Bistable metallic materials produced by ...

Materials and Design 141 (2018) 374–383

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Materials and Design journal homepage: www.elsevier.com/locate/matdes

Bistable metallic materials produced by nanocrystallization process Shenghui Yi a,c, Xiaoqiao He a,c, Jian Lu b,c,⁎ a b c

Department of Architecture and Civil Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China Centre for Advanced Structural Materials, City University of Hong Kong Shenzhen Research Institute, 8 Yuexing 1st Road, Shenzhen Hi-Tech Industrial Park, Nanshan District, Shenzhen, China

H I G H L I G H T S

G R A P H I C A L

A B S T R A C T

• Bistable rectangular shells with two stable symmetrical configurations are obtained. • The stable configurations can be further modified to obtain complex configurations. • Multistable shell is obtained with many localized nanocrystallization regions.

a r t i c l e

i n f o

Article history: Received 14 November 2017 Received in revised form 21 December 2017 Accepted 4 January 2018 Available online 05 January 2018 Keywords: SPD Nano grain Residual stress Bistable shell Finite element analysis

a b s t r a c t Through a localized nanocrystallization process using surface mechanical attrition treatment (SMAT), a new method is proposed to build bistable and multistable metallic shells. The impacts from randomly fast-moving balls during the nanocrystallization process accumulate plastic deformations, which induce nanotwins and mesh grains into nanoscales significantly increasing elastic behavior range of the treated shells. The in-plane self-equilibrium residual stress field, which is induced from the stretching plastic deformations in the treated region under the constraint of the untreated region, renders nanostructured shells bistable characteristics. An effective numerical modelling is carried out to analyze the bistable behavior and predict their stable configurations. A flat plate with multiple nanostructured regions is manufactured and numerically studied, which is capable of holding multiple stable configurations. In addition, the developed bistable and multistable shells can be further mechanically processed to modify their stable configurations. © 2018 Published by Elsevier Ltd.

1. Introduction Different from shape memory materials [1–3], bistable materials are manufactured based on their own mechanical properties [4,5] rather than material properties [6] to have two different stable configurations. No energy or support is compellingly required to hold transitioned ⁎ Corresponding author at: Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China. E-mail address: [email protected] (J. Lu).

https://doi.org/10.1016/j.matdes.2018.01.010 0264-1275/© 2018 Published by Elsevier Ltd.

shapes. Based on different mechanisms, conventional bistable composite shells can have different stable configurations [7–10], such as antisymmetric composite shells having two cylindrical configurations curving in one same side [11], unsymmetrical composite having two cylindrical states curving in different directions and sides [12]. The stable configurations can be designed in some extent during their manufacture by controlling laminate's layups, including transverse layups [13] and in-plane layups [14–16]. Tristable composite shells are achieved by selecting special initial configurations and proper material properties [17,18]. The nonlinear geometrical deformations play a critical role in

S. Yi et al. / Materials and Design 141 (2018) 374–383

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Fig. 1. SMAT setup. (a) Schematic illustration; (b) Zirconia ceramics balls (25 g) in SMAT chamber of 35 mm height in experiment.

the bistable characteristic to have two different stable states [19]. Those bistable shells are proposed to be combined together by joints to achieve discrete multistable structures [20,21]. Biasing strips are used to connect bistable unsymmetrical shells in one direction to approach multiple smooth configurations [22]. But it is failed to have bistable composite shells tessellated in plane for designable multistable shells and only two stable configurations can be held by the tessellated composite shells [23]. Besides anisotropic composite materials, isotropic metallic materials and soft materials are applied to build bistable shells, which are easily noticed, such as bistable rubber caps [24,25], hair clips, curving wet papers [26], and so on. The nonlinear coupling between stretching and bending deformations enables spherical rubber caps to hold reversed states, which can even automatically return to the initial stress-free state if the caps are with considerable viscoelastic properties [27,28]. Bistable metallic shells are obtained by plastically bending in two orthotropic directions [29]. Owing to isotropic material properties, neutrally stable shells with no torsional stiffness are further achieved by carefully processing plastic deformations [30]. Tristable corrugated metallic shells are proposed by combining two different bistable mechanisms [31]. Inspired by bistable caps, snapping surfaces with microarrays of spherical caps [32] and dimpled ultrathin metallic sheets [33] are manufactured with alternative configurations. Bistable and multistable materials are promising for engineering applications, especially in aerodynamic field [34]. Morphing wings have been experimentally built with bistable composite shells to adjust aerodynamic response using two different stable configurations [35], which can also help to increase efficiency of other vehicles. Energy harvester built from bistable materials can have higher efficiency and be capable of operating over wider frequency [36]. Bionic trapping robot [37] has been proposed based on Venus Flytrap's [38] natural bistable phenomenon.

