Skip to main content
Log in

Dual photo- and magneto-responses of layered beams composed of liquid crystal elastomers and magnetic responsive elastomers

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Wirelessly actuated soft smart materials have great potential applications in real-world actuation and sensing in robotics and biomedical engineering. On the other hand, layered structures can gain more versatile and functional properties then conventional structures. This paper studies the photo- and magneto-responses of a layered beam consisting of liquid crystal elastomers and magnetic responsive elastomers. Based on the finite deformation theory and taking into account the coupling effect of light incidence angle and deformation, governing equation of the layered beam is derived and solved by a new numerical mothed. The results are validated by previous experimental data. It is found that the coupling effect of light incidence angle and the deformation of beam should be taken into account, especially for soft materials with large deformation. For example, neglecting the coupling effect of the light incidence angle and deformation, the maximum deflection of the cantilever beam will be underdetermined by 20.5%, if the light intensity reaches at 1.2 kW/m2. Whether the coupling effect of the light incidence angle and deformation enhances or reduces bending deformation of the beam depends on its boundary conditions and the initial light incidence angle. These results may be useful for designing photo- and magneto-responsive soft robotic and other functional devices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Agrawal, A., Yun, T., Pesek, S.L., Chapman, W.G., Verduzco, R.: Shape-responsive liquid crystal elastomer bilayers. Soft Matter. 10(9), 1411–1415 (2014)

    Google Scholar 

  2. Aharoni, H., Xia, Y., Zhang, X., Kamien, R.D., Yang, S.: Universal inverse design of surfaces with thin nematic elastomer sheets. Proc. Natl. Acad. Sci. U.S.A. 115, 7206 (2018)

    Google Scholar 

  3. Chen, W., Wang, L., Yan, Z., Luo, B.: Three-dimensional large-deformation model of hard-magnetic soft beams. Compos. Struct. 266(15), 113822 (2021)

    Google Scholar 

  4. Chen, W., Wang, L., Peng, Z.R.: A magnetic control method for large-deformation vibration of cantilevered pipe conveying fluid. Nonlinear Dyn. 105, 1459–1481 (2021)

    Google Scholar 

  5. Chen, W., Yan, Z., Wang, L.: On mechanics of functionally graded hard-magnetic soft beams. Int. J. Eng. Sci. 157, 103391 (2020)

    MathSciNet  MATH  Google Scholar 

  6. Chen, W., Wang, L., Yan, Z.: On the dynamics of curved magnetoactive soft beams. Int. J. Eng. Sci. 183, 103792 (2023)

    MathSciNet  MATH  Google Scholar 

  7. Corbett, D., Warner, M.: Nonlinear photoresponse of disordered elastomers. Phys. Rev. Lett. 96(23), 237802 (2006)

    Google Scholar 

  8. Corbett, D., Xuan, C., Warner, M.: Deep optical penetration dynamics in photobending. Phys. Rev. E 92, 013206 (2015)

    Google Scholar 

  9. Cunha, M.P.D., Foelen, Y., Engels, T.A.P., Papamichou, K., Hagenbeek, M., Debije, M.G., Schenning, A.P.: On untethered, dual magnetoand photoresponsive liquid crystal bilayer actuators showing bending and rotating motion. Adv. Opt. Mater. 7, 1801604 (2019)

    Google Scholar 

  10. Dadgar-Rad, F., Hossain, M.: Finite deformation analysis of hard-magnetic soft materials based on micropolar continuum theory. Int. J. Solids Struct. 251, 111747 (2022)

    Google Scholar 

  11. Dadgar-Rad, F., Hossain, M.: Large viscoelastic deformation of hard-magnetic soft beams. Extrem. Mech. Lett. 54, 101773 (2022)

    Google Scholar 

  12. Dehrouyeh-Semnani, A.M.: On bifurcation behavior of hard magnetic soft cantilevers. Int. J. Non-Linear Mech. 134, 103746 (2021)

    Google Scholar 

  13. Diller, E., Miyashita, S., Sitti, M.: Remotely addressable magnetic composite micropumps. RSC Adv. 2(9), 3850–3856 (2012)

