Special Issue Article

Journal of Intelligent Material Systemsand Structures1–9� The Author(s) 2015Reprints and permissions:sagepub.co.uk/journalsPermissions.navDOI: 10.1177/1045389X15580656jim.sagepub.com

Morphing thickness in airfoils usingpneumatic flexible tubes and Kirigamihoneycomb

Jian Sun1,2, Fabrizio Scarpa2, Yanju Liu3 and Jinsong Leng1

AbstractThe work describes a concept to morph the thickness of airfoils using a combination of pneumatic flexible tubes withina Kirigami honeycomb configuration that represents the wingbox structure. The configuration of the honeycomb/inflata-ble tube structure is composed by a pair of flexible tubes sandwiched between two custom honeycomb layouts. At zeroinput pressure, the tube assumes a sinusoidal shape, which is reduced to a straight configuration and increase of the air-foil thickness when pressure is applied. An analytical model is developed for design purposes to consider the actuationauthority and thickness change provided by the system proposed. The results are benchmarked against experimentaltests carried out on a reduced-scale demonstrator.

KeywordsMorphing airfoil, modeling, inflatable structure, honeycomb, Kirigami

Introduction

During the last two decades, morphing technologieshave demonstrated their capability to provide signifi-cant enhancement of the aircraft performance andbroadening of the related flight envelope (Frommerand Crossley, 2005; Jha and Kudva, 2004; Roth et al.,2002). Several types of morphing techniques have beendeveloped in recent years, and examples span fromfolding technologies for morphing wingtips to adaptivetwist and variable camber (Barbarino et al., 2011;Gomez and Garcia, 2011; Rodriguez, 2007). The per-formance of a wing in a specific flight conditiondepends also on geometry properties of an airfoil pro-vided by the maximum camber of the mean line andthickness distribution along the chord (Secanell et al.,2006). A thick wing performs more efficiently from theaerodynamic point of view at low speeds, while a thinwing is adapted to high velocity flight (Ashraf et al.,2011; Yu et al., 2012). If the thickness of the airfoil canvary in a controllable way over the chord length, theaircraft can have a larger flight envelope and meet thedemands of multiple missions (Ahaus et al., 2012). Anexample of this concept is the morphing airfoil wingprototype based on shape memory alloy (SMA) actua-tors designed for subsonic cruise flight conditions,which has been tested in a subsonic wind tunnel(Brailovski et al., 2010).

Honeycomb and cellular structures are extensivelyused in airframe and sandwich applications for theirhigh specific shear and bending stiffness, and recentlyhave been proposed to morphing applications due totheir compliance (Bettini et al., 2010; Martin et al.,2008; Olympio and Gandhi, 2010). In morphing appli-cations, the honeycomb does not change shape by itself,but needs the use of smart material within its core, likein the cases of SMA (Hassan et al., 2008; Okabe andSugiyama, 2009) or shape memory polymers (SMP)(Perkins et al., 2004). An alternative concept to createan adaptive honeycomb consists in using pressured

1Center for Composite Materials and Structures, Harbin Institute of

Technology, Harbin, China2Advanced Composites Centre for Innovation and Science (ACCIS),

University of Bristol, Bristol, UK3Department of Astronautical Science and Mechanics, Harbin Institute of

Technology (HIT), Harbin, China

Corresponding authors:

Jinsong Leng, Center for Composite Materials and Structures, Harbin

Institute of Technology, P.O. Box 3011, No. 2 YiKuang Street, Harbin

150080, China.

Email: lengjs@hit.edu.cn

Fabrizio Scarpa, Advanced Composites Centre for Innovation and

Science (ACCIS), Queens School of Engineering, University Walk, BS8

1TR Bristol, UK.

Email: f.scarpa@bristol.ac.uk

fluid inside the cells. Variable camber wings have beenalready designed based on the use of a pneumatic pres-surized honeycomb to obtain an adaptive configurationby applying either a uniform pressure (Vos and Barrett,2011) or differential pressures at different cells locations(Pagitz and Bold, 2013; Pagitz et al., 2012). Pressuredflexible tubes can also be used within the honeycombsor in segmented structures, such as prosthetic hands(Schulz et al., 2005), robotic platforms (Berring et al.,2010; Lira et al., 2009; Menon and Lira, 2006), and bio-mimetic beam-steering antenna concepts (Chang et al.,2012; Mazlouman et al., 2013). Recently, a concept ofinflatable auxetic honeycomb for wing tip morphing hasbeen proposed by some of the authors (Sun et al., 2014).