Although there are various bistable shells with different stable configurations, it is still difficult to obtain bistable or multistable shells in complex configurations. A lot of effect has been spent to alter configurations of bistable shells [39,40]. There is no applicable method to obtain bistable or multistable shells with designable configuration. 2. Bistable shells using SMAT 2.1. Proposed method to build bistable shells SMAT is well applied to develop materials with high performance via physical treatments using fast moving balls to impact on the surface of metallic materials [41–45], and the setup is shown in Fig. 1. The highspeed moving balls obtain kinematic energies from a sonotrode and transit the energies into the treated material via random impacts, which induce nanotwins and mesh metallic material grains into nanoscales [41]. Simultaneously, residual stresses and plastic deformations are induced [42]. If a plate is entirely processed with SMAT, the plate stretches in-plane and shrinks transversely [46]. An in-plane uniform and transversely gradient residual stress field is left and the plate keeps a monostable flat configuration with negligible curvatures [42]. The orthotropic moments from residual stresses under the mechanism of unsymmetrical bistable composite shells [12,13] and bistable prestressed isotropis shells [19,29] cannot be achieved using the SMAT process. Also, the developed analytical model showed that the bistable mechanism in bistable antisymmetric composite shells does not work for isotropic shells [11]. Here, a new mechanism named as stretching mechanism is proposed to develop bistable shells using SMAT. It is well known that thin plates buckle transversely under in-plane compressions. However, there are no external supports or forces on bistable shells, and the two stable configurations should be held by their own mechanical properties. The stretching mechanism is to use

Fig. 2. Bistable shells with a sole elliptic SMAT region. (a) The original flat plates with an elliptic SMAT region formed by adhesive tapes; (b) The developed bistable shells with SMAT process on both surfaces for 420 s.

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Fig. 3. Deflections along x-axis in the stable configurations of the developed bistable shells measured by Form Talysurf PGI.

in-plane internal forces to buckle originally flat plates for obtaining bistable shells. Unlike conventionally applied SMAT process with samples entirely processed, the stretching mechanism is to use SMAT to locally treat plates on both sides by turns. When the plate surface becomes nanostructured with the random impacts in the process, severe plastic deformations accumulate and stretch the plate in the treated region. Internal compressive stresses are induced under the constraint from untreated regions with the accumulated plastic deformation. In contrast to the in-plane uniform and transversely gradient residual stress field left in plates after conventional SMAT processes [42], a three-dimensional residual stress field is induced after the localized treatment. When enough plastic deformations are accumulated, the compressive internal forces transversely buckle the plate in two directions and enable the processed shell to hold two different stable configurations even though there is no external support or force exerted on the shells. It should be emphasized that, the largely increased elastic deformation ability of the processed shells due to nanocrystallization is necessary for this bistable behavior, or the transitions between two stable configurations would lead to further plastic deformations which impede bistabilities.

2.2. Experimental work 304 stainless steel plates are used to develop the proposed bistable shells. The 304 stainless steel plates of 0.46 mm thickness are directly cut into 320 × 50 mm2 rectangular plates. Then adhesive tapes are stuck onto the untreated region on both sides to form the designed treating region. In this case, the SMAT region is an elliptic area with major radii r1 and minor radii r2, as shown in Fig. 2. During the SMAT process, two sides of the plate are treated for 10 s by turns to induce plastic deformations little by little using the same processing parameters, including the number and diameter of the used balls, the power, and the height of the chamber. To limit the difference of the accumulated plastic deformations during SMAT process due to the hardening effect of the used small balls from impacts, zirconia ceramics balls are used instead of commonly used stainless steel balls [43]. The plate keeps monostable flat state at the beginning of the treatment, and then becomes bistable to hold two curved stable states with the processed region capping down or up. When the plate becomes bistable, it is quite sensitive to external load and easy to transit into the other stable state. Also, the deflections of the shell are very small. With the further

