Design and Development of Active Bimorph Structure ...

Design and Development of Active Bimorph Structure for Deployable Space Application Rupal Srivastava1 , Arun Kumar Sharma1 , Arup Kumar Hait2 , and Bishakh Bhattacharya1 1

Department of Mechanical Engineering, Indian Institute of Technology Kanpur, India 2 Space Application Center, Indian Space Research Organisation, Ahmedabad, India ABSTRACT

Deployable structures are increasingly studied for their enormous potential of space application. In this paper, we report the fabrication and analysis of an Active Bimorph Structure (ABS) by evaluating the variation of the curvature and the tip-displacement of the top fiber layer with respect to the change in applied voltage. The composite showing the bi-directional bending behaviour was fabricated using E-Glass fibre and Room Temperature Vulcanising (RTV) Silicone Rubber, embedded with NiTiNOL Shape Memory Alloy wires in two layers, at 0 and 90 degrees. The study of the deflection motion of the ABS shows that with an increase in temperature of the SMA wire, the bending curvature initially increases almost proportionally and finally reaches a constant steady curvature and the experimental results satisfy this condition. The second layer of the ABS system when actuated gives the composite a bi-directional bending behaviour. The future aim is to create an Active Bimorph Box Structure (ABBS) with composites placed and glued in such a manner that upon excitation the structure transforms first into a cylinder and eventually into a curved cylindrical element following its property of bi-directional bending. Keywords: Active bimorph structure, glass fiber reinforced composites, shape memory alloys

1. INTRODUCTION The performance of a spacecraft and its launch cost is directly proportional to the launch volume and mass. Hence the research for compact and eventually deployable space structures has always been of importance. Project ECHO I and II in the late 1950’s and early 1960’s by NASA LaRC were the pioneer experiments in this field [1]. These deployable structures have the potential to achieve high mechanical packing efficiency, low weight with a considerably small stowed volume and low-cost space hardware. There are several mechanical, physical, and chemical methods that have been used and are currently being studied for the rigidization of thin-walled expandable structures. One of them being gas-based inflation and rigidization [2], however this method keeps the system at risk with its various limiting factors like leaking and thermal expansion of the gas. Leaks usually develop due to small holes in the wall of the inflatable structure, created by the impact of space debris and micrometeoroids [3]. The other most commonly used rigidization method is UV based curing of the composite and hence rigidization. The composites, in this case, are impregnated with UV curable resins, such that, they cure only at defined wavelengths by using a photoinitiated catalyst [1], [4], [5]. However simplistic and efficient this method is, its limitations like cure time being unpredictable, loss of control on the process due to shadowing leading to an unequal cure and deformation are critical. Since the composites suitable for this method are thermoset polymers hence the reversibility limitation. Materials like NiTiNOL and Shape Memory Polymer exhibit thermally induced shape memory effect[6]. Commercially these materials are available in wire, spring, and ribbon form. The two solid-state crystalline temperatures for these Shape Memory Alloys (SMA) are the room temperature martensite and high-temperature parent state austenite which are further characterised by martensite start temperature Ms , martensite finish temperature Mf , austenite start temperature As , and austenite finish temperature Af [7]. In simple terms, the material in its low-temperature martensitic condition, when plastically deformed and then removed of external Further author information: [email protected], [email protected], [email protected], [email protected]

stresses, regains its original shape upon heating [8]. Several smart and adaptive structural components have been developed by integrating the SMA actuators with the structure [9], through both non-embedding and embedding approaches, an example being inflatable booms which employ SMA wires attached to the membrane to reduce its wrinkling [10] and of adaptive SMA embedded airfoil wings[11] respectively.

