Research ArticleBionic Design of the Bumper Beam Inspired by the Bending andEnergy Absorption Characteristics of Bamboo

Meng Zou ,1 Jiafeng Song ,1 Shucai Xu,2 Shengfu Liu,1 and Zhiyong Chang 1

1Key Laboratory for Bionics Engineering of Education Ministry, Changchun 130022, China2State Key Lab of Automotive Safety and Energy, Beijing 100084, China

Correspondence should be addressed to Zhiyong Chang; zychang@jlu.edu.cn

Received 2 July 2018; Accepted 16 September 2018; Published 2 December 2018

Academic Editor: Jose Merodio

Copyright © 2018 Meng Zou et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work isproperly cited.

This study conducted quasistatic three-point bending tests to investigate the effect of bamboo node on the energyabsorption, bending, and deformation characteristics of bamboo. Results showed that the node had a reinforcing effecton the energy absorption and bending strength of the bamboo culm subjected to bending load. The experimental resultsdemonstrated that nodal samples (NS) significantly outperform internodal samples without node (INS). Under the three-point bending load, the main failure mode of bamboo is the fracture failure. The node also showed split and fractureprevention function obviously. Based on that, a series of bionic bumper beams were designed inspired by the bamboonode. The FEM results indicated that the performance of bionic bumpers was better than that of a normal bumper withregard to bending strength, energy absorption, and being lightweight. In particular, the bionic bumper beam has the bestperformance with regard to bending, energy absorption, and being lightweight compared with the normal bumper underpole impact. The characteristic of the bionic bumper beam is higher than that of the normal bumper beam by 12.3%for bending strength, 36.9% for EA, and 31.4% for SEA; moreover, there was a mass reduction of 4.9%, which stillneeds further optimization.

1. Introduction

Structures in nature have evolved to fit their environmentafter millions of years of evolution. Bamboo is a kind ofbiological structure reinforced by nodes [1]. In terms ofmorphology and mechanics, bamboo has the flexibility toadapt to bending damage caused by natural forces andexternal load, such as wind, snow, and rain. The hollowstructure and nodes play an important role in allowingthe plant to achieve optimal stiffness and stability withthe least material [2]. Moreover, the bamboo node iscrucial to improve stiffness and stability of the slenderbamboo culm during growth [3].

Previous researchers have discussed that these nodeshave a mechanical function, improving the stiffness andstrength of the culm. For example, Shao et al. [4–6] proposedthat bamboo nodes were crucial to improve stiffness and

stability of the slender bamboo culm during growth. Baratiand Alizadeh [7] claimed that nodes support the culm to pre-vent failure due to local buckling. Meng et al. [8] studied theenergy absorption characteristics and material parameters ofthe bamboo species by drop-weight and dynamic tensiletests. The results show that the energy absorption of nodalsamples is greater than that of the internode samples.

For applications that require large energy absorption andbending strength, bumper beams are one of the key struc-tures in passenger cars, which should be carefully designedand manufactured in order to achieve good impact behavior.Nowadays, some road components like roadside safety struc-tures and vehicle safety components have been widely used[9–11], where these structures are submitted to impact load-ing conditions, such as the bumper and crush box. As for thebumper, there has been much research. Hosseinzadeh et al.[12] studied a commercial front bumper beam made of glass

HindawiApplied Bionics and BiomechanicsVolume 2018, Article ID 8062321, 12 pageshttps://doi.org/10.1155/2018/8062321

mat thermoplastic (GMT) by impact modeling using LS-DYNA, and the result shows that this kind of bumper hasthe advantages of being lightweight, ease of manufacturing,and reduction of production cost. Belingardi et al. [13] com-pare the E-Glass/epoxy pultruded bumper beam with steeland E-Glass/epoxy fabric composite beam. And the resultshows that the pultruded bumper beam has comparableenergy absorption capability with respect to the steel normalproduction solution.

