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Vein Distribution on the Deformation Behavior and Fracture Mechanisms of Typical Plant Leaves by Quasi In Situ Tensile Test under a Digital Microscope

Vein Distribution on the Deformation Behavior and Fracture Mechanisms of Typical Plant Leaves by... Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 8792143, 12 pages https://doi.org/10.1155/2020/8792143 Research Article Vein Distribution on the Deformation Behavior and Fracture Mechanisms of Typical Plant Leaves by Quasi In Situ Tensile Test under a Digital Microscope 1 1 2 2 1 1 Jingjing Liu, Wei Ye , Zhihui Zhang , Zhenglei Yu, Hongyan Ding, Chao Zhang, and Sen Liu Faculty of Mechanical & Material Engineering, Huaiyin Institute of Technology, Huai’an 223003, China The Key Laboratory of Engineering Bionic (Ministry of Education, China) and the College of Biological and Agricultural Engineering, Jilin University, 5988 Renmin Street, Changchun 130025, China Correspondence should be addressed to Wei Ye; weiye_ciac@126.com and Zhihui Zhang; zhzh@jlu.edu.cn Received 12 December 2019; Revised 7 June 2020; Accepted 12 June 2020; Published 1 July 2020 Academic Editor: Raimondo Penta Copyright © 2020 Jingjing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Angiosperm leaf venation is based on two major patterns, typically dicotyledonous branching and monocotyledonous parallel veins. The influence of these patterns on deformation and fracture properties is poorly understood. In this paper, three species of dicotyledons with netted venation and three species of monocots with parallel venation were selected, and the effect of vein distribution of leaves on their mechanical properties and deformation behavior was investigated. Whole images of leaves were captured using a digital camera, and their vein traits were measured using the image processing software Digimizer. A self- developed mechanical testing apparatus with high precision and low load was used to measure the tensile properties of leaves. The deformation behavior of the leaf was captured using a digital microscope during the tensile test. Results showed that the vein architecture of monocots and dicots is different, which had a remarkable effect on their mechanical properties, deformation behavior, and crack propagation behavior. The greater the diameter and the more the number of veins parallel to the tensile direction, the higher the tensile force, tensile strength, and elastic modulus of the leaves. The netted venation leaves evinced the elastic-plastic fracture type, and the hierarchy venation provided resistance to fracture propagation of cracks in the leaves by lengthening the crack path. The leaves with parallel venation behaved in a predominantly brittle manner or elastic fracture type, and the parallel venation inhibited the initiation of cracks in the leaves by increasing the load at complete fracture of the leaves. The investigation provides reference for a stiffened plate/shell structure and bionic anticrack design. 1. Introduction According to the distribution patterns in the leaves, veins can be divided into three types, dichotomous venation, In nature, plants have different leaf and vein structures which parallel venation, and netted venation. Ginkgo biloba has may be related to competing selection pressures on the leaf distinctive fan-shaped leaves possessing an open dichoto- mous venation pattern that is common among ferns, but less form and function influenced by potential phylogenetic constraints. The form and function of the leaf venation research has been done on dichotomous venation [7]. structure are important for plant photosynthesis and ulti- Monocotyledonous leaves possess parallel or curved veins, mately overall plant performance. Interpreting leaf shape and their main vein and lateral veins of the parallel venation has important implications for paleoecology, paleoclimatol- are arranged in parallel in grass and Canna indica L. The netted venation of dicotyledonous plants is the most complex. ogy, agriculture, urban ecology, and biomimetic optimization design [1–6]. In particular, plant venation presents various In netted venation, the primary vein (1 vein) extends from the patterns and has attracted the attention of many botanists base to the tip of the leaf lamina. The 2 veins are defined as and physicists. those that branched from the 1 veins, distinct in size and 2 Applied Bionics and Biomechanics and propagation of cracks). Balsamo et al. [25] found that pattern from the 3 veins, which form the largest-gauge retic- ulate mesh in the leaf [2]. Global scaling relationships of vena- the tensile fracture planes differed between two species with tion traits with leaf size across dicotyledonous species P. serrulata fracturing along the secondary veins, while H. arbutifolia mainly fractured across the leaf irrespective of indicated that larger leaves had major veins of larger diameter but lower length per leaf area, whereas minor vein traits were the vein or mesophyll position. When leaves of P. serrulata independent of leaf size [8, 9]. and H. arbutifolia were subjected to tensile forces, the Leaf venation plays an important role in transport and stress-strain curve produced was consistently of the elastic- mechanical support. Leaves, which are plate structures stiff- plastic type. In tensile tests of leaves, Meidani et al. [26] also observed that when a crack tip propagated through a leaf and ened by venation, are valuable natural examples of stiffened plate structures and are worth investigating. In order to bet- intersected a strong vein, the crack was deflected along the ter understand the venation characteristics of leaves, the interface. However, few studies have focused on the effect venation morphogenesis mechanism has been widely investi- of vein distribution on leaf mechanical properties, deforma- gated. There are three basic areas to investigate morphoge- tion, and crack propagation behavior. In this paper, the venation morphology and tensile prop- netic mechanisms: auxin canalization [10, 11], mechanical force [12], and fluid transport [13, 14]. The distribution of erties of leaves from six species of plants were studied, and leaf venation follows the physiological principle of minimum the effects of vein distribution on leaf mechanical properties, investment of structure to achieve the requisite function deformation behavior, and crack propagation behavior were while ensuring that the vector sum of all forces is in equilib- also investigated. First, three species of dicotyledons with netted venation and three species of monocots with parallel rium for a self-supporting leaf [12, 13], then a better under- standing of venation helps us to apply biomimetics to solve venation were selected in this study. A digital camera was used similar engineering problems. For example, inspired by to capture whole images of leaves, and their vein traits were growth mechanism of leaf venation, Liu et al. [15] proposed extracted using the image processing software Digimizer. an adaptive morphogenesis algorithm to design stiffened Secondly, according to the distribution and orientation of veins, several typical test locations were taken from each leaf plate/shell structures in a growth manner, and this algorithm produced effective stiffeners along arbitrary directions. for quasi in situ tensile tests, and the deformation behavior Leaves of many species are thin, flat structures, suscepti- of the leaf was captured using a digital microscope during the tensile test. Thirdly, combining the leaf traits and the crack ble to herbivores, wind, and other sources of physical damage [16]. Studies on how leaves achieve their structural integrity propagation behavior through the leaf surface of different leaves, the effect of vein distribution on the deformation under complex natural conditions and the effect of different vein distribution on mechanical properties of leaves have behavior and fracture mechanisms was analyzed and attracted increasing attention. The mechanical properties of compared. This will give insights into designing a stiffened plate/shell structure and bionic anticrack materials. leaves have been revealed using punch, tear, bend, or shear types of techniques showing that highly scleromorphic leaves are an order of magnitude tougher and stronger than soft 2. Materials and Methods leaves [17–19]. Wang et al. [20] investigated the structures and mechanical properties of eight species of plant leaves 2.1. Materials. There is considerable variation in leaf venation using tensile and nanomechanical tests. The results indicated around two major patterns within the angiosperms, including that the ultimate strength of a leaf is related to both the mate- the branching and reticulate dicot pattern and the parallel rial composition and the structure, and the coriaceous leaves monocot pattern. For reticular venation, it includes pinnate usually exhibit higher tensile strength. In a recent study on and palmate. In parallel venation of leaves, the veins are either stiffness of leaf epidermis and mesophyll of 36 angiosperm strictly parallel, curved and approximately parallel, or penni- species, Onoda et al. [21] demonstrated that the stiffness of parallel (pinnate-parallel). A penni-parallel leaf has a central epidermis layers is higher in evergreen species than in decid- midvein with secondary veins that are essentially parallel to uous species and strongly associated with cuticle thickness. one another [27]. For parallel veins (parallelodromous), the Leaf venation geometry and density also influence the parallel 1 veins originate collaterally at the leaf base and mechanical stability and mechanical behavior of a leaf [22]. converge toward the leaf apex. For curved and approximately Greenberg et al. [23] studied the tensile behavior of ryegrass parallel veins (campylodromous), the parallel 1 veins origi- indicating that the tensile properties depend on the location nate collaterally at or near the leaf base and run in strongly where the tensile test was run on the specimen and the strain recurved arches that converge toward the leaf apex [28]. In rate of the tensile test. Whereas some of the grass leaf speci- order to examine characteristics of the dicotyledonous plant mens behaved in a predominantly brittle manner, others leaves and monocotyledonous plant leaves, the morphology evinced a semiductile mode. Lucas et al. [24] investigated and density of leaf veins and the branch angle between leaf the fracture toughness of the Calophyllum inophyllum L. leaf veins were considered in selecting plant species. Three species using cutting and notched tensile tests. The results show that of dicotyledons with netted venation (including Populus alba toughness was found to depend on the presence of veins in Linn. (Salicaceae), Syringa oblata Lindl. (Oleaceae), and the fracture path. Both tensile and cutting tests imply that Ailanthus altissima (Mill.) Swingle (Simaroubaceae)) and the fracture path at right angles to secondary veins was 3.0 three species of monocots with parallel venation (including times more than that parallel to them. To survive, the plant Canna indica Linn. (Cannaceae), Hosta