2. SMA HYBRID COMPOSITE CONSTITUTIVE RELATIONS

Embedded SMA wire z

} Matrix

}

y

Fibre

y

Mx

x Ny

Mxy Nxy

z

(a) Schematic of the SMA reinforced composite

x

My

Nxy

Mxy

Nx

(b) Loads acting on a laminate

Figure 1: Schematic of the SMA wire reinforced composite with 0o ply allignment For a SMAHC considering that the SMA and the glass fibers have the same direction, the stress-strain relations of the k th layer during a small temperature increment is expressed as [12]: ¯ k ({} − {α}k ∆T ), T < As {σ}k − {σ0 }k = [Q] ¯ k {} + {σr }k νs − ([Q] ¯ m {α}m νm )k ∆T, T ≥ As = [Q] k

(1)

where {σ0 }, {α} and {σr } denote initial stress, thermal expansion coefficient, and SMA recovery stress ¯ and [Q] ¯ m denote transformed reduced stiffness matrices of the SMA embedded lamina vectors, respectively; [Q] (νs 6= 0) and the composite matrix (νs = 0) ; νs and νm denote volume fractions of SMA and matrix. In eq. (1) the change of state of stress is {σ} − {σ0 } and {σr } is the increment of recovery stress (of SMA) during ∆T . The constitutive equations of the SMA embedded composite plate are: 

N M



 =

A B

B D

  o        Nr N∆T Nσ + − + κ Mr M∆T Mσ

(2)

here o is the mid-plane strain, κ the plate curvature, and N and M are the force and moment matrices respectively. The [A], [B] and [D] matrices are laminate stiffness and are temperature dependent, the incremental recovery stress resultants [Nr ] and [Mr ] depend upon prestrain, temperature and volume fraction of SMA, and [Nσ ] and [Mσ ] are the initial stress resultants due to the initial stress vector {σ0 }. In case of large thermal deflection, the in-plane strain {0 } and the curvature {κ} vectors are defined using the von-Karman strain-displacement relations [13]:   2    /2  u,x  w,x w,x w0,x  2 /2 + u,y w,y w0,y {0 } = + w,x    2    u,x + u,y w,x w0,y + w0,x w,y w,x /2  

{0 } = {0m } + {0b } + {0o }    −w,xx  {κ} = −w,yy   −2w,xy

{} = {0 } + z{κ} here u, v and w are in-plane and transverse displacements measured from initial position (u0 , v0 , w0 ).

3. SMA WIRE CHARACTERIZATION WITH ECTE MODELING The phase transformation of the SMA from Ms to Af is modelled as an Equivalent negative Coefficient of Thermal Expansion (ECTE) αec since the wire shrinks due to heat initiated phase transformation. The FE modeling for this behaviour can be easily done with αec , and Elastic modulus (αc (T ), E(T)) information. This modeling technique was first proposed by Turner [14]. Equation (3) gives the free strain (f ) produced in the SMA wire upon heating (it is typically 3 to 5% of its initial length ). αec is calculated from equation (4) with a prestrain value. f =

xf = αc (T − T0 ) L Z T = αec (τ )dτ

T < As

(3)

T > As

As

The relationship between αc and σr is given by, T

Z

αec (τ )dτ = − As

σr (T, 0 ) E(T )

(4)

4. EXPERIMENTAL SETUP 4.1 Determination of Phase transition temperatures To obtain the phase transformation temperatures a Differential Scanning Calorimeter (DSC) test was performed using PerkinElmer equipment on SMA HT375 sample (wire diameter 375 µm). The sample was subjected to temperatures from 0o C to 130o C at the rate of 10o C per minute. The sample was held for a minute and then cooled to 0o C at the same rate. The obtained results are shown in figure (2). The Austenite transformation in the first cycle occurred at a higher temperature (As = 82.9, Af = 87.5◦ C) than the next consecutive cycles due to some amount of pre-strain in the wire. The averaged values from the experiment first cycle onwards are Mf = 47.5◦ C, Ms = 57.9◦ C, Aso = 76◦ C and Afo = 82.2◦ C. These NiTiNOL wires come pre-strained from the manufacturer and are commercially known as Flexinol muscle wires.