This article describes a new morphing airfoil thick-ness concept based on the use of a Kirigami hexagonalhoneycomb supporting an inflatable tube structure,which provides the shape change of the wingbox.Kirigami is the ancient Japanese art of folding and cut-ting paper that spread in Asia since the 17th century,and it is particularly apt to build cellular structureswith complex shapes using different types of thermosetsand thermoplastics composites (Chen et al., 2013;Nojima and Saito, 2006; Saito et al., 2011; Virk et al.,2013), as well as other metal substrates. An analyticalmodel based on the geometry of the tube and approxi-mations of the output force behavior of the tube itselfis presented for design purposes. A demonstrator of themorphing inflatable honeycomb structure has also beenproduced, showing a general good agreement with thepredictions provided by the model in terms ofdisplacement–pressure actuation. A prototype ofmorphing airfoil has also been fabricated to furtherdemonstrate the feasibility of the concept.

Morphing thickness airfoil concept

The morphing thickness airfoil structure consists of acellular wingbox with pneumatic flexible tubes (PFTs)as actuators (Figure 1). The tubes are installed horizon-tally between the upper and lower hexagonal honey-comb wingbox. When the pressure inside the tube is

zero, the tube is contracted to follow an approximatesinusoidal shape. The input pressure in the inflatabletubes can control the thickness of the wing section. Inthe demonstrator developed in this work, a polyur-ethane (PU) foam filler is used to fill the cellular wing-box to increase the in-plane stiffness, to guarantee asmooth change of the thickness to follow the aerody-namic shape and to provide (together with the honey-comb structure) the transmission of the shear loadsthrough the airfoil section. There are two considera-tions that justify the choice of a wingbox structure withan embedded non-flat tubular structure. The first isrelated to the bending stiffness along the spanwisedirection. Compared to a flat configuration with thesame diameter, a tube with its axis following a sinusoi-dal path would increase the overall moment of inertiaof the structure, with a consequent increase of the con-tribution of the inflatable component to the bendingstiffness of the wing. The second rationale behind thechoice of a non-flat inflatable tube configuration is thedeformation authority of the tube itself. Compared to aflat tube configuration, a corrugated tube offers a com-bined larger deformation because of the superpositionof the radial one due to the inflation of the tube andthe tensile deformation along the axis. In the conceptproposed in this article, the corrugated inflatable hon-eycomb wingbox with the PU foam filler can providebending stiffness capabilities, while the PU foam pro-vides the torsional stiffening to the cellular structure.

Modeling

Geometric model

Figure 2 shows a schematic representation of the unitcell of the morphing structure. The black lines repre-sent the edge of hexagonal honeycomb cell, while theblue lines show the upper and lower surfaces of thetube sandwiched inside the cell. The model is developedfollowing four assumptions:

1. The tube is assumed to be symmetric withrespect to its centerline after compression. The

Figure 1. Schematic of the morphing thickness airfoil concept.

2 Journal of Intelligent Material Systems and Structures

final upper and lower surfaces of the tube areflat, while the left and right surfaces are consid-ered as semicircles. There is no contact insidethe tube.

2. Before compression (actuation), the upper andlower surfaces are sinusoidal.

3. No sliding is present between the tubes and thehoneycomb.

4. The honeycomb is considered to simply transferthe load and acts as a rigid body during thedeformation of the tubes.

The two curves defining the shape of the tubes aredescribed with the following equations

yI =A sin (vx+ t1)+B1 ð1Þ

yII =A sin (vx+ t2)+B2 ð2Þ

where v= 2p=3a and t1 = t2 = � p=2.The upper curve passes through the point

(a, (ffiffiffi3p

=2)a); therefore, the term B1 =(ffiffiffi3p

=2)a� (A=2)is constant. The point ((a=2), s+(

ffiffiffi3p

=2)a) belongs tothe lower curve; as a consequence, the value of B2 isB2 = s+(

ffiffiffi3p

=2)a+(A=2). By inspection, the followingrelation holds

b=B2 � B1 = s+A ð3Þ

Assuming that a linear relationship exists between theterms b and s

b= ks+B3 ð4Þ

When s= 2R0, b= 2R0 and s= � (ffiffiffi3p

=2)a, b= 0, thecoefficients k and B3 assume the following forms

k =2R0

2R0 +ffiffiffi3p

=2� �

a, B3 =

ffiffiffi3p

2ka ð5Þ

From observing Figure 3, the outside radius of thesemicircle can be described as

R=b

2ð6Þ

The length of the straight line is obtained as

c=2pR0 � pR� pR

2=p R0 �

b

2

� �ð7Þ

Figure 2. Morphing structure unit in rectangular coordinates.

t

R

Pb

cz

y

Figure 3. Geometry of a compressed tube.