plantaginea (Lam.) must have mechanisms for resisting fracture (the initiation Aschers. (Liliaceae), and Rhapis excelsa (Thunb.) Henry ex Applied Bionics and Biomechanics 3 2 cm from the base of the leaf with the long axis parallel to Rehd. (Palmae)) were collected at random from Jilin Univer- sity in Changchun, China. As shown in Figure 1, P. alba has the midrib. Sample 2 was cut parallel to and 2 cm lateral to palmate netted venation and both S. oblata and A. altissima the midrib. The sample was taken halfway along the leaf. In have pinnate netted venations. C. indica, H. plantaginea, sample 3, the long axis of the sample was perpendicular to and R. excelsa have penni-parallel, campylodromous, and par- the 2 vein so that the tensile force was applied at right angles allelodromous venation, respectively. All sampled leaves were to the vein. The sample was taken halfway along the 2 vein fully developed without any visual damage or senescence. The that diverged from the midrib in the centre of the leaf. Sam- samples were wrapped in inert waterproof plastic film and ple 4 is the intercostal lamina (lamina between secondary ° ° stored at 4 C to avoid loss of turgor pressure before the obser- veins). Sample 4 was cut parallel to the 2 vein and taken half- vation and mechanical measurements. Observations and way along the 2 vein that diverged from the midrib in the measurements were performed within a day of the collection. centre of the leaf. For parallel venation leaves, all samples are taken in the middle of the whole leaf. The diameter of 2.2. Measurement of Leaf Traits. Leaf traits have a major midrib of C. indica is large and cannot be measured under impact on leaf macroscale mechanical behavior. In order to the same test conditions, so the midrib is not considered. In measure leaf size, leaf shape, and major vein traits of leaves, order to get the same direction of the major vein in the tensile whole images of leaves of six plant species were captured samples of three parallel vein plants, the midrib of the H. using a digital camera (Model Nikon D7500, Tokyo, Japan) plantaginea leaf is not considered. The 1 vein or lateral vein and manually analyzed by the image processing software is parallel to the tensile direction in sample 1. The samples 2 Digimizer. Whole leaf images were measured for leaf area; of H. plantaginea and C. indica were cut parallel to and 2 cm maximum leaf length/width as an index of shape; lengths of lateral to the midrib. There is an acute angle between the long ° ° ° 1 ,2 , and 3 veins (or midrib and lateral veins) [9]; and axis of the sample 2 and the major vein, so the tensile force -2 branching angle. The vein density (mm mm ) was expressed was applied at the vein with acute angles. In order to get as the sum of the length of all its segments (mm) per unit area the same direction of the major vein in the sample 2 of three 2 ° (mm ) [2]. Vein lengths of netted venation plants A. altis- parallel vein plants, an angle of approximately 45 was set sima, S. oblata, and P. alba were measured for all 1 veins between the major vein and the tensile direction in sample ° ° and for 2 veins on one-half of the leaf and doubled for the 2of R. excelsa. The 1 vein or lateral vein is perpendicular ° ° total 2 vein length. The density of 3 veins was averaged for to the tensile direction in sample 3. The leaf of R. excelsa is one to three subsampled regions measured centrally in the very narrow, and its tensile samples contain all levels of veins. top, middle, and bottom thirds of the right side of the leaf. Since A. altissima leaves have a thicker 1 vein, the width For parallel venation plants, vein lengths of H. plantaginea of sample 1 was cut to 10 mm to observe the propagation of and R. excelsa were measured for all main veins from the cracks better. It is noted that only one tensile sample was base. Vein lengths of C. indica were measured from midrib excised from each leaf of S. oblata and P. alba. Each sample veins, and the density of lateral veins was averaged for one was excised just before the measurement so that the test to three subsampled regions measured centrally in the top, sample was kept as fresh as possible. The mean values were middle, and bottom thirds of the right side of the leaf. Angles calculated and recorded for three samples for each species. made by the secondary veins to the midvein were measured Vincent [29] suggested that the tensile sample can avoid on the distal side of the junction (the vertex) between the necking if the test piece was eight to ten times longer than secondary vein and the midvein. Following Ellis et al. [28], its width and that the tensile test on a notched specimen each angle was determined as the angle subtended by two can provide both the work to fracture (toughness) and infor- elements or rays. One ray followed the midvein distal to the mation about the ease of propagating a crack through the junction and the other intersected the secondary 25% along material. However, the samples were prepared differently the length of the secondary. The branching angle between from above in this paper. We were interested in the effect ° ° 2 and 3 veins was also measured in the same way. of vein distribution on mechanical properties, deformation behavior, and crack propagation behavior of leaves of three 2.3. Tensile Tests and Deformation Behavior of Leaves. dicot and three monocot plant species. When leaves with different vein distributions were subjected to tensile forces, Tensile tests were performed on the leaf samples using a self-developed mechanical testing apparatus (Model the initiation position and propagation path of cracks are Mtest50, China). The experiments were conducted at a strain important. Because of the irregular nature of the test samples, rate of 3.0 mm/min at room temperature. In the preparation it is not appropriate to use the long size of an effective sample of tensile samples, we were primarily concerned with the (initial distance between clamps). The results of mechanical angle between the direction of the relevant major vein and properties obtained from the leaf will be different because the direction of the tensile force on the sample. Unless indi- the whole edge and the supporting part of the leaf are cated, the width of all samples was 4.5 mm and the length destroyed. Meanwhile, if the material is “notch-sensitive,” was 30 mm. All samples were excised by a pair of parallel the crack will potentially have a dangerous effect on the razor blades. According to the distribution and orientation integrity of the material since a small crack may severely lead of veins, four samples of netted venation leaves and three to the whole material being broken. Therefore, we did not use samples of parallel venation leaves were taken for tensile a notch in the leaf sample as we did not want to control where tests, as shown in Figure 1. For netted venation leaves, sample the first crack appears. Our measurements may have some 1 includes the midrib which was cut distally from a point variation, but we maintain that our test conditions are better 4 Applied Bionics and Biomechanics 2 cm 2 cm 2 cm 3 cm (a) (b) (c) (d) 2 cm 3 cm (e) (f) Figure 1: The morphology, location, and orientation of test pieces of leaves of three dicot and three monocot plant species used for tensile tests: (a) P. alba, (b) S. oblata, (c) A. altissima, (d) H. plantaginea, (e) C. indica, and (f) R. excelsa. for comparing mechanical properties among the different during the tensile test, which was also used to obtain the test pieces. low-power microimage of leaf morphology after the test. In the tensile tests, the samples were clamped by a pair of According to the images of these leaf morphologies, the effect clamps, and the free length between the clamps was about of vein distribution on the deformation behavior and fracture 12 mm. A pair of rubber pads was fixed on the clamps of mechanisms of leaves of six plant species was analyzed. the testing machine in order to prevent the samples from being damaged by the clamps. The thickness and width for 3. Results and Discussion all leaves were measured using a Pro-Max digital caliper (Fowler Instruments, Boston, MA, USA), and then the 3.1. Leaf Traits of Leaves of Six Plant Species. Vein traits of cross-sectional areas of the samples were calculated. The leaves of three dicot and three monocot plant species are force-displacement curves were recorded automatically. The shown in Figure 2, and the structural parameters of the leaf linear portion of the curve, prior to the catastrophic failure morphology and vein traits are listed in Table 1. Compared of the tissue, was used to calculate the maximum slope. The with the three species of dicotyledons with netted venation, tensile strength (σ), elastic modulus (E), and elongation at three species of monocots with parallel venation have higher fracture (ε) are calculated by leaf length-to-width ratio values. Moreover, except for the leaves of C. indica, the thickness of the leaves of the other five species does not differ significantly. Tensile strengthðÞ σ = , The leaves with netted venation have the greatest diver- sity in vein structure but share key architectural elements, ΔF/A that is, a hierarchy of vein orders forming a reticulate mesh. Elastic modulusðÞ E = , ð1Þ Δl/l As shown in Figures 2(a)–2(c), at least five levels of veins with different diameters appear in the venation system of three Δl Elongation at fracture ε = × 100%, ðÞ species of netted venation plants. Midvein spreads from the petiole to the apex and grows with the lamina. The secondary veins start from midvein and run in parallel towards the mar- where F is the maximum load (N), A is the cross-section gin, and higher veins reconnect with the lower ones. In the area of the sample (mm ), l is the original length of the sam- hierarchical leaf vein system of angiosperms, veins of higher ple between the clamps, and Δl is the displacement (mm). branching orders in a given leaf have smaller diameters but A digital microscope (B011, Supereyes, China) was greater branching frequencies and lengths. The densities employed to capture the deformation behavior of the leaf (length/leaf area) of the major veins show declines in larger Applied Bionics and Biomechanics 5 drops are recorded in netted venation plants and the sample leaves. P. alba with palmate netted venation possesses the highest 1 vein densities. The leaf size of A. altissima was 1of H. plantaginea with parallel veins, which correspond to ° ° larger than that of S. oblata. However, the 1 and 2 vein successive fracture behaviors of veins. As shown in densities of A. altissima were smaller than those of S. oblata. Figures 3(a)–3(c), when leaves of P. alba, S. oblata, and A. Noteworthy, the density change of the 3 vein was not altissima with netted venation were stretched from tensile obvious between three species of netted venation plants. forces, the force-displacement curve displays the elastic- Quaternary and quinary veins of netted venation plants cover plastic type [25]. The descending curve is ragged, which most of the leaf area whilst having the smaller diameter. indicates that the veins break sequentially