The design of a crashworthy bumper beam underimpact load is a very challenging job because it involvesgeometric nonlinear, elastic-plastic deformation and non-linear contact deformation. Creatures in nature haveexperienced a long process of evolution to adapt to theenvironment, so they tend to have a better design thatallows them to adapt to a variety of conditions: their struc-ture often has superior mechanical and multifunctionalproperties. Bionics of biotical creativity engineering is theapplication of biological methods, which is aimed at thestudy and design of engineering applications; it has beensuccessfully applied in material and structure design [14].Yu et al. [15, 16] investigated the structure and mechanicalcharacteristics of cattle horns, then proposed that thestructure feature can also be used in the crashworthinessfield. Zhao et al. [17] investigated the giant water lily leafribs and cactus stem for their optimal framework andsuperior performance. Then they extracted their structuralcharacteristics and used them in the bioinspired design ofthe Lin MC6000 gantry machining center crossbeam,which has better load-carrying capacity than conventionaldistribution. As for bamboo, Ma et al. [18] designed abionic cylindrical structure to mimic the gradient distribu-tion of vascular bundles and parenchyma cells. Afterfinite-element analysis, the results show that the load-bearing capacity of a bionic shell increased by 124.8%.Inspired by the way in which the bamboo nodes andnodal diaphragms enhance the transverse strength ofbamboo, Liu et al. [19] designed the nonconvex multicor-ner thin-walled column by adding bulkheads in the column,and it was found that the bioinspired structure outperformedthe conventional structure.

In this paper, bamboo samples with node and withoutnode were studied to determine the influence of the nodeon the bending strength and energy absorption of bam-boo. Meanwhile, the structure of bamboo nodes was inves-tigated to study the influence of vascular bundles at thenodes on mechanical properties of the culm. Inspired bythe structure of bamboo nodes and nodal diaphragms, anew excellent bumper beam named as the bionic bumperbeam is proposed in this article, which is a high-strength,lightweight bumper beam.

2. Materials and Experiment

2.1. Materials. Bamboo (Phyllostachys pubescens) sampleswere collected from Jiangxi Province, near the middle YuanRiver, which has subtropical monsoon humid weather. Thebamboo was cut into three parts (upper, middle, and lower).When preparing samples with nodes, the nodes were

positioned at the center of the samples. Samples with andwithout nodes were taken from neighboring sections of thesame culm, thus giving an almost uniform thickness ofsamples, as shown in Figure 1(a). These samples weredivided into internodal samples without node (named INS)and nodal samples (named NS), as shown in Figures 1(b)and 1(c). The bamboo samples were 3 years old and closeto a complete plant with a culm of 20–70mm in diameter.The wall thickness of the bamboo is about 7–30mm. Thebamboo samples were numbered and sealed before beingcarried back, then the bamboo samples were processed underthe test requirements.

The dimension and number of bamboo samples areshown in Figure 1(d) and Table 1. Fifteen different sampleslocated at different parts of the bamboo culm and with adifferent number of nodes were investigated. The sampleswere named by letters and numbers. The first letter “U”stands for the upper part of the bamboo, “M” for the middlepart of the bamboo, and “D” for the lower part of the bam-boo; the last number stands for the number of bamboo nodes.

2.2. Experimental Procedure. The bamboo stem’s diametertapers from basal to top [20, 21]. Its top has a smallerdiameter than the basal. In this paper, its cross sectionwas assumed as a hollow cylinder according to the ISO22157-1:2004 [22, 23]. In this experiment, quasistaticthree-point bending tests were performed with the Elec-tronic Universal Testing Machine in Jilin University, modelCSS-44100 with the load capacity of 20 kN and an internaldisplacement transducer.

Figure 2 shows a schematic view of the three-point bend-ing test setup. The three-point bending test rig consists of twofixed supports and an indenter made of solid aluminum. Theupper indenter was mounted to the actuator of the testingframe. The samples were placed centrally between the twofixed lower supports. A camera was mounted on the groundto obtain footage on the damage mode of samples duringbending. The bamboo samples were fixed on two pivots,and the indenter compressed down with a constant bendingspeed of 5mm/min. Each sample was loaded to failure, andthe bending force was recorded during the bending collapse,together with the cylinder’s displacement continuously,giving a force-deflection curve of the bending process.

(a)

(d) (b) (c)

Bamboo culm

D1 M1 U1

Dav

Ltotal

L1 L2 L3 L4 L5

Figure 1: (a) Sample position; (b) internodal sample without node(INS); (c) nodal sample (NS); (d) dimension of nodal samples.

2 Applied Bionics and Biomechanics

In this paper, the bending strength (BS), radial energyabsorption (EA), and radial specific energy absorption(SEA) were applied to evaluate the characteristic of the bam-boo samples. The bending strength can be described by

BS = σb =3Pmaxl

2bh2, 1

where σb is the bending strength with a unit of MPa, Pmax isthe maximum broken force with the unit of N, l is the spandistance between the two supports with the unit of mm, his the sample width with the unit of mm, and h is the sampleheight with the unit of mm.

The expression of SEA [24] is shown by

SEA = EAm

, 2

where m is the mass of the destroyed sample and EA [25] isthe total energy absorbed by the sample, which can beobtained from

EA =s

0F s ds, 3

where F(s) is the instantaneous reacting force during bendingand s is the bending displacement.