16 14 M = 47.5 f

Heat flow (mW)

12 A

10

f0

o

C, M

s

o

= 82.2 C, A

s

o

= 57.9 C, A

s0

o

= 76 C

o

o

= 82.9 C, A = 87.5 C f

8 6

As0

4

Af Af0

2

As

Mf

0

Ms

-2 -4 0

20

40

60

80

100

o

Temperature ( C)

Figure 2: Heat flow variation v/s temperature in SMA wire (375 µm diameter)

4.2 Variation of elastic modulus (E) vs temperature (T) The tensile test was conducted on a Tinius Olsen machine with a loading rate of 0.6 mm/min. In the 1st , 2nd and 3rd cycle, the specimen was loaded to 30 N, 60 N and 90 N respectively. figure (3a) shows the tensile test result for the SMA wire at room temperature. The same test was carried out at different temperatures and the variation of elastic modulus over the temperature range of 25-160o C is shown in figure (3b). E(T) and σr are used to calculate the ECTE using equation (4).

80

140 Gauge length = 52 mm o

Rate of loading = 0.6 mm/min @ 25 C

Elastic modulus (GPa)

Stress (MPa)

120

100

80

60

40

70 60 50 40 30

20

20

0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Strain (%)

(a) Tensile testing for 4 cycles

3.5

0

20

40

60

80

100

120

140

160

o

Temperature ( C)

(b) E and α variation with temperature in SMA wire

Figure 3: Tensile test result and E variation corresponding to α (wire diameter 375µm)

4.3 Composite Mechanical Properties To obtain the material properties of the woven E-glass fiber and its composite with silicone laminate a uniaxial tensile test was carried out on the Instron 1195 Universal Testing Machine. The plain E-glass fiber sample was of an area of 23.34mm2 , and loaded axially at a strain rate of 2mm/min at room temperature.The behaviour obtained is shown in figure (5). The same test was carried out for a silicone laminated woven E glass fiber specimen of 25mm2 area and at a strain rate of 5mm/min. The strain rate was increased considering the tensile properties of silicone. The results are compared against the non-laminated fiber in the same figure (5)

(a) E-Glass Fiber

(b) Silicone+E-Glass Fiber

Figure 4: Plain fiber and composite specimen under tensile test

Initially, plain glass fiber specimen is tested attaining the peak stress of 10.71 MPa. This is followed by subjecting the silicone laminated woven E-glass fiber to the tensile test achieving a peak stress of 28.38 MPa. Thus there has been about 165% increase in peak stress capability as shown in figure (5). This is due to the fact that the matrix is yielding and deforming plastically while the fibers are continuing to stretch elastically since the tensile strength of the fiber is significantly higher than the yield strength of the matrix.

35

True Stress (MPa)

30

E-glass fibre+ Silicone E-glass fibre

25 20 15 10 5 0

0

5

10

15

20

25

True Strain (%)

Figure 5: True stress-strain curves for woven E-Glass fiber and Silicone laminated E-glass fiber Since there is always considerable variation in the fracture strength of brittle fiber materials, hence all fibers do not fracture at the same time. Additionally, even after fiber failure, the matrix still remains intact and the fractured fibers, which are shorter than the non-fractured ones, are still embedded inside the intact matrix, and are hence capable of sustaining a diminished load as the matrix continues to plastically deform. In the Silicone laminated E-glass fiber composite the volume fraction of glass fiber in the composite, vf , is 0.35, whereas for the matrix, vm , which is silicone, is 0.65. Since the sample was vacuum degassed hence it is assumed that there are no voids. The results of the test are tabulated in Table (1). Table 1: Parameter comparison of tensile test Composite Parameter E-glass fiber (E-glass fiber with silicone matrix) Peak stress (MPa) 10.71 28.38 Peak load (kN) 0.25 0.71 Yield load (kN) 0.203 0.321