Fig. 4. A symmetric plastic strain field induced in the SMAT process is replaced by an equivalent uniform plastic strain field in the numerical simulations. (a) Schematic of one impact from a perpendicularly moving ball on a solid material; (b) Assumed plastic strain field after the SMAT process along transverse direction; (c) Equivalent uniform plastic strain field; (d) Plate with an elliptic SMAT region in the numerical model.


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Fig. 7. Two stable configurations of the developed bistable shell with a sole elliptic region treated with SMAT for 420 s. (a) Stable configurations from experiments; (b) Stable configurations from the numerical simulations with εp = 1700 × 10−6. Fig. 5. The maximum deflections in equilibrium states with respect to the increasing applied equivalent uniform plastic strain for the developed shell with an elliptic SMAT region with r1 = 100 mm, r2 = 20 mm.

treatment, the deflections increase and the developed bistable shell becomes more capable of holding two stable configurations. The developed shells with the SMAT process for 420 s on both surfaces are shown in Fig. 2. The shell surface in the treated region becomes nanostructured and is less smooth compared with the untreated region, and the deflections of the stable configurations with different nanostructured regions are varied. The deflections along x-axis in the stable configurations are accurately measured by Form Talysurf PGI, which is designed to measure surface's roughness with an accuracy of dozens of nanometers for deflections, using a probe with an applied force of about 1 mN, as shown in Fig. 3. 3. Numerical simulation to predict stable configurations The numerical simulation using a commercial FEM software, ABAQUS, is used to predict the stable configurations. Though the entire SMAT process can be simulated using solid elements with existing plastic constitutional models [47], such as Johnson-Cook's material model, and the measured parameters, including the velocities, travelling angles of the balls and so on [43] in SMAT process, this numerical simulation is cumbersome and time consuming. With the assumptions that the stress field in the elastic impact is only induced by elastic contacts and the deceleration of the moving ball causes the normal force only, the dynamic loading in the impact from a perpendicularly moving ball can be

Fig. 6. Numerical results from modelling with different element densities for the maximum deflections of bistable shell with an elliptic SMAT region with r1 = 100 mm, r2 = 20 mm.

replaced by a static pressure in the contacting circular region [48] as P ðr Þ ¼ P 0

pffiffiffiffiffiffiffiffiffiffiffiffiffiffi a2 −r 2 a

ð1Þ

where geometrical parameters a and r are shown in Fig. 4(a). P0 is the maximum pressure calculated as [48] 2=3

2=3

P 0 ¼ 0:7213EH F 1=3 n dB =π

ð2Þ

where dB is impacting ball diameter and EH is the equivalent modulus. Fn is the maximum normal force expressed as [48] 2

6=5 2=5

F n ¼ dB ð2:5πρB Þ3=5 vB ES =6

ð3Þ

where vb and ρB are the velocity and density of the ball, and ES is the Young's modulus of the solid material. The depth of the plastic zone induced by the impact, as shown in Fig. 4(a), can be obtained as [49] 1=4 1=4 3ρB v2B 2 hp ¼ 3 dB 3 2P 0

ð4Þ

During the SMAT process, small balls impact on plate's surface with random oblique directions. As the fast moving balls randomly impact on the treated region, the induced plastic deformation is reasonably assumed to be in-plane uniform [42]. Due to the SMAT process on both surfaces of the plate by turns, the plastic deformations induced from impacts are transversely gradient and should be symmetric with respect to

Fig. 8. Deflections along x-axis in stable configurations of the developed bistable shell with an elliptic SMAT region with r1 = 100 mm, r2 = 20 mm.