in the leaves as the load increases. It is noted that H. plantaginea possesses Vein branching angles are also diverse across species. In mature leaves, venation patterns are extremely diverse, yet soft leaves and low vein density, and the tensile curves are similar to netted venation leaves. On the contrary, the force- their local structure satisfies a universal property: at junctions between veins, angles and diameters are related by a vectorial displacement curves of C. indica and R. excelsa show no clear equation analogous to a force balance [12]. This vectorial plastic phase before fracture and behave in a predominantly brittle manner [23]. Additionally, the descending curve equation can be expressed in the whole vein system; the angle within each three-way vein junction is proportional to the following catastrophic failure of the leaves remained linear, radii of the connecting veins [1, 30]. For that reason, the vec- indicating that the majority of the veins responsible for tor balance criterion gives proper angles existing in vein the tensile strength were breaking at about the same time. branches in the leaves of same plant species. The branching The toughness is defined as the work to fracture, measured as the area under the force-displacement curve [19]. In angles between secondaries and the major vein of P. alba, S. ° ° ° ° oblata, and A. altissima varies from 41 to 76 ,43 to 65 , Figures 3(a)–3(c), the toughness of sample 1 is higher than ° ° and 53 to 67 , respectively. And their mean angles were that of sample 2, and sample 4 is the lowest in the three species ° ° ° 61 ,53 , and 66 , respectively. Similarly, the mean branching of netted venation leaves. As shown in Figures 3(d)–3(f), the angles between secondaries and the major vein of P. alba, S. similar patterns are also shown in parallel venation leaves. ° ° ° But, the sample 3 of H. plantaginea is tougher than sample 2. oblata, and A. altissima were 76 ,74 , and 86 , respectively. It can be found that the vein branches are usually connected The variations in maximum load, tensile strength, elastic modulus, and elongation at the complete fracture of leaves of by the shortest path. In the larger plant leaves, tertiary veins are parallel to each other and approximately perpendicular three dicot and three monocot plant species in different test to the secondary veins. location of leaves are plotted in Figure 4, where the numbers 1-4 indicate the location on the leaves of the test samples. In leaves with parallel venation, the veins are either strictly parallel, curved and approximately parallel, or There are significant differences among species for each of penni-parallel, as shown in Figures 2(d)–2(f). C. indica has the tensile tests. However, the values of maximum load, dense and thin parallel secondary veins branching off the tensile strength, and elastic modulus of sample 1 of all six midrib. H. plantaginea possesses campylodromous veins, species are the largest. In particular, A. altissima possesses a larger main vein diameter and thinner leaf thickness than and thin transverse veins connect adjacent campylodromous veins. R. excelsa possesses parallel veins and thin transverse P. alba and S. oblata. The tensile strength and elastic modu- veins. Due to the presence of transverse veins, these leaves lus of the main vein sample 1 of A. altissima were 16 and 52 form a gridded system that is similar to that of dicotyledons. times larger than those of samples 2-4, respectively. However, Large and intermediate longitudinal veins are analogous to the maximum load, tensile strength, and elastic modulus of samples 2-4 of A. altissima were the smallest among those major vein orders, and small longitudinal veins and trans- verse veins are analogous to minor veins [31]. The small of the six species of plant leaves. Similarly, the maximum transverse veins in these leaves reinforce against bending load, tensile strength, and elastic modulus of sample 1 of R. forces [1]. Moreover, inherent folding or curling in the R. excels were 6 times larger than those of samples 2 and 3. excelsa leaf can also contribute to the structural stiffness Except for sample 1, samples 2 and 3 of the three species of [22]. The density of midribs or major veins of parallel vena- monocots with parallel venation have higher maximum load, tion leaves also decreases with increasing leaf area. tensile strength, and elastic modulus values when compared Although the leaves of the six species of plants have to samples 2-4 of the three species of dicots with netted vena- different venation systems, the veins show common hierar- tion. It is noted that the differences of maximum load, tensile chy characteristics. Hierarchy and network characteristics of strength, and elastic modulus of samples 2-4 of the same leaves guarantee the global rigidity and local isotropy that are species were not significant. required in the reinforcement layout [32]. In order to further The distribution and orientation of veins have a signifi- study the effect of vein distribution on the mechanical behav- cant influence on the tensile properties of leaves. The venation ior, the tensile properties of different leaf venation systems has better mechanical performance and antistretch ability were studied by in situ tensile tests in the following sections. compared with other tissues [20]. The main veins and parallel lateral veins bear the main load in plant leaves, which can 3.2. Mechanical Properties. The typical force-displacement provide a frame for the lamina to curl, or to allow flexural curves of tensile tests on leaves of three dicot and three bending, so as to reduce transpiration and mechanical load monocot plant species are plotted in Figure 3, where the [1]. The thin veins of leaves make a relatively small contribu- numbers 1-4 are the locations on the leaf of the four test tion to the mechanical properties of leaves. The greater the samples. Beyond the maximum force, several step-like force diameter and the more the number of veins parallel to the 6 Applied Bionics and Biomechanics 4° vein 1° vein 1° vein 5° vein 2° vein 4° vein 5° vein 3° vein 2° vein 3° vein 1 cm 5 mm (a) (b) 1° vein Lateral vein Midrib 2° vein 5° vein 4° vein 3° vein 1 cm 5 mm (c) (d) Parallel main vein Curved vein Parallel minor vein Transverse vein Transverse vein 5 mm 5 mm (e) (f) Figure 2: Vein traits of leaves of three dicot and three monocot plant species: (a) P. alba, (b) S. oblata, (c) A. altissima, (d) C. indica, (e) H. plantaginea, and (f) R. excelsa. Table 1: Leaf morphology and vein traits of six typical plant leaves. Netted venation plant Parallel venation plant P. alba S. oblata A. altissima C. indica H. plantaginea R. excelsa Family Salicaceae Oleaceae Simaroubaceae Cannaceae Liliaceae Palmae Leaf length (cm) 9.21 10.28 23.48 46.39 13.90 28.10 Leaf width (cm) 8.42 7.54 9.55 17.44 7.69 1.69 Leaf length-to-width ratio 1.09 1.36 2.46 2.66 1.81 16.63 Leaf thickness (mm) 0.24 0.21 0.19 0.35 0.22 0.25 Leaf area (cm ) 51.21 49.57 168.95 531.38 75.58 34.99 ° -2 1 vein density (mm mm ) 0.03 0.02 0.01 0.01 0.22 0.38 ° -2 2 vein density (mm mm ) 0.08 0.11 0.09 0.6 —— ° -2 3 vein density (mm mm ) 0.3 0.27 0.29 —— — ° ° ° ° ° ° ° ° ° ° Angle between 1 and 2 veins (α)41 -76 43 -65 53 -75 21 -59 —— ° ° ° ° ° ° ° ° Angle between 2 and 3 veins (β)63 -86 62 -90 65 -90 —— — tensile direction, the larger the tensile force, tensile strength, veins is smaller than that of P. alba, while elongation at and elastic modulus of the leaves. complete fracture of H. plantaginea is larger than that of P. The elongation at complete fracture among the six alba. The results show that the tensile properties of leaves species of plant leaves is significantly different. In addition, are related not only to vein direction but also with the elongation before fracture of C. indica with dense parallel material composition and structure of leaves. R. excelsa Applied Bionics and Biomechanics 7 3.5 5 2.8 2.1 1.4 2 2 0.7 0.0 0.0 0.3 0.6 0.9 1.2 1.5 1.8 0.0 0.5 1.0 1.5 2.0 Displacement (mm) Displacement (mm) (a) (b) 12 0.5 0.4 0.3 0.2 0.1 0.0 4 2 0.0 0.5 1.0 1.5 2.0 Displacement (mm) 3 0 0 0.0 0.4 0.8 1.2 0.0 0.5 1.0 1.5 2.0 Displacement (mm) Displacement (mm) (c) (d) 1 2 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 Displacement (mm) Displacement (mm) (e) (f) Figure 3: Typical load-displacement curves of tensile tests on leaves of three dicot and three monocot plant species: (a) P. alba, (b) S. oblata, (c) A. altissima, (d) C. indica, (e) H. plantaginea, and (f) R. excelsa. leaves are stronger, tougher, and stiffer than other soft leaves, figure shows the initiation of cracks. The third and fourth and elongation at complete fracture of leaves is smaller. In figures show the propagation of cracks. The fifth figure softer leaves, the major veins can improve the tensile strength reflects the final fracture state. The crack propagation of vein direction parallel to the tensile direction of sample 1 is shown and elastic modulus, while ensuring that the leaves have a higher elongation at complete fracture. Based on the above in Figures 5(a-1)–5(a-5). With elongation going on, sample 1 research, the mechanical deformation behaviors of leaves gradually reached the maximum elastic elongation of 7% at need to be discussed. the beginning of 106 s, and cracks occur at a zone of weak- ness at the mesophyll in Figure 5(a-2). Then, the crack continues to propagate in the mesophyll until the crack tip 3.3. Mechanical Deformation Behavior encounters the main vein and the crack stops propagating 3.3.1. Crack Propagation Behavior of Leaves with Netted in Figures 5(a-3) and 5(a-4). Finally, the main veins and Venation. The crack propagation behavior of leaf samples mesophyll snap at the gripping end long after the mesophyll ° ° with different vein patterns and distribution of P. alba in ten- separated. Samples 2 and 3 possess 2 and 3 veins; as elon- gation increases, cracks initiate in the mesophyll. The cracks sile tests is shown in Figure 5. The time marked in Figure 5 represents the time of the whole crack propagation process. deviate frequently, when the crack tip encounters the 2 and The corresponding first figure in (a-1)–(a-5), (b-1)–(b-5), 3 veins in Figures 5(b-3)–5(b-5) and 5(c-3)–5(c-5). The (c-1)–(c-5), and (d-1)–(d-5) is the initial state. The second tensile curve in Figure 3(a) also supports this observation. Force (N) Force (N) Force (N) Force (N) Force (N) Force (N) Force (N) 8 Applied Bionics and Biomechanics Populus Syringa Ailanthus Canna Hosta Rhapis Populus Syringa Ailanthus Canna Hosta Rhapis 1 3 2 4 2 4 (a) (b) 100 5 Populus Syringa Ailanthus Canna Hosta Rhapis Populus Syringa Ailanthus Canna Hosta Rhapis 1 3 1 3 2 4 2 4 (c) (d) Figure 4: Tensile properties of leaves of three dicot and three monocot plant species: (a) maximum load, (b) tensile strength, (c) elastic modulus, and (d) elongation at fracture. The mesophyll or small veins were breaking first, and due to different abilities to resist tensile stress. Cracks are usually the frequent deflection of the cracks, the descending curve produced in the mesophyll and deflected, delayed, or even was ragged. Thin veins play a minor role in preventing