4.4 Specimen Fabrication An alignment frame device made of aluminium as shown in figure (6) was designed and fabricated to ensure that during the curing of the composite the wires stayed longitudinally straight with the desired spacing between them. The design consists of an enclosure with movable plates inside to grip and strain the wires. The wire is kept between the vertically movable (and detachable) plates and fixed. Then the horizontal slider plates are pulled back until the wire is taut and their motion is constrained. M4 bolts are used for this purpose and the thread length and grip length are different in both directions and chosen to maintain the movable distance without interference. A sample with a maximum dimension of 185mmx60mm can be fabricated using this fixture, however, the size can be reduced by moving the adjustable plates. The crucial feature of this novel design is the successful embedding of SMA wires bi-directionally in the composite. Since the wire procured from the manufacturer was already pre-strained hence no memory training was required. For the first sample as shown in figure (7a) of the glass-silicone host one ply of multi-axial fiber orientation

(weave) E-glass fiber was laminated with silicone. The sample was of the dimension of 60.61mm x 54.77mm x 1mm. The SMA wires were placed at a distance of 3mm from each other on the top of the sample, strained using the moving plates of the fixture. The SMA wire is 1m in length embedded continuously in a digitated pattern as shown in figure (7a).

(a) Top view of fixtue with embedded composite

(b) Front view of fixtue

Figure 6: Fixture design and fabrication The fixture with the sample was then placed in a vacuum degassing chamber and left to cure for 4 hours at room temperature. No external load was applied during the curing process and the sample was cured under the vacuum pressure of 30mmHg. The final thickness obtained was of 1.04mm. The properties of SMA wire, silicone and the glass fiber are given in Table (2), (3), and (4) respectively. The same procedure was then followed for the sample with two-layers of SMA wire reinforcements. The SMA wire embedded 3mm apart in this sample was of 300µm diameter. The ply configuration for this sample was [SMA 00 /E Glass/SMA 900 /E Glass] in silicone matrix. The sample configuration for the same is shown in figure (7b). The sample when removed from the vacuum degassing chamber was cleaned of extra silicone rubber displaced due to high degassing pressure. Finally, the loose ends of the wire were cleaned and crimped to the wire connecting it to a 30V-2A DC supply. The sample dimensions for sample with two layers of SMA wire reinforcement were 62.28mm x 60.64mm x 2.24mm. Table 2: Flexinol HT90 SMA Wire properties Wire Diameter(µm) Resistance(Ω/m) Recommended Pull Force (N)

Table 3: Silicone Type Service Temperature Range (o C) Curing Temperature Cure Time(hrs) Pot Life(min.) Mixed Viscosity(cps) Specific Gravity(gm/cm3 ) Specific Volume(cm3 /gm) Tensile Strength(MPa) 100% Modulus(MPa) Elongation at break(%)

for 1m 250 18.5 8.74

wire with 3-5% deformation 300 375 12.2 8.3 12.55 22.06

Properties Dragon Skin 20 -53 to +232 Room Temperature(23o C) 4 25 20000 1.08 0.925 3.8 0.34 620

Table 4: E-Glass Fiber Properties Variety 13 MIL Fiber Glass Fabric Type of weave 4-H Satin Thickness (mm) 0.35 Width(mm) 150 Warp: 48 threads/inch Construction Weft: 32 threads/inch Weight per sq. mtr. (gms.) 442.50 Warp: 336 kgs Breaking Strength per 50mm Weft: 242 kgs

(a) One layer of SMA wire reinforcement

(b) Two layer of SMA wire reinforcement

Figure 7: Schematic of SMA embedded composite The entire setup to measure the voltage dependency of deflection of the sample is as shown in figure (8a). The sample was fixed on one side and a single point laser sensor ILD1420 (from Micro-Epsilon) was focussed at the centre of the sample tip to measure the vertical displacement. The voltage data from the DC supply was acquired using a single channel from dSpace CLP1103 and saved using its inbuilt software dSpace Control Desk. The data acquisition of the sensor output was done from its inbuilt software ILD1420. A voltage splitter was used before sending the data directly into dSpace and Vin was calculated from the recorded Vout .