3. Mechanical Properties of Bamboo underThree-Point Bending Test

3.1. Structure Analysis. The changing rules of internodal dis-tance and diameter along the growth direction of bamboo areshown in Figure 3, which illustrates that bamboo nodesappear at a changing interval along the stem.

According to the internodal distance along the growthdirection of bamboo, the internodal distance shows a normaldistribution. After nonlinear fitting regression, these data canbe described by (4), which illustrates that the number ofnodes at both ends is larger than that in the middle part ofthe bamboo.

For the bamboo’s diameter, as shown in Figure 3, thediameter decreased linearly approximately along the direc-tion of the growth, and it can also describe the mathematicalmodel (5) by data fitting. All those facts demonstrate thatbamboo is a changeable cone-shaped tubular structure.

y1 = −2836 + 3146∗e−2∗ x−23 6 /115 4 2 , 4

y2 = 91 − 1 62∗x, 5

where x is the number of bamboo nodes, y1 is the internodaldistance, and y2 is the diameter of the bamboo.

3.2. Three-Point Bending Tests. For the samples with an oddnumber of nodes, the indenter pressed on the node, and theindenter pressed in the middle of two nodes for the sampleswith an even number of nodes. The inner span was adjustedso as to always have at least two nodes in the central portionof the sample.

Figure 4 shows the failure mode of bamboo samplesunder the load of bending. When the bamboo was loaded

Table 1: Structure parameters of bamboo samples (unit: mm).

Sample Ltotal m (g) Dav Tav L1 L2 L3 L4 L5 Moisture content (%)

U0 250 124.61 41.91 4.65 250 20.81

U1 250 158.89 48.68 5.06 125 125 22.76

U2 735 442.46 44.41 5.27 145 440 150 16.18

U3 949 661.22 48.15 5.4 150 320 329 150 15.91

U4 1580 977.1 40.47 4.78 150 420 430 430 150 18.28

M0 247 247.17 58.54 5.65 247 25

M1 250 281.85 63.04 5.96 125 125 29.87

M2 658 787.37 63.4 6.61 145 363 150 31.47

M3 862 1088 65.48 6.3 150 277 285 150 28.12

M4 1425 1822.73 65.43 6.78 150 390 380 355 150 29.82

D0 232 337.7 74.55 7.55 232 25.88

D1 250 424.7 76.75 7.96 125 125 31.6

D2 545 861.18 71.12 7.79 145 250 150 20.78

D3 777 1312.32 72.12 8.07 145 230 252 150 18.4

D4 1052 1788.92 71.81 7.84 147 230 255 270 150 23.04

Bamboo samples

Bending load

Section view

Pivot pointL

1600

R50

ø50

Figure 2: Schematic illustration of the three-point bending testsetup. Note: all dimensions in millimeters.

3Applied Bionics and Biomechanics

to failure, it almost failed by splitting along its length. This isdue to the fibrous structure, which makes the material muchstronger in the longitudinal direction than in the transversedirection, and then split into 4 pieces. At this time, thebearing capacity reduced rapidly until compression was

completed. When the load was removed after the bendingtest, the sample could restore a little distance, which indi-cated that bamboo has good elasticity and toughness. Thebamboo damage was mainly brittle failure, and it almostwould not produce scattered debris.

A significant global buckling mode was observed inFigure 4: a sectional crushing zone and several cracks.The localised crack subsequently led to a reduced cross-sectional area, which was associated with the decreasingload-carrying capacity after the local crack occurred at asmall deflection.

3.3. Effect of the Existence of a Node on Bending and EnergyAbsorption. The experimental force-deflection curves andfinal broken modes under quasistatic three-point bendingconditions for NS and INS are given in Figures 5 and 6.The result shows that these curves have significant differ-ences depending on the broken modes. There are severalpeak points on these two curves (PF1, PF2, PF3, and PF4),and the force of the samples is linear elastic at the beginningof loading stages.

In the subsequent loading stages, when the curvesreached the Peak Force1 (PF1), two cracks occurred inthe direction parallel to the indenter due to the brittlefracture behavior in compression, just like the four “1/4

0 5 10 15 20 25 30 35 400

50

100

150

200

250

300

350

�e i

nter

noda

l dist

ance

(mm

)

�e d

iam

eter

of b

ambo

o (m

m)

Number of node

�e internodal distance�e diameter of bamboo

20

30

40

50

60

70

80

90

Figure 3: The distribution of internodal distance and diameter along the culm.