    Google Scholar 

  14. Diller, E., Sitti, M.: Robotics: three-dimensional programmable assembly by untethered magnetic robotic micro-grippers. Adv. Funct. Mater. 24(28), 4377 (2014)

    Google Scholar 

  15. Dong, Y., Wang, J., Guo, X., Yang, S., Ozen, M.O., Chen, P., Liu, X., Du, W., Xiao, F., Demirci, U., Liu, B.F.: Multi-stimuli-responsive programmable biomimetic actuator. Nat. Commun. 10, 4087 (2019)

    Google Scholar 

  16. Du, X., Cui, H., Xu, T., Huang, C., Wang, Y., Zhao, Q., Xu, Y., Wu, X.: Reconfiguration, camouflage, and color-shifting for bioinspired adaptive hydrogel-based millirobots. Adv. Funct. Mater. 30, 1909202 (2020)

    Google Scholar 

  17. Feng, W., Broer, D.J., Liu, D.: Oscillating chiral-nematic fingerprints wipe away dust. Adv. Mater. 30, 1704970 (2018)

    Google Scholar 

  18. Ford, M.J., Ambulo, C.P., Kent, T.A., Markvicka, E.J., Pan, C., Malen, J., Majidi, C.: A multifunctional shape-morphing elastomer with liquid metal inclusions. Proc. Natl. Acad. Sci. U. S. A. 116(43), 21438–21444 (2019)

    Google Scholar 

  19. Gelebart, A.H., Mulder, D.J., Michael, V., Konya, A., Vantomme, G., Meijer, E.W., Selinger, R.L.B., Broe, D.J.: Making waves in a photoactive polymer film. Nature 546, 632–636 (2017)

    Google Scholar 

  20. Hauser, A.W., Liu, D., Bryson, K.C., Hayward, R.C., Broer, D.J.: Reconfiguring nanocomposite liquid crystal polymer films with visible light. Macromolecules 49(5), 1575–1581 (2016)

    Google Scholar 

  21. Hellebrekers, T., Kroemer, O., Majidi, C.: Soft magnetic skin for continuous deformation sensing. Adv. Intell. Syst. 1, 1900025 (2019)

    Google Scholar 

  22. Hu, W., Lum, G.Z., Mastrangeli, M., Sitti, M.: Small-scale soft-bodied robot with multimodal locomotion. Nature 554(7690), 81–85 (2018)

    Google Scholar 

  23. Jin, L.H., Zeng, Z., Huo, Y.Z.: Thermomechanical modeling of the thermo-order-mechanical coupling behaviors in liquid crystal elastomers. J. Mech. Phys. Solids 58, 1907–1927 (2010)

    MathSciNet  MATH  Google Scholar 

  24. Jin, L.H., Lin, Y., Huo, Y.Z.: A large deflection light-induced bending model for liquid crystal elastomers under uniform or non-uniform illumination. Int. J. Solids Struct. 48, 3232–3242 (2011)

    Google Scholar 

  25. Kaiser, A., Winkler, M., Krause, S., Finkelmann, H., Schmidt, A.M.: Magnetoactive liquid crystal elastomer nanocomposites. J. Mater. Chem. 19, 538–543 (2009)

    Google Scholar 

  26. Kim, Y., Yuk, H., Zhao, R., Chester, S.A., Zhao, X.: Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature 558(7709), 274–279 (2018)

    Google Scholar 

  27. Kim, Y., Parada, G.A., Liu, S., Zhao, X.: Ferromagnetic soft continuum robots. Sci. Robot. 4, 7329 (2019)

    Google Scholar 

  28. Korner, K., Kuenstler, A.S., Hayward, R.C., Audoly, B., Bhattacharya, K.: A nonlinear beam model of photomotile structures. Proc. Natl. Acad. Sci. U.S.A. 117(18), 9762–9770 (2020)

    MathSciNet  MATH  Google Scholar 

  29. Li, M., Wang, Y., Chen, A., Naidu, A., Napier, B.S., Li, W., Rodriguez, C.L., Crooker, S.A., Omenetto, F.G.: Flexible magnetic composites for light-controlled actuation and interfaces. Proc. Natl. Acad. Sci. U.S.A. 115, 8119 (2018)