(a) Experimental setup for one layer SMA embedded composite test

(b) Experimental setup for two layer SMA embedded composite test

Figure 8: Experimental setup for measurement of volatge dependant composite deflection

(a)

(b)

(c)

(d)

(e)

(f)

Figure 9: Deflection profile of single layer SMA composite Four tests for the same sample were done and the averaged result showed a linear relation between the voltage increase and the deflection obtained. The results obtained from these experiments are discussed in the next section. The same test was again conducted afterwards and through image processing (as shown in figure (9)) the maximum deflection of the composite tip was calculated which came to be same as obtained from the single-point-laser sensor data. We next conducted the tests on a silicone-glass composite embedded with two layers of SMA wires as shown in figure (7b). On giving current to either of the SMA layer, the composite showed a bidirectional bending but with different amount of deflection depending on whcih layer was actuated. To understand this behaviour we used image processing, capturing images from the three free sides of the sample at a time for fixed voltage points. The sample was fixed on one side perpendicular to the orientation of the wire which was being actuated. The experiment was set up as shown in figure (8b), where the images were captured from side A, B, and C when the second layer of embedded SMA was actuated and side D was fixed; also from the side B, C, and D when the first layer of embedded SMA was actuated and side A was fixed. Due to the bi-directional bending of the sample, it was not possible to record this behaviour using one or multiple single-point-laser sensor as the data was inconsistent; the results obtained through image processing are discussed in the next section.

5. RESULTS AND DISCUSSION 5.1 Single layer SMA embedded smart composite E-glass/silicone beam with low flexural rigidity was expected to show substantially high deflection. Due to this fact it was expected to also give a curvature hence forming a half cylindrical shape. An averaged deflection summary of all tests is shown in fig (10). Figure (10a) shows a typical tip-deflection time curve and the voltagetime curve for sample with single layer SMA wire. A reverse phase transformation was complete in 25-28 seconds and the maximum deflection obtained was of an average 45mm. The cooling was allowed to happen naturally

at room temperature. Since the service temperature range of the silicone used as matrix is −530 C to +2320 C hence the actuation of wire at 900 C did not affect the properties of the material. The shortest duration for the sample to achieve an asymptote was around 21s. The voltage (V) and sample tip displacement (d) relation is shown in figure (10b) and the best curve fit equation for the same is:

V = 0.05117 + 0.03294d + 0.01681d2 + 0.01071d3 − 0.0011d4 + 4.277 × 10−5 d5 − 7.368 × 10−7 d6 + 4.765 × 10−9 d7

50

16

14

Tip displacement

14

40

lin g

20

6

10 0

Voltage (V)

o

8

Experimental data

Voltage (V)

o

He atin g

30

10

0

10

20

30

40

50

Cooling

12

12

C

Tip displacement (mm)

Voltage

10

Polynomial fit

Heating

8 6

4

4

2

2

0

0

0

10

20

30

40

Displacement (mm)

Time (s)

(a) End tip deflection

(b) Beam deflection

Figure 10: Top fiber tip deflection of single layer SMA embedded composite The voltage was increased linearly with two pauses at 12V and 14.3V. These pauses were to verify the possibility of shape control in future work by controlling the voltage source and hence the current flow. The displacement shows a linear behaviour with respect to voltage variation. An average of 4mm of residual displacement of tip is observed and is caused due to factors as sample rigidity, deformation of sample due to heating and wire-composite debonding after multiple test cycles. Figure (11) shows the results from the image processing of the same sample. A total of 5 different tip deflections of the sample were recorded and a maximum of 45mm of tip deflection was observed which matched the results obtained from single point laser sensor. The maximum voltage to which the wires were actuated was 14V at which the sample would maintain a constant deflection and curvature. The curvature calculated for maximum deflection comes out to be 15 corresponding to 14V.