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Fig. 9. The in-plane residual stress field in stable configurations from the numerical simulation. (a) The von mises stress field in the middle plane; (b) Three average shell section stress components along x-axis; (c) Three average shell section stress components along y-axis.

the middle plane (z = 0) of the plate [46], which result in gradient and symmetric stimulating stresses, as shown in Fig. 4(b). According to general plate theories, symmetric stimulating stress fields do not result in moments. Only stimulating in-plane forces are induced on the plate. So the stimulating stress field can be simplified by an equivalent uniform stimulating stress field which is induced by a uniform plastic deformation, as shown in Fig. 4(c). To largely reduce the resource required in the numerical simulation, shell elements were adopted with the assumption of an equivalent uniform plastic deformation within the treated region, as shown in Fig. 4(d). The shrinkage of the thickness in the treated region was ignored, as only about 10 micro shrinkage in 0.46 mm thickness was found in the experiments. Furthermore, the uniform plastic deformation was modelled via a permanent uniform thermal field with εp = εT. As the yield strength of the treated material is largely increased after the SMAT process [43], the transitions between two stable states would not bring further plastic deformation to the developed bistable shells. Thus, the shell is simulated as an elastic material with the Young's modulus E = 192 GPa and Poisson ratio μ =

0.29. To obtain different stable configurations for bistable shells, the applied uniform thermal strains are loaded by two steps in the SMAT region. To make the processed area caped down, the uniform thermal strains are firstly applied to the bottom part (z b 0) of the plate and then the strains are applied to the top part (z N 0). Otherwise, the uniform thermal strains firstly applied to the top part would result in the processed area capping up. 4. Results and discussion on bistable properties 4.1. Two stable configurations In the numerical modelling, the applied equivalent uniform plastic deformation increases from zero to a certain value and the maximum deflection at plate center is recorded to determine the specific equivalent plastic strain value by comparing the maximum deflections of the plate in experiments, as shown in Fig. 5. S4R reduced integration shell element is selected in the numerical simulations and the numerical

Fig. 10. The in-plane residual stress field in the unstable but equilibrium flat state from the numerical simulation. (a) The von mises stress field in the middle plane; (b) Three average shell section stress components along x-axis; (c) Three average shell section stress components along y-axis.


Fig. 11. Deflections along x-axis in stable configurations of the developed bistable shells with a sole elliptic SMAT region in different sizes.

results for the bistable shell modelled with different mesh densities are shown in Fig. 6. The average element size of 0.8 mm is selected for the applied numerical models considering the accuracy and efficiency of computation resource. Theoretically, there exists an unstable equilibrium flat state for the developed bistable shells, which is easily captured by numerical simulations but difficult to be observed in experiments. In this case, both surfaces of the plate are treated with SMAT for totally 420 s and the corresponding equivalent uniform plastic strain εp is 1700 × 10−6. The final stable configurations from the numerical modelling and experiments are shown in Fig. 7, and the deflections along x-axis are shown in Fig. 8. The results show that the numerical predictions are in good agreement with the experiment for stable configurations. 4.2. Residual stress field The in-situ residual stress field which enables the plate to hold two different stable configurations is difficult to measure. Thus, the in-

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plane residual stress field from the numerical simulation using shell elements is adopted, and three average shell section stress components along two middle lines in a stable configuration are shown in Fig. 9. The processed region is in compressive state for the plate in the equilibrium but unstable flat state, as shown in Fig. 10, but some parts near the center enter into tensile state due to the formed curvatures in stable configurations, as shown in Fig. 9. The untreated region is in a tensile state no matter the developed shell is in the stable configuration or in the unstable equilibrium flat state. The residual stress filed has a steep gradient near the boundary between the processed and untreated regions no matter the developed shell is in the stable configuration or in the unstable equilibrium flat configuration. The residual stresses in the treated region are almost in-plane uniform except the area near the boundary. Also, the residual stresses fast decrease from the boundary to the free edges. The average shell section stresses in the stable configuration are much decreased compared with the values in the unstable equilibrium flat state. Due to the symmetry of two stable configurations, the average shell section stress field is same as that in the other stable configuration, but the stresses along transverse direction are reversed with respect to the middle plane of the shell due to the reversed curvatures. 4.3. SMAT process There are many parameters determining the plastic deformations and changes of the microstructures of the treated material after the SMAT process, which are elaborately studied for improving material performance [45]. In contrast to conventional SMAT processes, the thin plates (t = 0.46 mm) are used and the treated region is constrained by the untreated region. The impacting effect can easily penetrate through thin plates from the fast moving balls. The diameter of the used balls should be limited according to the used power, which is indicated in Eqs. (2)–(4), to enable plastic deformations accumulated little by little. Furthermore, the treating time in each turn should be short, especially at the beginning of the process. During the SMAT process, the material in the treated region becomes hardening along transverse direction. If the plate is processed for a long time in one turn, the