the stopped once reaching the main vein or 2 vein. Some of propagation of cracks. As shown in Figures 5(d-3)–5(d-5), the stronger 3 veins can also cause crack deflections, but the cracks in the intercostal leaf sample 4 propagate through most of the thin veins are weak and have no noticeable effect the thin veins until the leaf finally breaks. on crack propagation. In Figure 6, S. oblata and A. altissima exhibit similar crack behaviors. The leaves of S. oblata are softer than P. alba, and 3.3.2. Crack Propagation Behavior of Leaves with Parallel the veins of S. oblata are weak. In addition to sample 1 with Venation. The crack propagation behaviors of leaf samples the main veins, the crack does not deflect obviously in samples with different vein distributions in C. indica are shown in 2-4 of the leaves without the main veins. Because A. altissima Figure 7. The corresponding first figure in (a-1)–(a-4), (b- has a larger main vein diameter and thinner leaf thickness, the 1)–(b-4), and (c-1)–(c-4) is the initial state. The second figure main vein of sample 1 bears the main load, and the sample shows the initiation of cracks, and white arrows show the crack breaks directly at the clamping end. The crack propagation initiation site. The third figure illustrates crack propagation. behaviors of samples 2-4 are similar to S. oblata. The results The fourth figure reflects the final fracture state. The crack show that the 3 veins and thin veins of S. oblata and A. altis- propagation in samples where the vein direction is parallel to sima play a minor role in the propagation of crack process. the tensile direction is shown in Figures 7(a-1)–7(a-4). With The hierarchy and network venation in netted venation elongation, the sample 1 specimen gradually reached its maxi- leaves have a significant effect in the crack propagation mum elastic elongation, 6.34% over the initial length at 98 s, in a process. The leaves with netted venation exhibit ragged main vein as shown in Figure 7(a-2). The cracks propagate breakage patterns indicating that tissues of the leaf have rapidly through the adjacent mesophyll in two directions Force (N) Elastic modulus (MPa) Elongation at break (%) Tensile strength (MPa) Applied Bionics and Biomechanics 9 (a-1) (a-2) (a-3) (a-4) (a-5) t = 0 s; 𝜀 = 0% 2 mm t = 106 s; 𝜀 = 7% t = 123 s; 𝜀 = 8.3% t = 167 s; 𝜀 = 11.4% t = 202 s; 𝜀 = 13.7% (a) (b-4) (b-1) (b-2) (b-3) (b-5) 2 mm t = 0 s; 𝜀 = 0% t = 108 s; 𝜀 = 9% t = 162 s; 𝜀 = 9.6% t = 167 s; 𝜀 = 9.9% t = 173 s; 𝜀 = 10.1% (b) (c-1) (c-2) (c-3) (c-4) (c-5) 2 mm t = 0 s; 𝜀 = 0% t = 102 s; 𝜀 = 6.9% t = 124 s; 𝜀 = 8.6% t = 149 s; 𝜀 = 10.3% t = 256 s; 𝜀 = 12.7% (c) (d-1) (d-2) (d-3) (d-4) (d-5) 2 mm t = 149 s; 𝜀 = 9% t = 112 s; 𝜀 = 7.8% t = 133 s; 𝜀 = 8.8% t = 0 s; 𝜀 = 0% t = 131 s; 𝜀 = 8.3% (d) Figure 5: Fracture growth in ((a-1)–(a-5)) sample 1, ((b-1)–(b-5)) sample 2, ((c-1)–(c-5)) sample 3, and ((d-1)–(d-5)) sample 4 with different vein distributions of P. alba leaves. (a-4) (a-1) (a-2) (a-3) t = 225 s t = 236 s t = 255 s t = 260 s 2 mm 𝜀 = 15.37% 𝜀 = 14.74% 2 mm 𝜀 = 16.51% 2 mm 𝜀 = 16.87% 2 mm (a) (b-1) (b-2) (b-3) (b-4) t = 154 s t = 204 s t = 181 s t = 265 s 2 mm 2 mm 2 mm 2 mm 𝜀 = 6.86% 𝜀 = 12.58% 𝜀 = 10.49% 𝜀 = 13.77% (b) Figure 6: Microscopic images of the fracture on the leaves with different vein distributions: ((a-1)–(a-4)) S. oblata and ((b-1)–(b-4)) A. altissima. (Figure 7(a-3)) with almost instantaneous failure of the adja- be loaded on the leaf to promote crack initiation. Compared cent main veins with only a further 0.12% increase in elonga- with sample 1, the cracks in samples 2 and 3 are produced at tion over 2 s for the complete fracture (Figure 7(a-4)). the interface of the veins and the mesophyll and then propa- During the stretching, the cracks propagate through the gate and break almost instantaneously along the mesophyll parallel veins in sample 1, so a larger tensile load needs to or interface, so the load at the break of samples 2 and 3 is 10 Applied Bionics and Biomechanics (a-4) (a-1) (a-2) (a-3) t = 0 s; 𝜀 = 0% 2 mm t = 98 s; 𝜀 = 6.34% t = 99 s; 𝜀 = 6.43% t = 100 s; 𝜀 = 6.46% (a) (b-1) (b-2) (b-3) (b-4) 2 mm t = 142 s; 𝜀 = 9.52% t = 146 s; 𝜀 = 9.58% t = 147 s; 𝜀 = 9.65% t = 0 s; 𝜀 = 0% (b) (c-1) (c-2) (c-3) (c-4) t = 0 s; 𝜀 = 0% 2 mm t = 165 s; 𝜀 = 9.76% t = 166 s; 𝜀 = 9.84% t = 167 s; 𝜀 = 9.89% (c) Figure 7: Fracture growth in ((a-1)–(a-4)) sample 1, ((b-1)–(b-4)) sample 2, and ((c-1)–(c-4)) sample 3 with different vein distributions of C. indica leaves. The white arrows in (a-2), (b-2), and (c-2) show the crack initiation sites. smaller than that of sample 1. Although the breaks almost Parallel venation has a significant effect on the process of appear instantaneously, we also observed that the fracture crack propagation. Parallel veins increased the force required starts at the interface of one vein but ends at the interface to fracture leaves in tensile tests by spreading the load across of another small longitudinal vein in sample 2. Additionally, many strong veins thereby inhibiting the initiation of cracks. most veins responsible for the tensile strength were breaking However, once a crack has initiated in one vein and it breaks, at about the same time. Fracture may also be dependent on the current load is suddenly spread across the remaining veins, the velocity of elongation not allowing the propagating crack exceeding their individual strength, causing the whole leaf to to be deflected at the interface of the next vein to fracture. fail catastrophically. In the case of leaves with parallel veins, This phenomenon also verifies that the descending curve the mesophyll, weak as it is, may act sufficiently to prevent following catastrophic failure of the leaves remained linear remaining veins from sliding and individually accommodat- in Figure 3(d). Although the maximum loads of samples 2 ing the increased load consequent on failure of one vein, and 3 are reduced by the changes of distribution direction leading to catastrophic failure. Therefore, a material can be of the veins, they increase the elongation at the complete designed to have parallel veins with slightly different strengths, fracture of the sample. rather than the same strength, which may make the material tougher. By adjusting the spacing between parallel veins, the H. plantaginea possesses soft leaves and low vein density (Figures 8(a-1)–8(a-3)), and its crack propagation behaviors fracture of the materials can be controlled more easily. are similar to netted venation leaves. There are a lot of thin The results of vein traits, mechanical tests, and deforma- transverse veins between campylodromous veins in the tion behavior show that the tensile properties, deformation leaves of H. plantaginea, but when tensile load is put on the behavior, and crack propagation behavior of plant leaves are related to the stiffness of the leaves, the degree of develop- leaf, the transverse veins provide little resistance. Therefore, the crack is usually produced in the mesophyll or at the inter- ment of the veins, and the distribution and orientation of the face between the mesophyll and the veins and then rapidly veins in the leaves during tensile tests. The leaves with netted propagates until the leaf fractures. The crack propagation venation evince the elastic-plastic fracture type, and a hierar- behavior of highly scleromorphic R. excelsa leaves is similar chy of different venation networks suppresses the propaga- tion of cracks in the leaves by deflecting, delaying, or even to that of C. indica leaves, as shown in Figures 8(b-1)–8(b- 3). However, the leaf has a greater density of veins, and the stopping the crack in the leaves. Most of the leaves with change of the distribution and orientation of veins has little parallel venation behave in a predominantly brittle manner, effect on the elongation at the complete fracture of the and parallel veins increased the force required to fracture sample. Most of the transverse veins are weak and have no leaves in tensile tests by spreading the load across many strong veins thereby inhibiting the initiation of cracks. noticeable effect on crack propagation. Applied Bionics and Biomechanics 11 (a-1) (a-2) (a-3) t = 195 s t = 151 s t = 160 s 𝜀 = 18.81% 2 mm 𝜀 = 14.11% 2 mm 2 mm 𝜀 = 15.56% (a) (b-1) (b-2) (b-3) t = 63 s t = 77 s t = 59 s 2 mm 2 mm 𝜀 = 5.39% 2 mm 𝜀 = 5.98% 𝜀 = 7.09% (b) Figure 8: Microscopic images of the fracture on the leaf with different vein distributions: ((a-1)–(a-3)) H. plantaginea and ((b-1)–(b-3)) R. excelsa. 4. Conclusions test leaves of six plant species. The effectiveness of resisting crack propagation is related to the stiffness In this study, the vein traits and mechanical properties of six of the leaves, the degree of development of the veins, species of plant leaves with different leaf venation systems and the distribution and orientation of the veins in were investigated. Based on the leaf morphology and vein the leaves during tensile tests. The hierarchy network traits of the leaf, several typical test locations from each leaf venation lengthens the crack path and provides were selected. The tensile properties and the deformation resistance to the fracture propagation. The parallel behavior were studied using quasi in situ tensile testing appa- venation increased the load at complete fracture of ratus under a digital microscope. According to the vein traits, the leaves and inhibits the initiation of cracks mechanical tests, and deformation behavior results, it was (4) Inspired by the branch pattern of the leaf, a material found that the vein distribution of leaves had a remarkable can be designed to have multilevel reticulated veins effect on their mechanical properties, deformation behavior, and/or parallel veins with slightly different strengths, and crack growth. The results can be summarized as follows: which may make the material tougher (1) Leaves have an excellent hierarchy of veins and network characteristics, which supports the stiffness Data Availability of the whole leaf. The density of major veins The data used to support the findings of this study are decreases with increasing leaf area, and the vein included within the article. branches usually take the shortest path to connect. ° ° A branching angle of 41 ~75 was observed between ° ° ° the 1 and 2 veins, and near 90 between higher veins Conflicts of Interest in dicotyledons. Leaf veins of monocotyledons are usually parallel to each other, or there are small trans- The authors declare that there are no competing interests verse veins perpendicular to them regarding the publication of this paper. (2) In situ tensile experiments show that the vein archi- Acknowledgments tecture has a remarkable effect on their mechanical properties. The greater the diameter and the more This work was supported by the National Natural Science the number of veins parallel to the tensile direction, Foundation of China (Nos. 51375006, 51975246, and the higher the tensile force that can be resisted and 51775221), Postdoctoral Science Foundation of China the overall higher tensile strength and elastic modu- (Nos. 801161050414 and 2016M590256), and Technology lus of the leaves. Compared with netted venation Development of Jilin Province (No. 20150520106JH). species, leaves of parallel venation species show com- paratively high tensile stiffness. The leaves with netted venation evince the elastic-plastic fracture References type, and most of the leaves with parallel venation [1] L. Sack and C. 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Vein Distribution on the Deformation Behavior and Fracture Mechanisms of Typical Plant Leaves by Quasi In Situ Tensile Test under a Digital Microscope