Beam deflection (in mm)

45 40 35

Deflection increasing with voltage

30 25 20 15 10 5 0

0

10

20

30

40

50

Beam length (in mm)

Figure 11: Beam deflection profile with increasing volatge for single layer SMA reinforcement

5.2 Two layer SMA embedded smart composite The experimental setup for capturing the deflection behaviour of the sample is shown in figure (7b) is discussed in the previous section. The images were taken for 7 different voltages when the first layer of embedded SMA wire was actuated and for 8 different voltages when the second layer of embedded SMA wire was actuated in the composite. The final value was chosen upon observing that the deflection and curvature of the sample was constant and did not change thereafter. The behaviour of the bi-directional SMA wire reinforced composite was interesting since actuating the first layer of embedded SMA wire which is laminated on the top and could dissipate heat to the surroundings led to lesser heat reaching the second layer of embedded SMA wire, whereas when the second layer of embedded SMA wire was actuated more heat was dissipated towards the first layer, it being embedded between glass fibers on both sides and unable to dissipate heat to the surrounding. This cause led to the behaviour change of the composite depending upon which layer of embedded SMA was actuated. The sample showed a considerable bidirectional bending and curving when the second layer of embedded SMA was actuated, hence figure (13f) is of importance to us. Figures (13a), (13b), and (13c), show the top fiber tip deflection of the composite when the first layer of embedded SMA is actuated and the result is captured from side B, C, and D respectively (refer figure (8b)). The trend of this result is very similar to the results obtained from first sample consisting of single layer embedded SMA. On side B a maximum of 22.7mm of deflection was observed, whereas on side D it reduced to 20mm which is caused due to partial excitation of second layer of embedded SMA and hence pulling down of top fiber tip on side D in the process. But since the deflection is only of 2.7mm hence the bi-directional behaviour observed in this case was not very significant. Figures (13d), (13e), and (13f) give the top fiber tip deflection of the composite when the second layer of embedded SMA in the composite is actuated. As we can observe in figure (13d) the maximum tip deflection obtained is of negative value, -8.8mm (in the negative x direction) when recorded from side A, but interestingly as the current flow increases leading to increase in the temperature of the embedded SMA wire the deflection starts in the opposite direction due to the activation of the first layer of embedded SMA wire as well. The deflection observed is of 3.3mm in opposite direction.

Figure 12: Bidirectional bending of the Active Bimorph Composite Figure (13f) shows this bidirectional behaviour clearly, where the top fiber tip on side A shows a deflection in negative x-direction whereas the top fiber tip on side B shows a deflection in positive x direction. This is caused due to bending of top layer upon actuation of the first layer of embedded SMA as shown in figure (12). Hence the sample is first curved about its x-axis and then about z-axis giving us an Active Bimorph Composite Structure.

30 25

12V

25

14V 16V 16.5V

20 15 10 5 0

6V 10V

Deflection (mm)

Deflection (mm)

30

6V 10V 12V

14V 16V 16.5V

20 15 10 5

0

10

20

30

40

50

0

60

0

10

Side length (mm)

20

30

40

50

60

Side length (mm)

(a)

(b)

30

10

6V

6V

12V

12V

14V

6

16V

16V

16.5V

Deflection (mm)

Deflection (mm)

25

10V

8

10V

20 15 10

18V

4

20V

2 0 -2 -4 -6

5

-8

0

0

10

20

30

40

50

60

-10 0

10

Side length (mm)

20

30

(c)

50

60

(d)

Deflection (mm)

30 6V

25

10V 12V 14V

Deflection (mm)

40

Side length (mm)

20

16V 18V 20V

15

20

6V

15

12V

10V

14V 16V

10

18V 20V

5

0 -30

-20

-10

0

10

20

30

-5

10

Side length (mm)

-10

5 0

-15

0

10

20

30

40

50

60

-20

Side length (mm)

(e)

(f)

Figure 13: Deflection profile of Active Bimorph Composite with two layers of SMA reinforcement

6. CONCLUSION The fabrication and behaviour of an Active Bimorph Composite Structure is studied in this paper. The results of bidirectional bending have been observed and recorded. This behaviour of composites finds useful application in the field of rigidization of membrane like deployable structures, morphing of airfoils, shape control, and many other such fields. The limitations of this structure are the continuous and optimum requirement of current based on varying resistance of the wire, multi-layer insulation for space applications, and challenging commercial fabrication. Further work can be done in the evaluation of silicone-SMA wire bonding strength at varying temperatures.