Fig. 12. Two stable configurations of the new bistable structure by further plastically bending at two sides of the bistable shell with an elliptic SMAT region with r1 = 3.5 cm, r2 = 2 cm. The SMAT processing time in experiment is 420 s and the equivalent plastic deformation in the numerical simulation isεp = 1700 × 10−6.

380


Fig. 13. Multistable shell with seven circular SMAT regions. (a) The original flat plate with circular SMAT regions formed by adhesive tapes; (b) Several stable configurations of the developed multistable shell with SMAT process on both surfaces for 420 s.

hardening effect would be considerably different for treatments on both surfaces. In fact, the plates could become bistable with unsymmetrical stable configurations, as the induced plastic deformation is not symmetric. This phenomenon indicates that unsymmetrical bistable shells can be obtained by controlling the treating time on both surfaces of the plate. There exists a minimum SMAT treating time to obtain bistable shells for plates with a certain SMAT region. In the numerical simulations, a minimum equivalent uniform plastic strain is required to obtain bistable shells, which is shown in Fig. 5. The deflections increase with the increase of the applied plastic strain. In the experiment, the deflections increase with the treating time of the nanocrystallization process. 4.4. SMAT region Similar to most conventional bistable shells, residual stress field determines stable configurations, even though a rough in-plane uniform

and transversely gradient residual stress field exists for conventional bistable shells [19]. For the proposed bistable shells, the threedimensional residual stress field induced from localized process renders bistable property to the nanostructured shells, and the stable configurations depend on the SMAT process and treated region. The numerical simulations are carried out to predict stable configurations. The deflections of the developed shells along x-axis with the same SMAT process but different elliptic treated regions are shown in Fig. 11. Usually the maximum deflection of the shell increases with the increase of the nanostructured region until the nanostructured region reaches a certain value. If the nanostructured region is too large, the limited untreated region could not constrain the stretching effect well, which decreases the deflections, as clearly indicated by the predicted deflections of the shells with the ratio of SMAT region equal to 0.75 (r1 = 160 mm, r2 = 24 mm) in Fig. 11. In the experiment, the further increase of the SMAT region for the shell with r1 = 159 mm, r2 = 20 mm slightly decreases the

Fig. 14. Seven symmetric stable configurations of the developed multistable shell with seven circular regions treated with SMAT for 420 s. The white circular regions in the right schematic indicate the treated regions capping up in the corresponding states and the black circular regions indicate the treated regions capping down.


381

Fig. 15. Four predicted symmetric stable configurations of the developed multistable shell with applied uniform equivalent plastic strain εp = 1700 × 10−6 from numerical models.

maximum deflection compared with the shell with r1 = 140 mm, r2 = 20 mm, which is consistent with the results from the numerical simulations. On the other hand, a limited SMAT region do not offer a good stretching effect to enable the plate to hold two stable configurations with large curvatures. 4.5. Modified bistable shell by further mechanical process Unlike the mechanism of conventional bistable shells based on an overall nonlinear geometric effect [19], the stretching mechanism relies on a local treatment. As shown in Fig. 9, the stresses in the untreated regions decrease fast into zero from the boundary. The untreated areas have little effect on residual stresses in the treated region. The further process on the nanostructured region away from the boundary only make little effect on the bistable property within the treated region, which make the stretching mechanism promising to obtain bistable shells with complex configurations. Fig. 12 shows two stable configurations of a new bistable structure by plastically folding with a rotation of 90° at x = 0.06 m and x = −0.06 m of the developed bistable shell. The distance between middle points in two short edges of the obtained bistable structure is decreased by 29.0 mm from stable state 1 transiting into stable state 2, and this distance is decreased by 27.9 mm in the numerical simulation. The treated region of the plate acts as a switcher to control the transitions between two stable configurations. 5. Multistable shells using SMAT 5.1. Multistable shell with seven circular SMAT regions The nanostructured region enables the plate to become a bistable shell and the further process in the untreated region away from the processed region has little effect on the localized bistabilities. So the sole nanostructured region can be separated into several parts and each part can cap down or up after the process. With different combinations of the separated nanostructured regions capping down or up, the developed shell can hold multiple stable configurations. In this case, seven circular regions of radii r = 20 mm were formed by adhesive tapes on both sides with spacing d = 5 mm, as shown in Fig. 13(a). Then the plate was processed by turns on both surfaces. The seven circular regions are treated on one surface and then on another surface to induce plastic deformation little by little on those regions. Each circular area is able to hold two stable states after several turns of treatment and the deflections increase with the further treatment. Several stable configurations of the developed multistable shell with the SMAT process for 420 s are shown in Fig. 13(b).