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Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 8792143, 12 pages https://doi.org/10.1155/2020/8792143 Research Article Vein Distribution on the Deformation Behavior and Fracture Mechanisms of Typical Plant Leaves by Quasi In Situ Tensile Test under a Digital Microscope 1 1 2 2 1 1 Jingjing Liu, Wei Ye , Zhihui Zhang , Zhenglei Yu, Hongyan Ding, Chao Zhang, and Sen Liu Faculty of Mechanical & Material Engineering, Huaiyin Institute of Technology, Huai’an 223003, China The Key Laboratory of Engineering Bionic (Ministry of Education, China) and the College of Biological and Agricultural Engineering, Jilin University, 5988 Renmin Street, Changchun 130025, China Correspondence should be addressed to Wei Ye; weiye_ciac@126.com and Zhihui Zhang; zhzh@jlu.edu.cn Received 12 December 2019; Revised 7 June 2020; Accepted 12 June 2020; Published 1 July 2020 Academic Editor: Raimondo Penta Copyright © 2020 Jingjing Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Angiosperm leaf venation is based on two major patterns, typically dicotyledonous branching and monocotyledonous parallel veins. The influence of these patterns on deformation and fracture properties is poorly understood. In this paper, three species of dicotyledons with netted venation and three species of monocots with parallel venation were selected, and the effect of vein distribution of leaves on their mechanical properties and deformation behavior was investigated. Whole images of leaves were captured using a digital camera, and their vein traits were measured using the image processing software Digimizer. A self- developed mechanical testing apparatus with high precision and low load was used to measure the tensile properties of leaves. The deformation behavior of the leaf was captured using a digital microscope during the tensile test. Results showed that the vein architecture of monocots and dicots is different, which had a remarkable effect on their mechanical properties, deformation behavior, and crack propagation behavior. The greater the diameter and the more the number of veins parallel to the tensile direction, the higher the tensile force, tensile strength, and elastic modulus of the leaves. The netted venation leaves evinced the elastic-plastic fracture type, and the hierarchy venation provided resistance to fracture propagation of cracks in the leaves by lengthening the crack path. The leaves with parallel venation behaved in a predominantly brittle manner or elastic fracture type, and the parallel venation inhibited the initiation of cracks in the leaves by increasing the load at complete fracture of the leaves. The investigation provides reference for a stiffened plate/shell structure and bionic anticrack design. 1. Introduction According to the distribution patterns in the leaves, veins can be divided into three types, dichotomous venation, In nature, plants have different leaf and vein structures which parallel venation, and netted venation. Ginkgo biloba has may be related to competing selection pressures on the leaf distinctive fan-shaped leaves possessing an open dichoto- mous venation pattern that is common among ferns, but less form and function influenced by potential phylogenetic constraints. The form and function of the leaf venation research has been done on dichotomous venation [7]. structure are important for plant photosynthesis and ulti- Monocotyledonous leaves possess parallel or curved veins, mately overall plant performance. Interpreting leaf shape and their main vein and lateral veins of the parallel venation has important implications for paleoecology, paleoclimatol- are arranged in parallel in grass and Canna indica L. The netted venation of dicotyledonous plants is the most complex. ogy, agriculture, urban ecology, and biomimetic optimization design [1–6]. In particular, plant venation presents various In netted venation, the primary vein (1 vein) extends from the patterns and has attracted the attention of many botanists base to the tip of the leaf lamina. The 2 veins are defined as and physicists. those that branched from the 1 veins, distinct in size and 2 Applied Bionics and Biomechanics and propagation of cracks). Balsamo et al. [25] found that pattern from the 3 veins, which form the largest-gauge retic- ulate mesh in the leaf [2]. Global scaling relationships of vena- the tensile fracture planes differed between two species with tion traits with leaf size across dicotyledonous species P. serrulata fracturing along the secondary veins, while H. arbutifolia mainly fractured across the leaf irrespective of indicated that larger leaves had major veins of larger diameter but lower length per leaf area, whereas minor vein traits were the vein or mesophyll position. When leaves of P. serrulata independent of leaf size [8, 9]. and H. arbutifolia were subjected to tensile forces, the Leaf venation plays an important role in transport and stress-strain curve produced was consistently of the elastic- mechanical support. Leaves, which are plate structures stiff- plastic type. In tensile tests of leaves, Meidani et al. [26] also observed that when a crack tip propagated through a leaf and ened by venation, are valuable natural examples of stiffened plate structures and are worth investigating. In order to bet- intersected a strong vein, the crack was deflected along the ter understand the venation characteristics of leaves, the interface. However, few studies have focused on the effect venation morphogenesis mechanism has been widely investi- of vein distribution on leaf mechanical properties, deforma- gated. There are three basic areas to investigate morphoge- tion, and crack propagation behavior. In this paper, the venation morphology and tensile prop- netic mechanisms: auxin canalization [10, 11], mechanical force [12], and fluid transport [13, 14]. The distribution of erties of leaves from six species of plants were studied, and leaf venation follows the physiological principle of minimum the effects of vein distribution on leaf mechanical properties, investment of structure to achieve the requisite function deformation behavior, and crack propagation behavior were while ensuring that the vector sum of all forces is in equilib- also investigated. First, three species of dicotyledons with netted venation and three species of monocots with parallel rium for a self-supporting leaf [12, 13], then a better under- standing of venation helps us to apply biomimetics to solve venation were selected in this study. A digital camera was used similar engineering problems. For example, inspired by to capture whole images of leaves, and their vein traits were growth mechanism of leaf venation, Liu et al. [15] proposed extracted using the image processing software Digimizer. an adaptive morphogenesis algorithm to design stiffened Secondly, according to the distribution and orientation of veins, several typical test locations were taken from each leaf plate/shell structures in a growth manner, and this algorithm produced effective stiffeners along arbitrary directions. for quasi in situ tensile tests, and the deformation behavior Leaves of many species are thin, flat structures, suscepti- of the leaf was captured using a digital microscope during the tensile test. Thirdly, combining the leaf traits and the crack ble to herbivores, wind, and other sources of physical damage [16]. Studies on how leaves achieve their structural integrity propagation behavior through the leaf surface of different leaves, the effect of vein distribution on the deformation under complex natural conditions and the effect of different vein distribution on mechanical properties of leaves have behavior and fracture mechanisms was analyzed and attracted increasing attention. The mechanical properties of compared. This will give insights into designing a stiffened plate/shell structure and bionic anticrack materials. leaves have been revealed using punch, tear, bend, or shear types of techniques showing that highly scleromorphic leaves are an order of magnitude tougher and stronger than soft 2. Materials and Methods leaves [17–19]. Wang et al. [20] investigated the structures and mechanical properties of eight species of plant leaves 2.1. Materials. There is considerable variation in leaf venation using tensile and nanomechanical tests. The results indicated around two major patterns within the angiosperms, including that the ultimate strength of a leaf is related to both the mate- the branching and reticulate dicot pattern and the parallel rial composition and the structure, and the coriaceous leaves monocot pattern. For reticular venation, it includes pinnate usually exhibit higher tensile strength. In a recent study on and palmate. In parallel venation of leaves, the veins are either stiffness of leaf epidermis and mesophyll of 36 angiosperm strictly parallel, curved and approximately parallel, or penni- species, Onoda et al. [21] demonstrated that the stiffness of parallel (pinnate-parallel). A penni-parallel leaf has a central epidermis layers is higher in evergreen species than in decid- midvein with secondary veins that are essentially parallel to uous species and strongly associated with cuticle thickness. one another [27]. For parallel veins (parallelodromous), the Leaf venation geometry and density also influence the parallel 1 veins originate collaterally at the leaf base and mechanical stability and mechanical behavior of a leaf [22]. converge toward the leaf apex. For curved and approximately Greenberg et al. [23] studied the tensile behavior of ryegrass parallel veins (campylodromous), the parallel 1 veins origi- indicating that the tensile properties depend on the location nate collaterally at or near the leaf base and run in strongly where the tensile test was run on the specimen and the strain recurved arches that converge toward the leaf apex [28]. In rate of the tensile test. Whereas some of the grass leaf speci- order to examine characteristics of the dicotyledonous plant mens behaved in a predominantly brittle manner, others leaves and monocotyledonous plant leaves, the morphology evinced a semiductile mode. Lucas et al. [24] investigated and density of leaf veins and the branch angle between leaf the fracture toughness of the Calophyllum inophyllum L. leaf veins were considered in selecting plant species. Three species using cutting and notched tensile tests. The results show that of dicotyledons with netted venation (including Populus alba toughness was found to depend on the presence of veins in Linn. (Salicaceae), Syringa oblata Lindl. (Oleaceae), and the fracture path. Both tensile and cutting tests imply that Ailanthus altissima (Mill.) Swingle (Simaroubaceae)) and the fracture path at right angles to secondary veins was 3.0 three species of monocots with parallel venation (including times more than that parallel to them. To survive, the plant Canna indica Linn. (Cannaceae), Hosta plantaginea (Lam.) must have mechanisms for resisting fracture (the initiation Aschers. (Liliaceae), and Rhapis excelsa (Thunb.) Henry ex Applied Bionics and Biomechanics 3 2 cm from the base of the leaf with the long axis parallel to Rehd. (Palmae)) were collected at random from Jilin Univer- sity in Changchun, China. As shown in Figure 1, P. alba has the midrib. Sample 2 was cut parallel to and 2 cm lateral to palmate netted venation and both S. oblata and A. altissima the midrib. The sample was taken halfway along the leaf. In have pinnate netted venations. C. indica, H. plantaginea, sample 3, the long axis of the sample was perpendicular to and R. excelsa have penni-parallel, campylodromous, and par- the 2 vein so that the tensile force was applied at right angles allelodromous venation, respectively. All sampled leaves were to the vein. The sample was taken halfway along the 2 vein fully developed without any visual damage or senescence. The that diverged from the midrib in the centre of the leaf. Sam- samples were wrapped in inert waterproof plastic film and ple 4 is the intercostal lamina (lamina between secondary ° ° stored at 4 C to avoid loss of turgor pressure before the obser- veins). Sample 4 was cut parallel to the 2 vein and taken half- vation and mechanical measurements. Observations and way along the 2 vein that diverged from the midrib in the measurements were performed within a day of the collection. centre of the leaf. For parallel venation leaves, all samples are taken in the middle of the whole leaf. The diameter of 2.2. Measurement of Leaf Traits. Leaf traits have a major midrib of C. indica is large and cannot be measured under impact on leaf macroscale mechanical behavior. In order to the same test conditions, so the midrib is not considered. In measure leaf size, leaf shape, and major vein traits of leaves, order to get the same direction of the major vein in the tensile whole images of leaves of six plant species were captured samples of three parallel vein plants, the midrib of the H. using a digital camera (Model Nikon D7500, Tokyo, Japan) plantaginea leaf is not considered. The 1 vein or lateral vein and manually analyzed by the image processing software is parallel to the tensile direction in sample 1. The samples 2 Digimizer. Whole leaf images were measured for leaf area; of H. plantaginea and C. indica were cut parallel to and 2 cm maximum leaf length/width as an index of shape; lengths of lateral to the midrib. There is an acute angle between the long ° ° ° 1 ,2 , and 3 veins (or midrib and lateral veins) [9]; and axis of the sample 2 and the major vein, so the tensile force -2 branching angle. The vein density (mm mm ) was expressed was applied at the vein with acute angles. In order to get as the sum of the length of all its segments (mm) per unit area the same direction of the major vein in the sample 2 of three 2 ° (mm ) [2]. Vein lengths of netted venation plants A. altis- parallel vein plants, an angle of approximately 45 was set sima, S. oblata, and P. alba were measured for all 1 veins between the major vein and the tensile direction in sample ° ° and for 2 veins on one-half of the leaf and doubled for the 2of R. excelsa. The 1 vein or lateral vein is perpendicular ° ° total 2 vein length. The density of 3 veins was averaged for to the tensile direction in sample 3. The leaf of R. excelsa is one to three subsampled regions measured centrally in the very narrow, and its tensile samples contain all levels of veins. top, middle, and bottom thirds of the right side of the leaf. Since A. altissima leaves have a thicker 1 vein, the width For parallel venation plants, vein lengths of H. plantaginea of sample 1 was cut to 10 mm to observe the propagation of and R. excelsa were measured for all main veins from the cracks better. It is noted that only one tensile sample was base. Vein lengths of C. indica were measured from midrib excised from each leaf of S. oblata and P. alba. Each sample veins, and the density of lateral veins was averaged for one was excised just before the measurement so that the test to three subsampled regions measured centrally in the top, sample was kept as fresh as possible. The mean values were middle, and bottom thirds of the right side of the leaf. Angles calculated and recorded for three samples for each species. made by the secondary veins to the midvein were measured Vincent [29] suggested that the tensile sample can avoid on the distal side of the junction (the vertex) between the necking if the test piece was eight to ten times longer than secondary vein and the midvein. Following Ellis et al. [28], its width and that the tensile test on a notched specimen each angle was determined as the angle subtended by two can provide both the work to fracture (toughness) and infor- elements or rays. One ray followed the midvein distal to the mation about the ease of propagating a crack through the junction and the other intersected the secondary 25% along material. However, the samples were prepared differently the length of the secondary. The branching angle between from above in this paper. We were interested in the effect ° ° 2 and 3 veins was also measured in the same way. of vein distribution on mechanical properties, deformation behavior, and crack propagation behavior of leaves of three 2.3. Tensile Tests and Deformation Behavior of Leaves. dicot and three monocot plant species. When leaves with different vein distributions were subjected to tensile forces, Tensile tests were performed on the leaf samples using a self-developed mechanical testing apparatus (Model the initiation position and propagation path of cracks are Mtest50, China). The experiments were conducted at a strain important. Because of the irregular nature of the test samples, rate of 3.0 mm/min at room temperature. In the preparation it is not appropriate to use the long size of an effective sample of tensile samples, we were primarily concerned with the (initial distance between clamps). The results of mechanical angle between the direction of the relevant major vein and properties obtained from the leaf will be different because the direction of the tensile force on the sample. Unless indi- the whole edge and the supporting part of the leaf are cated, the width of all samples was 4.5 mm and the length destroyed. Meanwhile, if the material is “notch-sensitive,” was 30 mm. All samples were excised by a pair of parallel the crack will potentially have a dangerous effect on the razor blades. According to the distribution and orientation integrity of the material since a small crack may severely lead of veins, four samples of netted venation leaves and three to the whole material being broken. Therefore, we did not use samples of parallel venation leaves were taken for tensile a notch in the leaf sample as we did not want to control where tests, as shown in Figure 1. For netted venation leaves, sample the first crack appears. Our measurements may have some 1 includes the midrib which was cut distally from a point variation, but we maintain that our test conditions are better 4 Applied Bionics and Biomechanics 2 cm 2 cm 2 cm 3 cm (a) (b) (c) (d) 2 cm 3 cm (e) (f) Figure 1: The morphology, location, and orientation of test pieces of leaves of three dicot and three monocot plant species used for tensile tests: (a) P. alba, (b) S. oblata, (c) A. altissima, (d) H. plantaginea, (e) C. indica, and (f) R. excelsa. for comparing mechanical properties among the different during the tensile test, which was also used to obtain the test pieces. low-power microimage of leaf morphology after the test. In the tensile tests, the samples were clamped by a pair of According to the images of these leaf morphologies, the effect clamps, and the free length between the clamps was about of vein distribution on the deformation behavior and fracture 12 mm. A pair of rubber pads was fixed on the clamps of mechanisms of leaves of six plant species was analyzed. the testing machine in order to prevent the samples from being damaged by the clamps. The thickness and width for 3. Results and Discussion all leaves were measured using a Pro-Max digital caliper (Fowler Instruments, Boston, MA, USA), and then the 3.1. Leaf Traits of Leaves of Six Plant Species. Vein traits of cross-sectional areas of the samples were calculated. The leaves of three dicot and three monocot plant species are force-displacement curves were recorded automatically. The shown in Figure 2, and the structural parameters of the leaf linear portion of the curve, prior to the catastrophic failure morphology and vein traits are listed in Table 1. Compared of the tissue, was used to calculate the maximum slope. The with the three species of dicotyledons with netted venation, tensile strength (σ), elastic modulus (E), and elongation at three species of monocots with parallel venation have higher fracture (ε) are calculated by leaf length-to-width ratio values. Moreover, except for the leaves of C. indica, the thickness of the leaves of the other five species does not differ significantly. Tensile strengthðÞ σ = , The leaves with netted venation have the greatest diver- sity in vein structure but share key architectural elements, ΔF/A that is, a hierarchy of vein orders forming a reticulate mesh. Elastic modulusðÞ E = , ð1Þ Δl/l As shown in Figures 2(a)–2(c), at least five levels of veins with different diameters appear in the venation system of three Δl Elongation at fracture ε = × 100%, ðÞ species of netted venation plants. Midvein spreads from the petiole to the apex and grows with the lamina. The secondary veins start from midvein and run in parallel towards the mar- where F is the maximum load (N), A is the cross-section gin, and higher veins reconnect with the lower ones. In the area of the sample (mm ), l is the original length of the sam- hierarchical leaf vein system of angiosperms, veins of higher ple between the clamps, and Δl is the displacement (mm). branching orders in a given leaf have smaller diameters but A digital microscope (B011, Supereyes, China) was greater branching frequencies and lengths. The densities employed to capture the deformation behavior of the leaf (length/leaf area) of the major veins show declines in larger Applied Bionics and Biomechanics 5 drops are recorded in netted venation plants and the sample leaves. P. alba with palmate netted venation possesses the highest 1 vein densities. The leaf size of A. altissima was 1of H. plantaginea with parallel veins, which correspond to ° ° larger than that of S. oblata. However, the 1 and 2 vein successive fracture behaviors of veins. As shown in densities of A. altissima were smaller than those of S. oblata. Figures 3(a)–3(c), when leaves of P. alba, S. oblata, and A. Noteworthy, the density change of the 3 vein was not altissima with netted venation were stretched from tensile obvious between three species of netted venation plants. forces, the force-displacement