases from the base to the apex. The narrow cross-sectional shape of the emergent leaf causes a considerable anisotropy of the bending stiffness. For an emergent leaf without twisting chirality, the me-chanical responses will be greatly different when the wind blows perpendicular to its wide or narrow faces. The severely anisotropic mechanical properties hinder efficient material utilization. Corresponding to the in-crease in the cross-sectional aspect ratio from the base to the apex, the twist angle per unit length also increases along this direction.

3.2 Multiscale structures

Besides the macroscopic chiral morphologies and cross-sectional geometry of the cattail leaves, we also observed and measured the interior microstructures of the leaves. They have evolved multiscale structures to improve their stability against failure by efficient mate-rial utilization (e.g., high structural rigidity and low density) and by lowering the maximal stress. Fig. 3a

Zhao et al.: Synergistic Effects of Chiral Morphology and Reconfiguration in Cattail Leaves 639

demonstrates that an emergent cattail leaf is comprised of epidermis, diaphragm, mediastinum, non-lignified fiber cables, and foam tissues. The epidermis consists of hollow vascular bundles aligned along the length direc-tion of the leaf. The intine of the vascular bundle is composed of wavy fibers. The emergent leaf is divided into individual air chambers by the mediastinum and diaphragm. The mediastinum, as a tissue that connects the ventral and dorsal leaf surfaces, contains lignified fiber bundles and vascular bundles. The fiber cables, anchored in the diaphragms, traverse the air chambers of the leaf. The long cables are stiff and strong under ten-sion and contribute to a tensegrity structure, which en-sures that no particular structure is overstressed by cre-ating multiple load paths to redistribute stresses[37]. The average Young’s modulus and tensile strength of the fiber cables in different species of Typha are 22.8±7.4 GPa and 0.45±0.17 GPa, respectively[38]. Fig. 3b shows the microstructures of the foam tissues in the porous chambers. The foam tissues form a three-dimensional network and are mainly distributed in regions remote from the epidermis. Fig. 3c shows that the diaphragm, a planar network, is somewhat like a sifter. The diaphragm, composed of two or three layers of thin-walled stellate cells of aerenchyma tissue, can effectively protect the shell-like epidermis and plate-like mediastinum from buckling. ESEM observations indicate that the inner structures exhibit functional gradient distributions along the height direction. The distance between the neighboring diaphragm decreases from 1.6 mm at the base to 0.4 mm near the apex, whereas the distance between the neighboring mediastinum decreases from 1.7 mm to 0.8 mm along this direction. It is also ob-served that foam tissues disappear near the apex of the leaf. The inner structures of the leaves can significantly improve their bending resistance, as demonstrated by mechanical tests in this study. 3.3 Mechanical properties

Three typical stress–strain curves of the hollowed emergent leaves, i.e., epidermis, are plotted in Fig. 4a. The numbers 1–3 are used to designate leaves of dif-ferent lengths (or ages), where 1 and 3 represent the longest and shortest leaves, respectively. The elongation at break of all specimens is approximately 2% on aver-age. The longitudinal elastic modulus of the specimens can be determined from the linear region of the

stress–strain curves, which are plotted as a function of their relative positions in Fig. 4b. The solid lines are linearly fitted by the moduli of the three leaves. The longitudinal elastic moduli of the hollowed specimens vary from 0.5 GPa to 2 GPa. For a specialized relative position, the longer (older) the emergent leaf is, the higher the elastic modulus becomes. The modulus of an emergent leaf significantly decreases along its height direction, mainly because for an individual leaf, more cellulose is contained in the epidermis at the base than that at the apex. The basal portion of a leaf in wind is usually subjected to the maximum bending moments and stresses. Thus, the leaf base is endowed with the highest elastic modulus and strength, as a result of the functional gradients of both chemical compositions and geometric structures. Our three-bending tests demonstrate that the basal portion of an individual leaf has the greatest bending resistance along its height direction.

The load–displacement curves are plotted in Fig. 5, where the solid and dashed lines correspond to the intact and hollowed specimens, respectively. The maximal bearing load of the intact leaves varies from 8.75 N to 12.52 N. The bending resistance of an emergent leaf, characterized by the maximal load, varies distinctly along its longitudinal direction, resulting from the variation in, e.g., the cross-sectional area, cellulose content, water content, and gradient distributions of inner structures. The bending resistance of the intact specimens is significantly higher than that of the hol-lowed ones. Both the parenchyma walls and foam tissues can effectively improve the stability of the plants against bending failure, although the epidermis is the main load-bearing element. 3.4 Fluid dynamics simulation

In nature, emergent leaves generally reconfigure themselves to accommodate heavy wind loads. The chiral morphology of a cattail plant allows for a high structural stiffness, whereas a wind-adaptive reconfigu-ration can reduce externally applied loads. When inves-tigating the synergistic effect of chiral morphology and wind-adapted reconfiguration in cattail leaves, the fluid–structure interaction should be taken into consid-eration. For example, the bending and twisting recon-figuration will reduce the windward area and stream-lining will decrease the drag force due to wind, both of which are beyond the scope of static analysis. Therefore,

Journal of Bionic Engineering (2015) Vol.12 No.4 640

fluid dynamics simulations are performed to elucidate the synergistic effects of the intrinsic and adaptive morphologies of the cattail leaves.