7. ACKNOWLEDGEMENT The authors acknowledge partial support of this research from ISRO-Space Technology Cell; Sponsored project ME/IITK/2014086.

REFERENCES [1] Cadogan, D. and Scarborough, S., [Rigidizable materials for use in Gossamer Space Inflatable Structures], Fluid Dynamics and Co-located Conferences, American Institute of Aeronautics and Astronautics (June 2001). [2] Freeland, R. E., Bilyeu, G. D., Veal, G. R., and Mikulas, M. M., [Inflatable Deployable Space Structures Technology Summary], IAF 49th Congress, Melbourne, Australia (2004). [3] Lou, M. C. and Feria, V. A., “Development of space inflatable/rigidizable structures technology,” IUTAMIASS Symposium on Deployable Structures: Theory and Applications: Proceedings of the IUTAM Symposium held in Cambridge, U.K., 6–9 September 1998, 251–260, Springer Netherlands, Dordrecht (2000). [4] Hoyt, A. E., Harrah, L. A., Sprouse, M. R., Allred, R. E., McElroy, P. M., Scarborough, S. E., and Cadogan, D. P., “Light curing resins for rigidizing inflatable space structures,” Proceedings of 49th International SAMPE Symposium and Exhibition , Society for the Advancement of Material and Process Engineering, Longbeach, California (May 2004). [5] Allred, R. E., Hoyt, A. E., McElroy, P. M., Scarborough, S. E., and Cadogan, D. P., “Uv rigidizable carbonreinforced isogrid inflatable booms,” Proceedings of 43rd Structural Dynamics, and Materials Conference (April 2002). [6] Lendlein, A. and Kelch, S., “Shape-memory polymers,” Angewandte Chemie International Edition 41(12), 2034–2057 (2002). [7] Zhou, G. and Lloyd, P., “Design, manufacture and evaluation of bending behaviour of composite beams embedded with sma wires,” Composites Science and Technology (13), 2034 – 2041 (2009). [8] Jia, J. and Rogers, C. A., “Formulation of a mechanical model for composites with embedded sma actuators,” Journal of Mechanical Design 114, 670–676 (Dec 1992). [9] Kalra, S., Bhattacharya, B., and Munjal, B. S., “Design of shape memory alloy actuated intelligent parabolic antenna for space applications,” Smart Materials and Structures 26(9), 095015 (2017). [10] Yoo, E.-J., Roh, J.-H., and Han, J.-H., “Wrinkling control of inflatable booms using shape memory alloy wires,” Smart Materials and Structures 16(2), 340 (2007). [11] Sippola, M. and Brander, T., “Adaptive composite structures in shape control applications,” Journal of Structural Mechanics 40(1), 65–79 (2007). [12] Zhong, Z., R. Chen, R., Mei, C., and Pates III, C., “Buckling and postbuckling of shape memory alloy fiber-reinforced composite plates,” 41, 115–132 (01 1994). [13] Duan, B., Tawfik, M., Goek, S. N., Ro, J. J., and Mei, C., “Analysis and control of large thermal deflection of composite plates using shape memory alloy,” in [Smart Structures and Materials 2000: Industrial and Commercial Applications of Smart Structures Technologies ], Jacobs, J., ed., procspie (June 2000). [14] Turner, T. L., “A new thermoelastic model for analysis of shape memory alloy hybrid composites,” Journal of Intelligent Material Systems and Structures 11(5), 382–394 (2000).