curve displays the elastic- Quaternary and quinary veins of netted venation plants cover plastic type [25]. The descending curve is ragged, which most of the leaf area whilst having the smaller diameter. indicates that the veins break sequentially in the leaves as the load increases. It is noted that H. plantaginea possesses Vein branching angles are also diverse across species. In mature leaves, venation patterns are extremely diverse, yet soft leaves and low vein density, and the tensile curves are similar to netted venation leaves. On the contrary, the force- their local structure satisfies a universal property: at junctions between veins, angles and diameters are related by a vectorial displacement curves of C. indica and R. excelsa show no clear equation analogous to a force balance [12]. This vectorial plastic phase before fracture and behave in a predominantly brittle manner [23]. Additionally, the descending curve equation can be expressed in the whole vein system; the angle within each three-way vein junction is proportional to the following catastrophic failure of the leaves remained linear, radii of the connecting veins [1, 30]. For that reason, the vec- indicating that the majority of the veins responsible for tor balance criterion gives proper angles existing in vein the tensile strength were breaking at about the same time. branches in the leaves of same plant species. The branching The toughness is defined as the work to fracture, measured as the area under the force-displacement curve [19]. In angles between secondaries and the major vein of P. alba, S. ° ° ° ° oblata, and A. altissima varies from 41 to 76 ,43 to 65 , Figures 3(a)–3(c), the toughness of sample 1 is higher than ° ° and 53 to 67 , respectively. And their mean angles were that of sample 2, and sample 4 is the lowest in the three species ° ° ° 61 ,53 , and 66 , respectively. Similarly, the mean branching of netted venation leaves. As shown in Figures 3(d)–3(f), the angles between secondaries and the major vein of P. alba, S. similar patterns are also shown in parallel venation leaves. ° ° ° But, the sample 3 of H. plantaginea is tougher than sample 2. oblata, and A. altissima were 76 ,74 , and 86 , respectively. It can be found that the vein branches are usually connected The variations in maximum load, tensile strength, elastic modulus, and elongation at the complete fracture of leaves of by the shortest path. In the larger plant leaves, tertiary veins are parallel to each other and approximately perpendicular three dicot and three monocot plant species in different test to the secondary veins. location of leaves are plotted in Figure 4, where the numbers 1-4 indicate the location on the leaves of the test samples. In leaves with parallel venation, the veins are either strictly parallel, curved and approximately parallel, or There are significant differences among species for each of penni-parallel, as shown in Figures 2(d)–2(f). C. indica has the tensile tests. However, the values of maximum load, dense and thin parallel secondary veins branching off the tensile strength, and elastic modulus of sample 1 of all six midrib. H. plantaginea possesses campylodromous veins, species are the largest. In particular, A. altissima possesses a larger main vein diameter and thinner leaf thickness than and thin transverse veins connect adjacent campylodromous veins. R. excelsa possesses parallel veins and thin transverse P. alba and S. oblata. The tensile strength and elastic modu- veins. Due to the presence of transverse veins, these leaves lus of the main vein sample 1 of A. altissima were 16 and 52 form a gridded system that is similar to that of dicotyledons. times larger than those of samples 2-4, respectively. However, Large and intermediate longitudinal veins are analogous to the maximum load, tensile strength, and elastic modulus of samples 2-4 of A. altissima were the smallest among those major vein orders, and small longitudinal veins and trans- verse veins are analogous to minor veins [31]. The small of the six species of plant leaves. Similarly, the maximum transverse veins in these leaves reinforce against bending load, tensile strength, and elastic modulus of sample 1 of R. forces [1]. Moreover, inherent folding or curling in the R. excels were 6 times larger than those of samples 2 and 3. excelsa leaf can also contribute to the structural stiffness Except for sample 1, samples 2 and 3 of the three species of [22]. The density of midribs or major veins of parallel vena- monocots with parallel venation have higher maximum load, tion leaves also decreases with increasing leaf area. tensile strength, and elastic modulus values when compared Although the leaves of the six species of plants have to samples 2-4 of the three species of dicots with netted vena- different venation systems, the veins show common hierar- tion. It is noted that the differences of maximum load, tensile chy characteristics. Hierarchy and network characteristics of strength, and elastic modulus of samples 2-4 of the same leaves guarantee the global rigidity and local isotropy that are species were not significant. required in the reinforcement layout [32]. In order to further The distribution and orientation of veins have a signifi- study the effect of vein distribution on the mechanical behav- cant influence on the tensile properties of leaves. The venation ior, the tensile properties of different leaf venation systems has better mechanical performance and antistretch ability were studied by in situ tensile tests in the following sections. compared with other tissues [20]. The main veins and parallel lateral veins bear the main load in plant leaves, which can 3.2. Mechanical Properties. The typical force-displacement provide a frame for the lamina to curl, or to allow flexural curves of tensile tests on leaves of three dicot and three bending, so as to reduce transpiration and mechanical load monocot plant species are plotted in Figure 3, where the [1]. The thin veins of leaves make a relatively small contribu- numbers 1-4 are the locations on the leaf of the four test tion to the mechanical properties of leaves. The greater the samples. Beyond the maximum force, several step-like force diameter and the more the number of veins parallel to the 6 Applied Bionics and Biomechanics 4° vein 1° vein 1° vein 5° vein 2° vein 4° vein 5° vein 3° vein 2° vein 3° vein 1 cm 5 mm (a) (b) 1° vein Lateral vein Midrib 2° vein 5° vein 4° vein 3° vein 1 cm 5 mm (c) (d) Parallel main vein Curved vein Parallel minor vein Transverse vein Transverse vein 5 mm 5 mm (e) (f) Figure 2: Vein traits of leaves of three dicot and three monocot plant species: (a) P. alba, (b) S. oblata, (c) A. altissima, (d) C. indica, (e) H. plantaginea, and (f) R. excelsa. Table 1: Leaf morphology and vein traits of six typical plant leaves. Netted venation plant Parallel venation plant P. alba S. oblata A. altissima C. indica H. plantaginea R. excelsa Family Salicaceae Oleaceae Simaroubaceae Cannaceae Liliaceae Palmae Leaf length (cm) 9.21 10.28 23.48 46.39 13.90 28.10 Leaf width (cm) 8.42 7.54 9.55 17.44 7.69 1.69 Leaf length-to-width ratio 1.09 1.36 2.46 2.66 1.81 16.63 Leaf thickness (mm) 0.24 0.21 0.19 0.35 0.22 0.25 Leaf area (cm ) 51.21 49.57 168.95 531.38 75.58 34.99 ° -2 1 vein density (mm mm ) 0.03 0.02 0.01 0.01 0.22 0.38 ° -2 2 vein density (mm mm ) 0.08 0.11 0.09 0.6 —— ° -2 3 vein density (mm mm ) 0.3 0.27 0.29 —— — ° ° ° ° ° ° ° ° ° ° Angle between 1 and 2 veins (α)41 -76 43 -65 53 -75 21 -59 —— ° ° ° ° ° ° ° ° Angle between 2 and 3 veins (β)63 -86 62 -90 65 -90 —— — tensile direction, the larger the tensile force, tensile strength, veins is smaller than that of P. alba, while elongation at and elastic modulus of the leaves. complete fracture of H. plantaginea is larger than that of P. The elongation at complete fracture among the six alba. The results show that the tensile properties of leaves species of plant leaves is significantly different. In addition, are related not only to vein direction but also with the elongation before fracture of C. indica with dense parallel material composition and structure of leaves. R. excelsa Applied Bionics and Biomechanics 7 3.5 5 2.8 2.1 1.4 2 2 0.7 0.0 0.0 0.3 0.6 0.9 1.2 1.5 1.8 0.0 0.5 1.0 1.5 2.0 Displacement (mm) Displacement (mm) (a) (b) 12 0.5 0.4 0.3 0.2 0.1 0.0 4 2 0.0 0.5 1.0 1.5 2.0 Displacement (mm) 3 0 0 0.0 0.4 0.8 1.2 0.0 0.5 1.0 1.5 2.0 Displacement (mm) Displacement (mm) (c) (d) 1 2 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2 0.4 0.6 0.8 1.0 Displacement (mm) Displacement (mm) (e) (f) Figure 3: Typical load-displacement curves of tensile tests on leaves of three dicot and three monocot plant species: (a) P. alba, (b) S. oblata, (c) A. altissima, (d) C. indica, (e) H. plantaginea, and (f) R. excelsa. leaves are stronger, tougher, and stiffer than other soft leaves, figure shows the initiation of cracks. The third and fourth and elongation at complete fracture of leaves is smaller. In figures show the propagation of cracks. The fifth figure softer leaves, the major veins can improve the tensile strength reflects the final fracture state. The crack propagation of vein direction parallel to the tensile direction of sample 1 is shown and elastic modulus, while ensuring that the leaves have a higher elongation at complete fracture. Based on the above in Figures 5(a-1)–5(a-5). With elongation going on, sample 1 research, the mechanical deformation behaviors of leaves gradually reached the maximum elastic elongation of 7% at need to be discussed. the beginning of 106 s, and cracks occur at a zone of weak- ness at the mesophyll in Figure 5(a-2). Then, the crack continues to propagate in the mesophyll until the crack tip 3.3. Mechanical Deformation Behavior encounters the main vein and the crack stops propagating 3.3.1. Crack Propagation Behavior of Leaves with Netted in Figures 5(a-3) and 5(a-4). Finally, the main veins and Venation. The crack propagation behavior of leaf samples mesophyll snap at the gripping end long after the mesophyll ° ° with different vein patterns and distribution of P. alba in ten- separated. Samples 2 and 3 possess 2 and 3 veins; as elon- gation increases, cracks initiate in the mesophyll. The cracks sile tests is shown in Figure 5. The time marked in Figure 5 represents the time of the whole crack propagation process. deviate frequently, when the crack tip encounters the 2 and The corresponding first figure in (a-1)–(a-5), (b-1)–(b-5), 3 veins in Figures 5(b-3)–5(b-5) and 5(c-3)–5(c-5). The (c-1)–(c-5), and (d-1)–(d-5) is the initial state. The second tensile curve in Figure 3(a) also supports this observation. Force (N) Force (N) Force (N) Force (N) Force (N) Force (N) Force (N) 8 Applied Bionics and Biomechanics Populus Syringa Ailanthus Canna Hosta Rhapis Populus Syringa Ailanthus Canna Hosta Rhapis 1 3 2 4 2 4 (a) (b) 100 5 Populus Syringa Ailanthus Canna Hosta Rhapis Populus Syringa Ailanthus Canna Hosta Rhapis 1 3 1 3 2 4 2 4 (c) (d) Figure 4: Tensile properties of leaves of three dicot and three monocot plant species: (a) maximum load, (b) tensile strength, (c) elastic modulus, and (d) elongation at fracture. The mesophyll or small veins were