different combinations of the seven circular SMAT regions capping down or up, the developed shell is able to hold various stable configurations, which are well predicted by the numerical simulation as shown in Fig. 15. Only four stable configurations are shown as the other three stable states are symmetric to the first three stable configurations. The measured deflections along x-axis are close to the predicted results from the numerical simulations, as shown in Fig. 16. The deformations of the circular region interplay with the nearby SMAT regions, so the final stable configuration is determined by all the seven SMAT regions. This property makes the stretching mechanism promising to obtain multistable shells with designable configurations. Theoretically there exist 2n stable configurations in which n is the number of separated nanostructured regions on the developed shell. 5.3. Residual stress field The residual stress fields are different in stable configurations, which are shown in Fig. 17 for the four stable configurations from the numerical simulation. The processed regions are always in compressive states for all the stable configurations. This is due to the limited size of the processed region with respect to the thickness. The compressive residual stresses caused by the stretching plastic deformations in the treated regions under the constraints from the untreated regions could not be compensated by the relieved strains from the formed curvatures in stable configurations. The average shell section stress components are minimum in the first stable configurations compared with values in the other stable configurations. The differences among them are small for the four stable configurations, however, the deflections are quite different, as shown in Figs. 14–16. The average shell section stresses in one circular processed region are only affected by the deformations of nearby two circular processed regions. In the first four stable configurations,

5.2. Multiple stable configurations Seven symmetrical stable configurations of the developed multistable shell are shown in Fig. 14 with corresponding combinations of circular nanostructured regions capping down or up. With the

Fig. 16. Deflections along x-axis for the first four stable configurations of the developed multistable shell with seven circular SMAT regions.

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size of separated SMAT regions and then decrease. There is an optimal size and spacing for the developed multistable shell to have the largest deflections under a certain stimulating plastic strain. The numerical simulation gives a good approach for the optimal design of the multistable shells. Of course, the deflections always increase with the increase of the stimulating plastic strain. 6. Conclusion

Fig. 17. The average shell section stress component SSAVG1 (a) and SSAVG2 (b) along xaxis in four stable configurations.

the third and the fifth circular processed regions are capping up, so the residual stresses in the middle circular processed region are the same when this region is capping up in stable states 1 and 3, and the residual stresses are the same when this region is capping down in stable states 2 and 4, clearly shown in Fig. 17(b). Of course, the residual stresses along transverse direction are totally different for SMAT regions capping down and capping up as the curvatures are reversed. 5.4. SMAT regions and their spacings As the size of the sole processed region has a considerable effect on the stable configurations of the developed bistable shells, as shown in Fig. 11, the sizes of the separated treated regions also have an important effect on the multiple stable configurations as well as the spacing between the separated treated regions. Fig. 18 shows the numerically predicted deflections along x-axis in the first stable configuration of multistable shells with seven circular SMAT regions with different sizes and spacings. To make the shell to have seven circular SMAT regions, the radii and the spacing are confined as 2r + d = 45 mm. The deflections of the mulstistable shells first increases with the increase of the

Fig. 18. Deflections along x-axis for the first stable configuration of multistable shells with seven circular SMAT regions in different sizes and spacings from the numerical simulation.