Without node

(a)

One node

1

(b)

�ree nodes

1

2

3

(c)

Figure 4: Bending test process: (a) without node, (b) one node, and (c) three nodes.

(40.29,1.67)

(15.25,2.37)

INSNS

PF1 PF2PF3

PF4

(8.9,2.75)(17.96,2.42)

(16.07,1.51)(8.68,1.52)

0 5 10 15 20 25 30 35 40 45 500.0

0.5

1.0

1.5

2.0

2.5

3.0

Forc

e (kN

)

Displacement (mm)

Figure 5: Displacement vs force of NS and INS.

4 Applied Bionics and Biomechanics

cracks” in Figure 6(a). The two “1/4 cracks” in Figure 6(b)propagated throughout the INS, which led to a greatbreakage. However, due to the existence of the node inNS, where the fibers are thick and diverge from their lon-gitudinal orientations, as shown in Figure 7, the two “1/4cracks” in Figure 6(c) appeared at the two pivot pointsfirstly, leading to a slow force increase in Figure 5, andthe culm of NS did not break completely.

When the curves reached the Peak Force2 (PF2),cracks of INS appeared throughout the sample at anothertwo “1/4 cracks” of the bamboo, and the whole culmbroke completely, leading to a rapid force drop. However,the bamboo wall cracked in the vicinity of the bamboonode in the NS, which also led to a rapid load drop inFigure 5.

In the subsequent loading stages, when force reached thePeak Force3 (PF3), the remaining two “1/4 cracks” alsoappeared on NS, and the cracks propagated throughout thesample directly due to the bamboos already being broken.

Eventually, for the last Peak Force4 (PF4), the followingforce of the bending is the elastic deformation stage, andthe bending force started to slowly climb up to a plateauagain, owing to the fact that these two kinds of bamboo sam-ples have been divided into 4 pieces completely. Due to thefiber direction being consistent in INS, the curve went downsmoothly. The bamboo fiber at the node is more and thick,which results in rising force. Then “1/8 cracks” appeared inNS, and the NS ruptured eventually.

As might be expected, more cracks along the culm, likethe “1/8 cracks” in Figure 6(a), were observed in NS due tothe bamboo node. Therefore, multiple cracks were formedinstead of a single penetrating crack, resulting in a higherload-carrying capacity than that of the INS.

Figure 5 shows that the force of the NS has four peakpoints (PF1/PF2/PF3/PF4), while the INS only has two peakpoints (PF1/PF2). The energy absorption of the sample is theintegration of force during the compression process. Accord-ing to Figure 8, NS (with 1 node) is 56.7% higher than INS(with 0 node) with regard to energy absorption. Moreover,NS is 31.4% higher with regard to specific energy absorptionand 78.8% higher with regard to bending strength than INS.At the same time, according to the crack in Figure 6, thecracking mode and crack number of the two samples are dif-ferent. INS only has 3 cracks, and the third crack didn't splitentirely, while the NS has 4 cracks, which splited entirely.The additional fracture may be the result of the connectionof the node, which caused the extra destruction point andthen improved the bending strength and energy absorptioncharacteristics. This suggested that the antibending abilityof the node part in the intact culm was enforced by swellingof local tissues at the bamboo node.

3.4. Effect of the Number of Nodes on Bending and EnergyAbsorption. According to the above analysis, the existenceof the bamboo node enhances the radial restraint force ofthe bamboo wall and restrains the fracture’s extension, soas to improve the resistance to bending and the energy-absorbing ability.

Figure 8 shows the energy absorption and bending prop-erties of the samples with different nodes and in differentparts of the bamboo. For the upper samples, they are slenderwith large internodal distances. As a result, the nodes deviat-ing off the loading point were so difficult to destroy whichabsorbed more energy, resulting in the bending strengthbeing the biggest by 11.1MPa among them. With theincrease in the number of nodes, the length and mass of thesamples had a greater increase and specific energy absorptiondecreased gradually. Because of the node’s compact struc-ture, which is close to the solid structure, the bendingstrength increased gradually. As for the middle samples, theyhave larger internodal distances and wall thicknesses. Themore nodes and bigger mass caused the decline of specificenergy absorption. Moreover, due to the small internodaldistance, the bending strength was getting larger. In the lowerpart of the culm, there were small internodal distances andlarge wall thicknesses and mass. With the increase of thenumber of nodes, the specific energy absorption decreased,while the bending strength was getting larger because of theshort internodal distance.

Load

1/8 cracks

1/4 cracksSupport

(a) Diagram of cracks

1/4

(b) The sectional view of INS

1/4

Bamboo node

1/8

(c) The sectional view of NS

Figure 6: Diagram of cracks and the section view of broken samples with zero, single, and three nodes.