breaking first, and due to different abilities to resist tensile stress. Cracks are usually the frequent deflection of the cracks, the descending curve produced in the mesophyll and deflected, delayed, or even was ragged. Thin veins play a minor role in preventing the stopped once reaching the main vein or 2 vein. Some of propagation of cracks. As shown in Figures 5(d-3)–5(d-5), the stronger 3 veins can also cause crack deflections, but the cracks in the intercostal leaf sample 4 propagate through most of the thin veins are weak and have no noticeable effect the thin veins until the leaf finally breaks. on crack propagation. In Figure 6, S. oblata and A. altissima exhibit similar crack behaviors. The leaves of S. oblata are softer than P. alba, and 3.3.2. Crack Propagation Behavior of Leaves with Parallel the veins of S. oblata are weak. In addition to sample 1 with Venation. The crack propagation behaviors of leaf samples the main veins, the crack does not deflect obviously in samples with different vein distributions in C. indica are shown in 2-4 of the leaves without the main veins. Because A. altissima Figure 7. The corresponding first figure in (a-1)–(a-4), (b- has a larger main vein diameter and thinner leaf thickness, the 1)–(b-4), and (c-1)–(c-4) is the initial state. The second figure main vein of sample 1 bears the main load, and the sample shows the initiation of cracks, and white arrows show the crack breaks directly at the clamping end. The crack propagation initiation site. The third figure illustrates crack propagation. behaviors of samples 2-4 are similar to S. oblata. The results The fourth figure reflects the final fracture state. The crack show that the 3 veins and thin veins of S. oblata and A. altis- propagation in samples where the vein direction is parallel to sima play a minor role in the propagation of crack process. the tensile direction is shown in Figures 7(a-1)–7(a-4). With The hierarchy and network venation in netted venation elongation, the sample 1 specimen gradually reached its maxi- leaves have a significant effect in the crack propagation mum elastic elongation, 6.34% over the initial length at 98 s, in a process. The leaves with netted venation exhibit ragged main vein as shown in Figure 7(a-2). The cracks propagate breakage patterns indicating that tissues of the leaf have rapidly through the adjacent mesophyll in two directions Force (N) Elastic modulus (MPa) Elongation at break (%) Tensile strength (MPa) Applied Bionics and Biomechanics 9 (a-1) (a-2) (a-3) (a-4) (a-5) t = 0 s; 𝜀 = 0% 2 mm t = 106 s; 𝜀 = 7% t = 123 s; 𝜀 = 8.3% t = 167 s; 𝜀 = 11.4% t = 202 s; 𝜀 = 13.7% (a) (b-4) (b-1) (b-2) (b-3) (b-5) 2 mm t = 0 s; 𝜀 = 0% t = 108 s; 𝜀 = 9% t = 162 s; 𝜀 = 9.6% t = 167 s; 𝜀 = 9.9% t = 173 s; 𝜀 = 10.1% (b) (c-1) (c-2) (c-3) (c-4) (c-5) 2 mm t = 0 s; 𝜀 = 0% t = 102 s; 𝜀 = 6.9% t = 124 s; 𝜀 = 8.6% t = 149 s; 𝜀 = 10.3% t = 256 s; 𝜀 = 12.7% (c) (d-1) (d-2) (d-3) (d-4) (d-5) 2 mm t = 149 s; 𝜀 = 9% t = 112 s; 𝜀 = 7.8% t = 133 s; 𝜀 = 8.8% t = 0 s; 𝜀 = 0% t = 131 s; 𝜀 = 8.3% (d) Figure 5: Fracture growth in ((a-1)–(a-5)) sample 1, ((b-1)–(b-5)) sample 2, ((c-1)–(c-5)) sample 3, and ((d-1)–(d-5)) sample 4 with different vein distributions of P. alba leaves. (a-4) (a-1) (a-2) (a-3) t = 225 s t = 236 s t = 255 s t = 260 s 2 mm 𝜀 = 15.37% 𝜀 = 14.74% 2 mm 𝜀 = 16.51% 2 mm 𝜀 = 16.87% 2 mm (a) (b-1) (b-2) (b-3) (b-4) t = 154 s t = 204 s t = 181 s t = 265 s 2 mm 2 mm 2 mm 2 mm 𝜀 = 6.86% 𝜀 = 12.58% 𝜀 = 10.49% 𝜀 = 13.77% (b) Figure 6: Microscopic images of the fracture on the leaves with different vein distributions: ((a-1)–(a-4)) S. oblata and ((b-1)–(b-4)) A. altissima. (Figure 7(a-3)) with almost instantaneous failure of the adja- be loaded on the leaf to promote crack initiation. Compared cent main veins with only a further 0.12% increase in elonga- with sample 1, the cracks in samples 2 and 3 are produced at tion over 2 s for the complete fracture (Figure 7(a-4)). the interface of the veins and the mesophyll and then propa- During the stretching, the cracks propagate through the gate and break almost instantaneously along the mesophyll parallel veins in sample 1, so a larger tensile load needs to or interface, so the load at the break of samples 2 and 3 is 10 Applied Bionics and Biomechanics (a-4) (a-1) (a-2) (a-3) t = 0 s; 𝜀 = 0% 2 mm t = 98 s; 𝜀 = 6.34% t = 99 s; 𝜀 = 6.43% t = 100 s; 𝜀 = 6.46% (a) (b-1) (b-2) (b-3) (b-4) 2 mm t = 142 s; 𝜀 = 9.52% t = 146 s; 𝜀 = 9.58% t = 147 s; 𝜀 = 9.65% t = 0 s; 𝜀 = 0% (b) (c-1) (c-2) (c-3) (c-4) t = 0 s; 𝜀 = 0% 2 mm t = 165 s; 𝜀 = 9.76% t = 166 s; 𝜀 = 9.84% t = 167 s; 𝜀 = 9.89% (c) Figure 7: Fracture growth in ((a-1)–(a-4)) sample 1, ((b-1)–(b-4)) sample 2, and ((c-1)–(c-4)) sample 3 with different vein distributions of C. indica leaves. The white arrows in (a-2), (b-2), and (c-2) show the crack initiation sites. smaller than that of sample 1. Although the breaks almost Parallel venation has a significant effect on the process of appear instantaneously, we also observed that the fracture crack propagation. Parallel veins increased the force required starts at the interface of one vein but ends at the interface to fracture leaves in tensile tests by spreading the load across of another small longitudinal vein in sample 2. Additionally, many strong veins thereby inhibiting the initiation of cracks. most veins responsible for the tensile strength were breaking However, once a crack has initiated in one vein and it breaks, at about the same time. Fracture may also be dependent on the current load is suddenly spread across the remaining veins, the velocity of elongation not allowing the propagating crack exceeding their individual strength, causing the whole leaf to to be deflected at the interface of the next vein to fracture. fail catastrophically. In the case of leaves with parallel veins, This phenomenon also verifies that the descending curve the mesophyll, weak as it is, may act sufficiently to prevent following catastrophic failure of the leaves remained linear remaining veins from sliding and individually accommodat- in Figure 3(d). Although the maximum loads of samples 2 ing the increased load consequent on failure of one vein, and 3 are reduced by the changes of distribution direction leading to catastrophic failure. Therefore, a material can be of the veins, they increase the elongation at the complete designed to have parallel veins with slightly different strengths, fracture of the sample. rather than the same strength, which may make the material tougher. By adjusting the spacing between parallel veins, the H. plantaginea possesses soft leaves and low vein density (Figures 8(a-1)–8(a-3)), and its crack propagation behaviors fracture of the materials can be controlled more easily. are similar to netted venation leaves. There are a lot of thin The results of vein traits, mechanical tests, and deforma- transverse veins between campylodromous veins in the tion behavior show that the tensile properties, deformation leaves of H. plantaginea, but when tensile load is put on the behavior, and crack propagation behavior of plant leaves are related to the stiffness of the leaves, the degree of develop- leaf, the transverse veins provide little resistance. Therefore, the crack is usually produced in the mesophyll or at the inter- ment of the veins, and the distribution and orientation of the face between the mesophyll and the veins and then rapidly veins in the leaves during tensile tests. The leaves with netted propagates until the leaf fractures. The crack propagation venation evince the elastic-plastic fracture type, and a hierar- behavior of highly scleromorphic R. excelsa leaves is similar chy of different venation networks suppresses the propaga- tion of cracks in the leaves by deflecting, delaying, or even to that of C. indica leaves, as shown in Figures 8(b-1)–8(b- 3). However, the leaf has a greater density of veins, and the stopping the crack in the leaves. Most of the leaves with change of the distribution and orientation of veins has little parallel venation behave in a predominantly brittle manner, effect on the elongation at the complete fracture of the and parallel veins increased the force required to fracture sample. Most of the transverse veins are weak and have no leaves in tensile tests by spreading the load across many strong veins thereby inhibiting the initiation of cracks. noticeable effect on crack propagation. Applied Bionics and Biomechanics 11 (a-1) (a-2) (a-3) t = 195 s t = 151 s t = 160 s 𝜀 = 18.81% 2 mm 𝜀 = 14.11% 2 mm 2 mm 𝜀 = 15.56% (a) (b-1) (b-2) (b-3) t = 63 s t = 77 s t = 59 s 2 mm 2 mm 𝜀 = 5.39% 2 mm 𝜀 = 5.98% 𝜀 = 7.09% (b) Figure 8: Microscopic images of the fracture on the leaf with different vein distributions: ((a-1)–(a-3)) H. plantaginea and ((b-1)–(b-3)) R. excelsa. 4. Conclusions test leaves of six plant species. The effectiveness of resisting crack propagation is related to the stiffness In this study, the vein traits and mechanical properties of six of the leaves, the degree of development of the veins, species of plant leaves with different leaf venation systems and the distribution and orientation of the veins in were investigated. Based on the leaf morphology and vein the leaves during tensile tests. The hierarchy network traits of the leaf, several typical test locations from each leaf venation lengthens the crack path and provides were selected. The tensile properties and the deformation resistance to the fracture propagation. The parallel behavior were studied using quasi in situ tensile testing appa- venation increased the load at complete fracture of ratus under a digital microscope. According to the vein traits, the leaves and inhibits the initiation of cracks mechanical tests, and deformation behavior results, it was (4) Inspired by the branch pattern of the leaf, a material found that the vein distribution of leaves had a remarkable can be designed to have multilevel reticulated veins effect on their mechanical properties, deformation behavior, and/or parallel veins with slightly different strengths, and crack growth. The results can be summarized as follows: which may make the material tougher (1) Leaves have an excellent hierarchy of veins and network characteristics, which supports the stiffness Data Availability of the whole leaf. The density of major veins The data used to support the findings of this study are decreases with increasing leaf area, and the vein included within the article. branches usually take the shortest path to connect. ° ° A branching angle of 41 ~75 was observed between ° ° ° the 1 and 2 veins, and near 90 between higher veins Conflicts of Interest in dicotyledons. Leaf veins of monocotyledons are usually parallel to each other, or there are small trans- The authors declare that there are no competing interests verse veins perpendicular to them regarding the publication of this paper. (2) In situ tensile experiments show that the vein archi- Acknowledgments tecture has a remarkable effect on their mechanical properties. 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Applied Bionics and BiomechanicsHindawi Publishing Corporation

Published: Jul 1, 2020

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