Figure 4. Distances between the upper and lower surfacesversus the internal height of the tube cell.

Sun et al. 3

The relationships between the terms b, c, and A versus sare shown in Figure 4 for R0 = 2:75 mm and a= 6 mm.The terms A and c decrease linearly with the increase of s,while the constant b has an opposite behavior.

Mechanical model

The recovery force in y direction provided by the tubeis considered to consist of two parts (shown inFigure 5): one referring to the compressed circular con-figuration of the tube itself (FR) and the other onebeing related to the sum of the force in y directioncaused by the elongation stress of the tube along itsaxial direction (FS).

According to the Saint-Venant’s principle (Gregory andWan, 1985), the shearing force on the two sides of the semi-circle creates a momentM about x direction (Figure 6)

M =Ftr ð8Þ

Where r=(b� t)=2, while the original central radiusof the semicircle is r0 =R0 � (t=2).

Assuming pure bending occurring within the walls ofthe tube, the moment can be represented as

M =1

rEI ð9Þ

where the moment of inertia about x axis is I =wt3=12,for the compressed structure shown in Figure 2,w= 30 mm.

The original shape of the tube is circular, whichimplies the presence of an internal pre-stress. Therefore,the recovery force FR of the tube should be composedby the shearing force, minus the original shearing force

present in the two semicircles. From inspecting Figure4, the relationship between FR and s can be calculatedand shown in Figure 7

FR = 2(Ft � Ft0)= 8EI1

b� tð Þ2� 1

2R0 � tð Þ2

!ð10Þ

The force FS is given by the sum of the forces alongthe y direction in each unit of the curve. Due to thesymmetry of the sinusoidal curve, we use the 1/4-periodcurve shown in Figure 8 to calculate the force FS. Thefunction of the blue curve is represented by

f (x)=A cos (vx) ð11Þ

Figure 5. Schematic of FR and FS.

M

M

ρρ

Ft

Ft

⇒

z

y

Figure 6. Mechanical model of semicircle.

Figure 7. Curves of s versus FR.

x

y

ΔFSΔx

3a/4

( )( )2'1x f xΔ +

( ) ( )cosf x A xω=

circleE Aε

Figure 8. Principle of the recovery force FS.

4 Journal of Intelligent Material Systems and Structures

From a horizontal straight line to sinusoidal curve,the strain at position x in an increment Dx is

e=Dx

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1+ f 0 xð Þð Þ2

q� Dx

Dx=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1+ f 0 xð Þð Þ2

q� 1 ð12Þ

So, the force in y direction is

DFS =EeAcirclef 0 xð Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1+ f 0 xð Þð Þ2q ð13Þ

Here, Acircle =p(R20 � (R0 � t)2). The resultant force FS

along the y direction can be obtained from the follow-ing equation

FS =

Z3a=4

0

DFSdx ð14Þ

The relation between the shearing force FS and the dis-tance s is shown in Figure 9.

The output force caused by the input pressure can bedefined as

FP =Pwc ð15Þ

Experiments

A prototype of the morphing structure fabricated wasused as a hexagonal cellular structure made from0.1 mm thickness steel with 6 mm length of side andfilled with PU foam (Polycell Expanding FoamPolyfilla, density of 25 kg/m3; Polycell Products Ltd,Slough, UK). The upper and lower honeycomb struc-tures are connected by sandwiching two parallel tubes(polyvinyl chloride (PVC), outside radius R0: 2.75 mm,thickness t: 0.84 mm, valid length L: 30 mm; ShenzhenLongxiang Electronic Co., Ltd). Tensile tests carriedout on the PVC tubes indicated Young’s modulus of

the PVC material equal to E = 0.94 MPa. The morph-ing demonstrator was subjected to compressive loadingusing a tensile machine (Shimadzu AGS-X, maximumforce: 1000 N; Shimadzu Corp., Kyoto, Japan) with aspeed of 1 mm/min. The force–displacement diagrams ofthe specimen repeated four times are shown in Figure 10.The curves show a good level of repeatability and followapproximately a quadratic dependence with the cross-bardisplacement. Fluctuations are present between 3.5 and4.5 mm due to possible contact or friction occurringbetween the upper and lower surfaces of the tubes.