    Google Scholar 

  30. Liu, S., Huang, K.Z., Wang, K.F., Wang, B.L.: Programmable deformation of liquid crystal elastomer plates subjected to concentrated light illumination. Mech. Mater. 175, 104501 (2022)

    Google Scholar 

  31. Liu, X., Liu, Y.: Spontaneous photo-deformation of a liquid crystal network membrane. Int. J. Mech. Sci. 184, 105842 (2020)

    Google Scholar 

  32. Liu, Y., Ma, W., Dai, H.H.: On a consistent finite-strain plate model of nematic liquid crystal elastomers. J. Mech. Phys. Solids 145, 104169 (2020)

    MathSciNet  Google Scholar 

  33. Liu ,Y., Zhao, D.: Boundary effect on the spontaneous deformation of a liquid crystal elastomer plate with arbitrary director orientation Phys. Rev. E 103(1) (2021). https://doi.org/10.1103/PhysRevE.103.012701

  34. Lum, G.Z., Ye, Z., Dong, X., Marvi, H., Erin, O., Hu, W., Sitti, M.: Shape-programmable magnetic soft matter. Proc. Natl. Acad. Sci. U.S.A. 113, E6007 (2016)

    Google Scholar 

  35. Mihai, A.L., Goriely, A.: A plate theory for nematic liquid crystalline solids. J. Mech. Phys. Solids 144, 104101 (2020)

    MathSciNet  Google Scholar 

  36. Mohammad, D., Samir, A.: A new technique for large deflection analysis of non-prismatic cantilever beams. Mech. Res. Commun. 32, 692–703 (2005)

    MATH  Google Scholar 

  37. Mukherjee, D., Danas, K.: A unified dual modeling framework for soft and hard magnetorheological elastomers. Int. J. Solids Struct. 257, 111513 (2022)

    Google Scholar 

  38. Pacchierotti, C., Ongaro, F., van den Brink, F., Yoon, C., Prattichizzo, D., Gracias, D.H., Misra, S.: Steering and control of miniaturized untethered soft magnetic grippers with haptic assistance. IEEE Trans. Autom. Sci. Eng. 15(1), 290–306 (2017)

    Google Scholar 

  39. Qiu, Y., Wang, C.J., Lu, X.Y., Wu, H.P., Ma, X.L., Hu, J.H., Qi, H.C., Tian, Y., Zhang, Z., Bao, G.J., Chai, H., Song, J.Z., Liu, A.P.: A biomimetic drosera capensis with adaptive decision-predation behavior based on multifunctional sensing and fast actuating capability. Adv. Funct. Mater. (2021). https://doi.org/10.1002/adfm.202110296

    Article  Google Scholar 

  40. Rajan, A., Arockiarajan, A.: Bending of hard-magnetic soft beams: a finite elasticity approach with anticlastic bending. Eur. J. Mech. A/Solids 90, 104374 (2021)

    MathSciNet  MATH  Google Scholar 

  41. Ren, Z., Hu, W., Dong, X., Sitti, M.: Multi-functional soft-bodied jellyfish-like swimming. Nat. Commun. 10(1), 1–12 (2019)

    Google Scholar 

  42. Sano, T.G., Pezzulla, M., Reis, P.M.: A Kirchhoff-like theory for hard magnetic rods under geometrically nonlinear deformation in three dimensions. J. Mech. Phys. Solids 160, 104739 (2022)

    MathSciNet  Google Scholar 

  43. Schuhladen, S., Preller, F., Rix, R., Petsch, S., Zentel, R., Zappe, H.: Iris-like tunable aperture employing liquid-crystal elastomers. Adv. Mater. 26, 7247–7251 (2014)

    Google Scholar 

  44. Shankar, M.R., Smith, M.L., Tondiglia, V.P., Lee, K.M., McConney, M.E., Wang, D.H., Tan, L.-S., White, T.J.: Contactless, photoinitiated snap-through in azobenzene functionalized polymers. Proc. Natl. Acad. Sci. U.S.A. 110, 18792–18797 (2013)