Bamboo fiber

Figure 7: The sectional and electron macroscopic views of theinternal diaphragm and external ridge of a bamboo node.

5Applied Bionics and Biomechanics

According to Figure 8, for each part of the bamboo, therewas a clear tendency showing that bamboo samples with ahigher number of nodes achieved a stronger stabilization ofthe cross section during the bending process. For example,in the case of the lower part of the bamboo, as shown inFigure 8, the bamboo node provided the culm with lateralsupport to force the plastic deformation to propagatetowards adjacent parts. And more nodes can improve theflexural strength but lower the specific energy absorption.

The quantitative comparison between the NS and INSclearly indicates that the antibending and energy absorptionability of the bamboo sample can be significantly improvedby the bamboo node. Moreover, it is evident that the numberof bamboo nodes and structure size parameters significantlyaffect the antibending and energy absorption ability, which

means that the antibending and energy absorption abilityincrease with the number of bamboos. For example, D4reached nearly 3.3 and 1.8 times higher bending strengthand energy absorption, respectively, than D1.

4. Bionic Design and Analysis

4.1. Bionic Bumper Beam Design. The above three-pointbending test result proved that the bending and energyabsorption ability of bamboo was affected by the node struc-ture. Thin-walled metallic beams are widely applied as struc-tural components in various engineering fields, especially inmoving vehicles such as automobiles, ships, and aircrafts.Their performance under accidental impact or loadingevents is therefore of interest to the researchers for

UpperMiddleLower

0 1 2 3 40

50

100

150

200

250

300EA

(J)

Number of nodes

(a)

UpperMiddleLower

0 1 2 3 40.0

0.1

0.2

0.3

0.4

0.5

SEA

(kJ/k

g)

Number of nodes

(b)

0 1 2 3 40

10

20

30

40

50

Bend

ing

stren

gth

(MPa

)

Number of nodesUpperMiddleLower

(c)

Figure 8: Mechanical properties of samples with a different number of nodes under bending load: EA, SEA, and BS.

6 Applied Bionics and Biomechanics

occupant safety considerations. In particular, the bumperbeam is the primary energy absorption component in car-pole impact. In such crash scenarios, this component absorbskinetic energy during bending collapse. At the same time,as the important components in the field of vehicle colli-sion, the bending strength and energy absorption character-istics of the bumper beam are particularly important. Atpresent, it is noted that in most cases, the bumper energyabsorber system is mostly designed with some compositematerials and normal structures for their high-energyabsorption capability [12, 13, 26, 27]; however, in the energyabsorber field of bionic design, there is still little research. Forexample, Zou et al. [28] designed a bionic tube composed of 1bionic node and 3 bionic inner tubes with 18, 9, and 4bionic elements in each inner tube. Numerical results indi-cated that the bionic design enhances the specific energyabsorption of tubes.

Based on the above research on the relationship betweenbending and energy absorption properties and structuralparameters of bamboo, the bamboo node and changeablediameter play an important role in the process of bendingand energy absorption. Inspired from the way by which thebamboo nodes and nodal diaphragms enhance the transversestrength of bamboo, a series of bumper beams were proposedfor improving the energy absorption property under theprinciple of bionic design.

Figure 9 is the design idea for the bionic bumper beam,and the bionic rib is simulated by the bamboo node, whichplays the role of reinforcing the strength of the bumper likethe bamboo node.

For the Bionic1 bumper beam, the beam comprised fourpanels. These panels located at the front/rear and top/bottomformed a beam with rectangle-shaped profiles. The distancebetween the front and rear panels was changing accordingto the changing rules of the bamboo diameter in (1). The dis-tance is getting larger from both sides to the middle part,which gradually increases from D2 to D1, as shown inFigures 10(a) and 10(b) and Table 2.

Because of that, the cavity structure has difficulty in bear-ing the large load and absorbing higher energy, and the bam-boo node can improve the bending performance of thebamboo. Therefore, on the basis of the Bionic1 bumper beam,the Bionic2 bumper beam was designed with the same cross-

sectional dimension with a reinforcing bionic rib to solve theproblem of low strength and utilization rate of the structure.These ribs were distributed like the bamboo node along theculm. The distance between two adjacent ribs was deter-mined by the model of (2). At the same time, a Bionic2Swas designed, in which thickness T1 of the bionic rib is thin-ner than that of Bionic2. The top view and size parameters ofBionic1 and Bionic2 are as shown in Figures 10(a) and 10(b)and Table 2. For the design of the bionic rib, as shown inFigure 11(a), the section view of the bamboo node shows thatthere is an internal and external ridge at the node. Byengineering treatment, a simplified bionic stiffener rib wasdesigned according to the structure of the bamboo node,which contains one stiffener rib and inner chamfer connectedto the panels all around, as shown in Figure 11(b).