Figure 11 shows the output force of the system ver-sus the tubes’ input pressure at different positions ofthe crosshead. At constant imposed displacements, themeasurements were taken in such a way that the forcesensor was reset to zero to exclude the influence of therecovery force within the tubes. It is possible to observethe existence of a quasi-linear relationship between theinput pressure and output force for compression defor-mations at 4 and 6 mm. It is also apparent that a lower

Figure 9. Curves of s versus FS.

0 1 2 3 4 5 6 70

5

10

15

20

25

30

35

Forc

e [N

]

Displacement [mm]

Test 1 Test 2 Test 3 Test 4

Figure 10. Curves of force versus displacement incompressing test.

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0

10

20

30

40

50

60

Forc

e [N

]

Pressure P [MPa]

2mm4mm6mm

Figure 11. Output force versus the input pressure at differentconstant displacements.

Sun et al. 5

level of pre-compression (2 mm) does not guarantee aquasi-linear behavior above an input pressure of0.15 MPa, also likely due to the fact that the compres-sive deformation is not able to provide a continuousbonding and adhesion between the foam, honeycomb,and corrugated tube above a certain input pressurethreshold.

Another set of tests was conducted by imposing aconstant load to the composite cellular core/inflatabletube systems (Figure 12(a)). The lower part of the hon-eycomb was fixed, and the loading was applied with aweight on the upper surface. During the test, the uppersurface was maintained parallel to the bottom surface.The displacements were measured through image dataprocessing tracking the deformation of six markers.The images were recorded using a camera (number ofpixels: 16 million; Canon Inc., Tokyo, Japan), with aprecision of 0.27 mm. The average distances measuredbetween the upper and lower honeycombs are shown in

Figure 12(b). At the conditions of 2 kg loading and0.4 MPa input pressure, the displacement of upper sur-face could reach 2.72 mm.

Results and discussions

Figure 13 shows the relationship of the input pressureversus the output force from equation (15) and theexperimental data. For s = 3.5 mm, the experimentalresults show a good agreement with the ones generatedfrom the model. At smaller displacements (s = 1.5 mmand 0.5 mm), the model tends to be conservative, espe-cially for higher input pressures. It is worth mentioningthat the model neglects the expansion of the tube, whichmakes the term c larger than the one predicted by themodel, and therefore leads to a larger output force.

When the morphing structure is compressed (asshown in Figure 10), the force measured by the forcesensor equals the recovery force of the tubes. FromFigure 2, one can observe the presence of two sinusoi-dal waves. The deformation conditions of the left andright sides of a tube are free, so only the middle 1/2period of the tube is elongated, as also observed inFigure 10. Therefore, the recovery caused by the stressin one tube is 2FS. Because of the presence of two tubesin the system, the total recovery force is 2FR + 4FS.From equations (10) and (12), the relationship betweenthe distance between the upper and lower honeycombsurfaces and the recovery force is shown in Figure 14,together with the analogous curve from the experimen-tal results. While s . 2, the modeling value is smallerthan the experimental one. In the model, we assumethere is no contact inside the tube, and no sliding existsbetween the tube and the honeycomb. However, itappears that contact occurs at s = 2 with the conse-quent reduction of the value of s itself. Therefore, themodel for s \ 2 tends to overestimate the overallrecovery force produced by the tube.

(a)

0.00 0.08 0.16 0.24 0.32 0.40

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Dis

tanc

e s

[mm

]

Pressure P [MPa]

1kg loading sample 1 1kg loading sample 2 2kg loading sample 1 2kg loading sample 2

(b)

Figure 12. Inflating test with weight loading: (a) setup of thetest rig and (b) displacement/pressure results.

Figure 13. Output force versus input pressure provided by themodel and the experimental demonstrator.