    Google Scholar 

  45. Smith, M. L., Shankar, M. R., Backman, R., Tondiglia, V. P., White, T. J.: Designing light responsive bistable arches for rapid, remotely triggered actuation. In: Proceedings of SPIE-Behavior and Mechanics of Multifunctional Materials and Composites. International Society for Optics and Photonics (2014)

  46. Tan, K., Chen, L.L., Yang, S.Y., Deng, Q.: Dynamic snap-through instability and damped oscillation of a flat arch of hard magneto-active elastomers. Int. J. Mech. Sci. 230, 107523 (2022)

    Google Scholar 

  47. Wang, C., Sim, K., Chen, J., Kim, H., Rao, Z., Li, Y., Chen, W., Song, J., Verduzco, R., Yu, C.: Soft ultrathin electronics innervated adaptive fully soft robots. Adv. Mater. 30, 1706695 (2018)

    Google Scholar 

  48. Wang, L., Kim, Y., Guo, C.F., Zhao, X.H.: Hard-magnetic elastic. J. Mech. Phys. Solids 142, 104045 (2020)

    MathSciNet  Google Scholar 

  49. Wang, L., Zheng, D.C., Harker, P., Patel, A.B., Guo, C.F., Zhao, X.H.: Evolutionary design of magnetic soft continuum robots. Proc. Natl. Acad. Sci. U.S.A. 118(21), e2021922118 (2021)

    Google Scholar 

  50. Wang, K.F., Wang, B.L.: Is there only one equilibrium configuration for spontaneous bending of liquid crystal elastomer circular plates with free edges? Eur. Phys. J. E 44, 1–6 (2021)

    Google Scholar 

  51. Wani, O.M., Zeng, H., Priimagi, A.: A light-driven artificial flytrap. Nature. Communications 8, 15546 (2017)

    Google Scholar 

  52. Ware, T.H., McConney, M.E., Wie, J.J., Tondiglia, V.P., White, T.J.: Voxelated liquid crystal elastomers. Science 347(6225), 982–984 (2015)

    Google Scholar 

  53. Warner, M., Terentjev, E.: Nematic elastomers—a new state of matter? Prog. Polym. Sci. 21, 853–891 (1996)

    Google Scholar 

  54. Winkler, M., Kaiser, A., Krause, S., Finkelmann, H., Schmidt, A. M.: Liquid crystal elastomers with magnetic actuation. In: Macromol. Symp. 291–292, 186–192 (2010)

  55. Xia, Y., Cedillo-Servin, G., Kamien, R.D., Yang, S.: Guided folding of nematic liquid crystal elastomer sheets into 3D via patterned 1D microchannels. Adv. Mater. 28, 9637 (2016)

    Google Scholar 

  56. Xiao, Y., Jiang, Z., Tong, X., Zhao, Y.: Biomimetic locomotion of electrically powered “Janus” soft robots using a liquid crystal polymer. Adv. Mater. 31(36), 1903452 (2019)

    Google Scholar 

  57. Yan, D., Abbasi, A., Reis, P.M.: A comprehensive framework for hard-magnetic beams: reduced-order theory, 3D simulations, and experiments. Int. J. Solids Struct. (2021). https://doi.org/10.1016/j.ijsolstr.2021.111319

    Article  Google Scholar 

  58. Yan, D., Aymon, B.F.G., Reis, P.M.: A reduced-order, rotation-based model for thin hard-magnetic plates. J. Mech. Phys. Solids 170, 105095 (2023)

    Google Scholar 

  59. You, Y., Xu, C.W., Ding, S.R., Huo, Y.Z.: Coupled effects of director orientations and boundary conditions on light induced bending of monodomain nematic liquid crystalline polymer plates. Smart Mater. Struct. 21, 125012 (2012)

    Google Scholar 

  60. Yuan, C., Ding, Z., Wang, T.J., Dunn, M.L., Qi, H.J.: Shape forming by thermal expansion mismatch and shape memory locking in polymer/elastomer laminates. Smart Mater. Struct. 26(10), 105027 (2017)

    Google Scholar 

  61. Yun, G., Tang, S.Y., Sun, S., Yuan, D., Zhao, Q., Deng, L., Li, W.: Liquid metal-filled magnetorheological elastomer with positive piezoconductivity. Nat. Commun. 10(1), 1–9 (2019)