For comparison purposes, one kind of bumper with norib, which is named Normal, was also investigated as a ref-erence bumper beam, as shown in Figures 10(a) and 10(b)and Table 2.

Due to the great changes in mechanical properties of thebamboo which appeared at the bamboo node, the structure ofthe internal diaphragm plays an important role in themechanical properties of bamboo. By engineering treatment,combined with the microscopic structure in Figure 7, twokinds of the bionic bumper were designed, the Bionic3 andBionic4 bumper beams, as shown in Figure 10(c). For thesetwo bumper beams, a design with a reinforced stiffener platefor the structure of the node was adopted to improve thestrength in the bending zone. The Bionic3 bumper beamhad a single front panel and a vertical stiffener plate, whilethe Bionic4 bumper beam had double panels connected bya vertical stiffener plate.

Figure 12 shows the radius size parameters of the bamboonode section view and the inner chamfer near the corner ofthe node. After calculation, based on the structure parame-ters, the range of the inner chamfer is 8–32mm, which canguide the design of the inner chamfer in Figure 11(b) andthe internal structure of R1 and R2 of the Bionic3 and Bionic4bumper beams in Figure 10(b). The detailed size parametersof these bumper beams are as shown in Table 2.

4.2. Numerical Analysis. At present, the automotive industrydeals with a large variety of crash situations. The wide varietyof accidents makes it desirable to consider them in groupswith basic similarities. The largest proportion of accidents,about 60%, occurs at the front of the vehicle, and of these,pole impact is an accident situation commonly seen on roads,and they also give rise to the highest portion of deaths [29]. Inthis paper, these 5 kinds of bumper beams were simulatedunder the pole impact by finite-element software. The bum-per beam was completely fixed at two points on the ground,and a rigid column with the diameter of 254mm crashestoward the bumper beam at a certain speed. The collisiondiagram is as shown in Figure 13.

The FE models of bumper beams were built using thefinite-element software “Hypermesh” and solved by LS-DYNA. The beam was modeled with the Belytschko thin shellelements, and the column was a rigid wall. To simulate thecontact between the rigid column and beam, the “automatic

Stiffener rib

Crush box

Bamboo nodeBionic design

Bamboo

Bumper

Figure 9: The design idea of the Bionic1 and Bionic2 bumperbeams.

7Applied Bionics and Biomechanics

Bionic2

Bionic1

Normal

D1

D1

D1

D2

L

T0T1

R0

R0

R0 L5 L4 L3 L2 L1

(a) Top views of the Bionic1, Bionic2, and Normal beams

Bionic2

H

H

H

Bionic1

Normal

(b) 3D diagrams of the Bionic1, Bionic2, and Normal beams

R2

R1

R

Bionic4IX

XIII

Bionic3

T

T

L1

L1

L2

L2

(c) Shaft side view and partial view of Bionic3 and Bionic4

Figure 10: The diagram of bionic bumper beams.

Table 2: Structure parameter of bionic bumpers (mm).

Parameter Normal Bionic1 Bionic2 Bionic2S Bionic3 Bionic4

L 1200 1200 1200 1200 1200 1200

H 80 80 80 80 — —

L1 — — 52 52 80 80

L2 — — 76 76 50 50

L3 — — 88 88 — —

L4 — — 100 100 — —

L5 — — 85 85 — —

R — — — — 1400 1400

R0 1400 1400 1400 1400 — —

R1 — — — — 30 —

R2 — — — — — 15

D1 50 50 50 50 — —

D2 50 25 25 25 — —

T — — — — 2 2

T0 2 2 2 2 2 2

T1 — — 2 1 — —

m (kg) 1.635 1.509 1.705 1.555 1.47 2.04

8 Applied Bionics and Biomechanics

surface to surface” contacts with static and dynamic frictioncoefficients of 0.3 and 0.2, respectively, were defined. An“automatic single surface” contact was defined for the contactof the beam itself during crushing. Stiffness-based hourglasscontrol was employed to avoid a spurious zero-energy defor-mation mode, and reduced integration was used to avoidvolumetric locking. The rigid column impacts the beam atthe velocity of 10m/s with the mass of 1000 kg.