6 Journal of Intelligent Material Systems and Structures

From the balance of the forces in y direction undera vertical loading G, the following equation can beobtained

2FR + 4FS +FP =G ð16Þ

Under a prescribed external loading G, the distancebetween the upper and lower honeycomb surfaces atdifferent input pressures can be calculated using equa-tion (16). A comparison between the results from equa-tion (16) and the experimental measured data is shownin Figure 15. Especially for the lowest external loadapplied (1 kg), one can observe an excellent agreementbetween the theoretical and test results.

A prototype of a reduced-scale model of a morphingthickness airfoil (original airfoil: NACA0030) was

fabricated with a chord of 140 mm and maximum ini-tial thickness of 43 mm. Using a similar manufacturingprocess to the one adopted for the composite cellulardemonstrator, an airfoil was made using a 0.1 mmthickness steel honeycomb, with PU expanding foamfiller injected into the cellular structure and on the restof the wingbox. After curing for 24 h at room tempera-ture, the final prototype was finished by cutting manu-ally any extra polymer debonding from the wingbox.Two parallel tubes were installed between the upperand lower honeycombs. Rubber bands were used toapply the loading along the lift force direction on thewing structure. Two points A1 and A2 (the verticalprojections on the upper surface of the middle of upperhoneycomb horizontal ribs) were selected to highlightthe deformation of the airfoil thickness. Moreover, thepoint A1 represents the maximum thickness of the air-foil. Figure 16 shows the vertical locations of points A1and A2 on the top of the wing, which increase with theinput pressure. A thickness change of 7.6% (3.28 mm)at point A1 can be obtained for a 0.28 MPa input. Ademonstration of the morphing processing under dif-ferent input pressures is shown in Figure 17.

Conclusion

This article has described the concept of a morphingthickness airfoil based on pneumatic flexible tubes andcellular wingbox structure. An analytical model hasbeen developed to calculate pressure/thickness relationsand the mechanics of the actuation system. An experi-mental prototype of the composite cellular/inflatabletube structure has been manufactured and tested. Theexperimental and analytical results showed a goodagreement, indicating that the model can be used as ini-tial design tool. A prototype of a reduced-scale morph-ing thickness airfoil has also been fabricated and

Figure 14. Recovery force versus distance between upper andlower honeycomb surfaces.

Figure 15. Distance between upper and lower honeycombsurfaces versus input pressure from the model and theexperimental prototype.

A2 A141

42

43

44

45

46

47

Hei

ght [

mm

]

Position

0MPa0.04MPa0.08MPa0.12MPa0.16MPa0.20MPa0.24MPa0.28MPa

Figure 16. Variation of the heights of points A1 and A2 of thetop surface of the morphing wing airfoil under different inputpressures.

Sun et al. 7

showed the feasibility of further exploring this conceptas an alternative morphing wing strategy.

Declaration of conflicting interests

The authors declared no potential conflicts of interest withrespect to the research, authorship, and/or publication of thisarticle.

Funding

This work is supported by the National Natural ScienceFoundation of China (Grant No. 11225211, No. 11272106).J.S. would also like to thank Chinese Scholarship Council(CSC) for funding his research work at the University ofBristol. F.S. is also grateful to the European Commission forthe FP7-AAT-2012-RTD-L0-341509 project Morphelle thatprovides the infrastructure logistics of the activities describedin this article.

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Appendix 1

Notation

a length of the side of hexagonalhoneycomb

A amplitude of the sinusoidal curvesAcircle tube’s area in loop sectionb distance between the upper and lower

surfaces in the section of the compressedtube

B1, B2 constant term of the sinusoidal curvesB3 constant term of the curve of s-bc length of upper/lower surface in the

section of the compressed tubeE Young’s modulus of the tubeFP force referring to input pressureFR recovery force of a tube caused by the

circle structureFS recovery force of 1/4-period in a tube

caused by stressFt shearing force on the two sides of

semicircle unitFt0 shearing force on the two sides of

semicircle unit while the tube is a circleG loading forceI rotary inertia of the semicircle unit about

x axisk gradient of the curve of s-bM moment on the two sides of semicircle unitP input pressure in the tubeR outside radius of the semicircle of the tubeR0 original outside radius of the tubes distance between the upper and lower

honeycombt thickness of the tubet1, t2 offset angle of the sinusoidal curvesw valid width of a tube

DFS recovery force occurring at x positionDx increment in x directione strain at x positionr central radius of the semicircle unitr0 original central radius of the semicircle

unitv frequency of the sinusoidal curves

Sun et al. 9