Fig. 6 shows the deflection of the beam in the flow field for twist angles of θ = 0˚ and θ = 360˚, together with streamlines and contours of wall-normal vorticity ωz on two planes located at z = L/2 and z = 3L/4. For the flat beam, i.e., θ = 0˚ (Fig. 6a), the beam is bended toward the streamwise direction, with the upper part subjected to stronger wind forces due to the boundary layer flow distribution, as demonstrated by comparing the vorticity ωz on the two planes. On the other hand, for the case of θ = 360˚ (Fig. 6b), the windward area of the beam is varied along the length direction, altering the wind load on the beam in both the streamwise and spanwise directions. Generally, the deflection of the beam in the streamwise direction is reduced relative to that in the flat case due to both the increase in the bending stiffness of the beam and the decrease in the windward area, whereas the de-flection in the spanwise direction is induced by the twisting chirality.

The deflections of the cross-sectional centroid at the free end of the beam in the spanwise and streamwise directions are normalized by the beam length L and denoted as xU and yU , respectively. By changing the Young’s modulus of the material, the time evolution of xU and yU is plotted in Fig. 7 for several represen-tative dimensionless bending rigidities γ. For both the θ = 0˚ and θ = 360˚ cases, the streamwise deflection yU decreases as the bending rigidity increases, as expected.

The spanwise deflection xU is kept zero for the θ = 0˚ case, whereas it is deviated from zero for the θ = 360˚ case. However, the spanwise deflection xU is small compared with the streamwise deflection yU .

Let sxU and s

yU designate the normalized deflec-tions in the steady state, and let s

xUΔ (or syUΔ ) des-

ignate the difference of sxU (or s

yU ) between the θ = 0˚ and θ = 360˚ cases. The differences in the normalized deflections as a function of the dimensionless bending rigidity γ are shown in Fig. 8a. It is shown that the re-duction in s

yUΔ exceeds 10%, whereas the increase in sxUΔ is less than 5%. Both the streamwise and spanwise

normalized deflections are reduced as the bending ri-gidity increases. As a result, an approximately 8% re-duction in the absolute deflection is observed due to the twisting effect for the different bending rigidities con-sidered in the present simulations.

Moreover, variations in the spanwise and stream-wise normalized deflections s

xU and syU with the twist

angle θ are plotted in Fig. 8b, where the dimensionless bending rigidity γ = 0.1. It is shown that the streamwise deflection s

yU is reduced gradually as the twist angle increases. To compensate for this effect, the spanwise deflection s

xU is induced by twisting, but the magnitude is also reduced as θ increases from 180˚ to 720˚ in the present simulations. Accordingly, the bending resistance to the wind load is enhanced as θ increases, which is reasonable because the windward area is decreased and the asymmetry is reduced for a more twisted beam.

Normalized time t

Nor

mal

ized

def

lect

ions

(b)

0 4 62

0.6

0.4

0.0

−0.2

0.2

˚ γ

0.0670.1

0.33

0.67

0.67

0.067

Normalized time t

0.8

0.6

0.4

0.0

−0.20 4 6

˚ γ0.067

0.10.33

0.67

2

Nor

mal

ized

def

lect

ions

(a)

0.2

Solid: Ux

Dashed: Uy

Solid: Ux

Dashed: Uy

Fig. 7 Time evolution of the normalized deflections of (a) the flat and (b) the pre-twisted beams, where the dimensionless bending rigidity γ = 0.067, 0.1, 0.33, and 0.67.

Zhao et al.: Synergistic Effects of Chiral Morphology and Reconfiguration in Cattail Leaves 641

D

iffer

ence

of d

efle

ctio

ns (%

)

Nor

mal

ized

def

lect

ions

Fig. 8 (a) Difference in normalized deflections between θ = 0˚ and θ = 360˚ for different bending rigidities and (b) the normalized de-flections at the steady state for different twist angles.

5 Conclusion

In this study, we investigated, both experimentally and theoretically, the superior mechanical properties of cattail leaves. The emergent leaves exhibited a high slenderness ratio and a distinct twisting chiral morphology. It was found that the leaves have evolved multiscale structures and superior mechanical properties, both of which feature functionally gradient variations, to improve their resistance to failure. Fluid dynamics simulations demonstrated the synergistic enhancing effects of the intrinsic chiral morphologies and wind-adaptive reconfigurations of cattail leaves on their lodging resistance and survivability under wind loads. This work provides a deeper understanding of some biomechanical strategies adopted by cattail leaves and a biomimetic reference for developing artificial materials. Finally, it is pointed out that the structural hierarchy of cattail leaves has not been taken into account in our theoretical analysis and numerical simulations. Of great interest is to establish a multiscale model to investigate the mechanical behavior of the leaves and the physical mechanisms underlying the formation of the twisting morphology.

Acknowledgment

Financial support from the National Natural Sci-ence Foundation of China (Grant Nos. 11432008, 11322221, and 11372162), the 973 Program of MOST (2012CB934001), and Tsinghua University (20121087991) are acknowledged.

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