The finite-element model and material parameters ofthe beam are as shown in Table 3. In the finite-element

modeling process, the bumper beam was modeled usingan elastic-plastic material constitutive model (i.e., thematerial model 24 in LS-DYNA). The rate-dependenteffect was neglected due to the insensitivity of aluminumalloy to the relatively low strain rate.

4.3. Results and Discussion. The deformation mode andstress pattern of 5 bumpers for pole impact are as shownin Figure 14. They have different deformation styles. Forthe Normal bumper, due to the hollow structure, a largefolding with a “V” shape appeared at the middle impact-ing point. And the stress was mainly located at the rearflat and middle crushing point; as for the Bionic1 bumper,the distance between the front and rear flats is short; as aresult, the angle of the folding scale was large but the areawas small, and the stress was mainly located at the twopivot points and middle crushing point; due to the exis-tence of the bionic rib structure in the Bionic2/Bionic2Sbumper beams, the strength of the beam gets strongerand the rib can make the beam more stable. The foldingalmost fit the rigid column at the impacting points, andthe stress distributed in the whole beam uniformly.

The bumper beams of Bionic3 and Bionic4 are mainlymade of flat and radial plates; thus, the main deformation isthe laceration of the flat and radial plates. The Bionic3 has aperfect folding, fitting the rigid column completely, whichbenefits from the flat front plate that is easy to fit. The rearradial plate plays an important role in the process of crushingaccording to the stress distribution; because the Bionic4 has adouble plate and lower rib angle, the folding was muchtighter, and the stress distributed uniformly.

Internaldiaphragm

External ridge structure

Bamboo node

Inner chamfer

(a) The section view of the bamboo node

External ridge

Stiffener rib

Inner chamfer

Front panel

Rear panel

(b) The top section view of the bionic stiffener rib

Figure 11: Simplified engineering design of the bionic rib according to the structure of the bamboo node.

20

22

24

26

28

30

32

34

36

38

40

Inner chamfer

Radi

us (m

m)

Inner chamfer

−15 −10 −5 0 5 10 15Distance away from diaphragm (mm)

InnerOuter

Figure 12: The outer and inner radii taken from a longitudinalsection of the culm.

Fixed

V Rigid columnar

Bumper beam

Figure 13: The schematic diagram of columnar collision.

Table 3: Finite-element model parameters.

Model parameters Parameter values

Element size 5mm

Density of the material 2.7e−6kg/mm3

Elastic modulus 70GPa

Yield strength 0.25GPa

Poisson’s ratio 0.3

Collision mass 1000 kg

Collision speed 10m/s

9Applied Bionics and Biomechanics

According to the deformation and stress distribution ofthe bionic and normal bumpers, the utilization of structurewas low during the crushing owing to the hollow structureof Normal and Bionic1 bumpers. However, the Bionic2 bum-per has the bionic rib, which made its deformation compli-cated and difficult. For the Bionic3 and Bionic4 bumperbeams, the main deformation was the laceration. Therefore,the deformation and stress distribution of bionic bumperswere better than those of the normal bumper beam.

Figure 15 shows the curves of force vs displacement forfive bumpers. Table 4 has the detailed bending and energyabsorption properties of five bumpers. During the crushingdistance of 200mm, the force curves increased to the initial

peak force firstly and then dropped down when the bumperwas broken. Finally, the force increases again for bendingand laceration.

The force curve of the Normal bumper is steady, which isin accordance with the deformation; Bionic1 has the samevariation range with Normal, and the difference betweenthem is small, while the force of the Bionic1 bumper is lowerthan that of the Normal bumper for the tight structure at twosides, because the structure size of Bionic1 at the two sides isdiminished, and the mass is smaller. Therefore, the SEA ofthe Bionic1 bumper is higher than that of theNormal bumperby 7.3% but 11.3% lower than BS. For the Bionic2, the bionicrib made the force increase a lot, which is higher than that ofthe Normal and Bionic1. The characteristic of Bionic2 ishigher than that of Normal by 12.3% for BS, 36.9% for EA,and 31.4% for SEA. Moreover, the Bionic2 is higher than thatof Bionic1 by 26.6% for BS, 38.3% for EA, and 22.5% for SEA,indicating that the bionic rib has a great effect on the proper-ties of the bumper beam. As for the Bionic2S bumper beam,the bending strength and energy absorption are slightly lowerthan those of the Bionic2 bumper beam. However, the massof the Bionic2S bumper beam is lower than that of the Bionic2and Normal bumper beams, which is the lightweight effect.