A novel method to achieve bistable and multistable shells is proposed by using the nanotechnology, SMAT, which is studied experimentally and numerically in this study. The results indicate that the residual stresses play a vital role to enable the developed shell to hold different stable configurations. It should be emphasized that the largely increased elastic deformation ability of the treated plates from the nanocrystallization process is necessary for this localized bistabilities, or the further plastic deformation during their shape transitions would impede this bistable property. As all the parameters, including the applied process, sizes and shapes of the treated region and the distributions of the treated regions, can be conveniently controlled, this new method using SMAT offers a promising approach to obtain bistable and multistable shells with designable features. Their stable configurations can be accurately predicted by the proposed numerical modelling. Furthermore, the developed bistable or multistable shells can be further processed by other mechanical modifications. The nanostructured regions can act as a switcher to control their different stable configurations. Acknowledgement The financial supports from NSFC (Ref: 11372264) and the National Key R&D Program of China (Ref: 2017YFA0204403) are gratefully acknowledged. J. Lu and X.Q. He also acknowledge financial supports from the Research Grants Council of Hong Kong (Ref: CityU 114013), the Science and Technology Innovation Commission of Shenzhen Municipality (Refs: ZDSYS201602291653165, JCYJ20160229165310679, JCYJ20150601102053069) and the Guangdong Science and Technology Department (Ref: 2014B050504003). References [1] L. Sun, W.M. Huang, T.X. Wang, H.M. Chen, C. Renata, L.W. He, et al., An overview of elastic polymeric shape memory materials for comfort fitting, Mater. Des. 136 (2017) 238–248. [2] Y.Y.C. Chong, S. Maleksaeedi, H. Eng, J. Wei, P.C. Su, 4D printing of high performance shape memory polymer using stereolithography, Mater. Des. 126 (2017) 219–225. [3] L. Sun, W.M. Huang, Z. Ding, Y. Zhao, C.C. Wang, H. Purnawali, et al., Stimulus responsive shape memory materials: a review, Mater. Des. 33 (2012) 577–640. [4] S. Daynes, C.G. Diaconu, K.D. Potter, P.M. Weaver, Bistable prestressed symmetric laminates, J. Compos. Mater. 44 (2010) 1119–1137. [5] M. Brunetti, A. Vincenti, S. Vidoli, A class of morphing shell structures satisfying clamped boundary conditions, Int. J. Solids Struct. 82 (2016) 47–55. [6] P. Ghosh, A. Rao, A.R. Srinivasa, Design of multi-state and smart-bias components using shape memory alloy and shape memory polymer composites, Mater. Des. 44 (2013) 164–171. [7] A. Pirrera, D. Avitabile, P.M. Weaver, On the thermally induced bistability of composite cylindrical shells for morphing structures, Int. J. Solids Struct. 49 (2012) 685–700. [8] Z. Zhang, H.L. Wu, X.Q. He, H.P. Wu, Y.M. Bao, G.Z. Chai, The bistable behaviors of carbon-fiber/epoxy anti-symmetric composite shells, Compos. Part B 47 (2013) 190–199. [9] L. Giomi, L. Mahadevan, Multi-stability of free spontaneously curved anisotropic strips, Proc. R. Soc. A Math. Phys. Eng. Sci. 468 (2012) 511–530. [10] H. Li, F.H. Dai, P.M. Weaver, S.Y. Du, Bistable hybrid symmetric laminates, Compos. Struct. 116 (2014) 782–792. [11] S.D. Guest, S. Pellegrino, Analytical models for bistable cylindrical shells, Proc. R. Soc. A Math. Phys. Eng. Sci. 462 (2006) 839–854. [12] M.A. Cantera, J.M. Romera, I. Adarraga, F. Mujika, Modelling of [0/90] laminates subject to thermal effects considering mechanical curvature and through-the-thickness strain, Compos. Struct. 110 (2014) 77–87. [13] D.N. Betts, A.I.T. Salo, C.R. Bowen, H.A. Kim, Characterisation and modelling of the cured shapes of arbitrary layup bistable composite laminates, Compos. Struct. 92 (2010) 1694–1700. [14] A.F. Arrieta, I.K. Kuder, T. Waeber, P. Ermanni, Variable stiffness characteristics of embeddable multi-stable composites, Compos. Sci. Technol. 97 (2014) 12–18.

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