    Google Scholar 

  62. Ze, Q., Kuang, X., Wu, S., Wong, J., Montgomery, S.M., Zhang, R., Kovitz, J.M., Yang, F., Qi, H.J., Zhao, R.: Magnetic shape memory polymers with integrated multifunctional shape manipulation. Adv. Mater. 32, 1906657 (2020)

    Google Scholar 

  63. Zeng, H., Lahikainen, M., Liu, L., Ahmed, Z., Wani, O.M., Wang, M., Yang, H., Priimagi, A.: Light-fuelled freestyle self-oscillators. Nat. Commun. 10, 5057 (2019)

    Google Scholar 

  64. Zeng, H., Wani, O.M., Wasylczyk, P., Kaczmarek, R., Priimagi, A.: Self-regulating iris based on light-actuated liquid crystal elastomer. Adv. Mater. 29, 1701814 (2017)

    Google Scholar 

  65. Zeng, H., Wasylczyk, P., Parmeggiani, C., Martella, D., Burresi, M., Wiersma, D.S.: Light-fueled microscopic walkers. Adv. Mater. 27, 3883 (2015)

    Google Scholar 

  66. Zhang, J., Guo, Y., Hu, W., Soon, R.H., Davidson, Z.S., Sitti, M.: Liquid crystal elastomer-based magnetic composite films for reconfigurable shape-morphing soft miniature machines. Adv. Mater. 33(8), 2006191 (2021)

    Google Scholar 

  67. Zhang, J.C., Guo, Y.B., Hu, W.Q., Sitti, M.: Wirelessly actuated thermo- and magneto-responsive soft bimorph materials with programmable shape-morphing. Adv. Mater. 33, 2100336 (2021)

    Google Scholar 

  68. Zhang, J., Diller, E.: Untethered miniature soft robots: modeling and design of a millimeter-scale swimming magnetic sheet. Soft Robot. 5(6), 761–776 (2018)

    Google Scholar 

  69. Zhang, Y., Xuan, C., Jiang, Y.F., Huo, Y.Z.: Continuum mechanical modeling of liquid crystal elastomers as dissipative ordered solids. J. Mech. Phys. Solids 126, 285–303 (2019)

    MathSciNet  MATH  Google Scholar 

  70. Zhao, D., Liu, Y.: Photomechanical vibration energy harvesting based on liquid crystal elastomer cantilever. Smart Mater. Struct. 28, 075017 (2019)

    Google Scholar 

  71. Zhao, D., Liu, Y.: A prototype for light-electric harvester based on light sensitive liquid crystal elastomer cantilever. Energy 198, 117351 (2020)

    Google Scholar 

  72. Zhao, D., Liu, Y.: Light-induced spontaneous bending of a simply supported liquid crystal elastomer rectangular plate. Phys. Rev. E 101, 042701 (2020)

    Google Scholar 

  73. Zhao, R.K., Kim, Y., Chester, S.A., Sharma, P., Zhao, X.H.: Mechanics of hard-magnetic soft materials. J. Mech. Phys. Solids 124, 244–263 (2019)

    MathSciNet  Google Scholar 

  74. Zhu, Q.L., Du, C., Dai, Y., Daab, M., Matejdes, M., Breu, J., Hong, W., Zheng, Q., Wu, Z.L.: Light-steered locomotion of muscle-like hydrogel by self-coordinated shape change and friction modulation. Nat. Commun. 11, 5166 (2020)

    Google Scholar 

Download references

Acknowledgements

This research was supported by Guangdong Basic and Applied Basic Research Foundation (Project No. 2022B1515020099) and Shenzhen Science and Technology Program (Project No. JCYJ20220818102409020).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to K. F. Wang or L. Zheng.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, K.F., Wang, B.L. & Zheng, L. Dual photo- and magneto-responses of layered beams composed of liquid crystal elastomers and magnetic responsive elastomers. Acta Mech 234, 4095–4110 (2023). https://doi.org/10.1007/s00707-023-03599-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-023-03599-y

Navigation