ELEMENT_SHELL 23671Max = 4.097E − 01

No result0.000E + 00

4.552E − 02

9.104E − 02

1.366E − 01

1.821E − 01

2.276E − 01

2.731E − 01

3.187E − 01

3.642E − 01

4.097E − 01

Contour plotStress (von Mises, max)Analysis system

Min = 0.000E + 00ELEMENT_SHELL 19543

FulcrumFulcrumFulcrumFulcrum

Bionic3

Bionic2

Normal

Bionic4

Bionic2S

Bionic1

Figure 14: The deformation, enlarged partial view, and von Mises of the bumper’s pole impact.

0 20 40 60 80 100 120 140 160 180 2000

2

4

6

8

10

12

14

16

18

20

Forc

e (kN

)

Distance (mm)

Bionic Bumper1Bionic Bumper2Bionic Bumper2s

Bionic Bumper3Bionic Bumper4Normal bumper

Figure 15: The force curve vs displacement for five bumpers.

Table 4: The impact performance parameters of the bumpers.

BS (MPa) EA (kJ) SEA (kJ/kg)

Normal 50.23 0.97 0.593

Bionic1 44.53 0.96 0.636

Bionic2 56.39 1.328 0.779

Bionic2S 56.04 1.282 0.824

Bionic3 55.99 1.06 0.72

Bionic4 87.68 1.89 0.926

10 Applied Bionics and Biomechanics

The initial peak force of Bionic3 is equal to that ofBionic2, but it has many large fluctuations, and the latter partof the curve tends to be jagged, indicating that the structurehad unsatisfied deformation. The characteristic of Bionic3 ishigher than that of Normal by 11.5% for BS, 9.3% for EA,and 21.4% for SEA. However, the Bionic4 has the highestforce and initial peak force among them. The characteristicof Bionic4 is higher than that of Normal by 74.6% for BS,94.8% for EA, and 56.2% for SEA, but the mass is the biggestone among them. Above all, it can be concluded that thebionic bumper with the best performance is the Bionic2S,which has the 4.9% mass reduction. And the Bionic2Sbumper beam improved by 12.3% for BS, 36.9% for EA,and 31.4% for SEA compared to the Normal bumper beam.

The above results indicated that the bionic method couldimprove the crashworthiness of a beam structure undercertain conditions; however, the bionic structure still hassome limitation, for example, the material is relatively simpleand the structure is relatively complex. Further research andfinite-element analyses should be conducted by couplingdifferent materials or topological optimization.

5. Conclusions

This work has investigated the mechanical role of thenodes in the bamboo culm under bending load. Conduct-ing three-point bending test was attempted to determinethe effect of the node on culm bending strength andenergy absorption. It was concluded that the result of thepresent work suggests that the morphological features ofthe node, the internal diaphragm, and the external thick-ening of the culm play an important role in the mechani-cal properties of bamboo.

The experiment result shows that the node increasesthe bearing area, which can be explained as an attemptto reinforce a biologically essential feature. Moreover, themicrofiber of bamboo appeared thicker and to migrate.The characteristics of the samples with nodes are higherthan those of the samples without nodes by 56.7% forEA, 31.4% for SEA, and 78.8% for bending strength. Withthe increase of the number of nodes, the bending strengthis getting larger but the SEA is getting lower.

The failure mode of bamboo is mainly rupturing underthe bending force. Moreover, the existence of a bamboo nodecan hinder the propagation of internodal cracks to make upfor the defect of weak opening-mode fracture toughnessalong interlamination.

Based on the above investigation, a series of bionic bum-pers were designed under the principle of bionic design. Aftersimulation by the finite-element analysis, the result showsthat the performance of the bionic bumper is better than thatof the normal bumper with regard to bending strength,energy absorption, and being lightweight. The Bionic2S hasthe best performance. The characteristic of Bionic2S is higherthan that ofNormal by 12.3% for bending strength, 36.9% forEA, and 31.4% for SEA, which still need further optimization.Moreover, there was a mass reduction of 4.9% compared tothe Normal bumper beam. The above research can providereference and basis for crashworthiness of structure design.

Data Availability

We have submitted the raw data used in our manuscriptand the other supplementary date are shown in the attach-ment. Other researchers can access the data supporting theconclusions of the study. (1) The nature of the data is thesource data of the image in the paper; (2) the data can beaccessed on the submitting system or through email toiansongjiafeng@163.com; (3) there are no restrictions onthe data access.

Conflicts of Interest

No potential conflict of interest was reported by the authors.

Acknowledgments

Wewould like to thank the National Natural Science Founda-tion of China [Grant Nos. 51305159 and 51405191] and theScience Fund of State Key Laboratory of Automotive Safetyand Energy [Grant No. KF11211] for the financial support.

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