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Snap-through path in a bistable dielectric elastomer actuator

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Abstract

The dielectric elastomer (DE) has attracted significant attention due to its desired features, including large deformation, fast response, and high energy density. However, for a DE actuator (DEA) utilizing a snap-through deformation mode, most existing theoretical models fail to predict its deformation path. This paper develops a new finite element method (FEM) based on the three-parameter Gent-Gent model suitable for capturing strain-stiffening behaviors. The simulation results are verified by experiments, indicating that the FEM can accurately characterize the snap-through path of a DE. The method proposed in this paper provides theoretical guidance and inspiration for designing and applying DEs and bistable electroactive actuators.

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References

  1. PELRINE, R., KORNBLUH, R., PEI, Q., and JOSEPH, J. High-speed electrically actuated elastomers with strain greater than 100%. Science, 287, 836–839 (2000)

    Article  Google Scholar 

  2. CARPI, F., BAUER, S., and ROSSI, D. D. Stretching dielectric elastomer performance. Science, 330, 1759–1761 (2010)

    Article  Google Scholar 

  3. AN, L., WANG, F., CHENG, S., LU, T., and WANG, T. J. Experimental investigation of the electromechanical phase transition in a dielectric elastomer tube. Smart Materials and Structures, 24, 035006 (2015)

    Article  Google Scholar 

  4. GU, G., ZOU, J., ZHAO, R., ZHAO, X., and ZHU, X. Soft wall-climbing robots. Science Robotics, 3, eaat2874 (2018)

    Article  Google Scholar 

  5. CHEN, Y., ZHAO, H., MAO, J., CHIRARATTANANON, P., HELBLING, E. F., HYUN, N. S. P., CLARKE, D. R., and WOOD, R. J. Controlled flight of a microrobot powered by soft artificial muscles. Nature, 575, 324–329 (2019)

    Article  Google Scholar 

  6. LI, G., CHEN, X., ZHOU, F., LIANG, Y., XIAO, Y., CAO, X., ZHANG, Z., ZHANG, M., WU, B., YIN, S., XU, Y., FAN, H., CHEN, Z., SONG, W., YANG, W., PAN, B., HOU, J., ZOU, W., HE, S., YANG, X., MAO, G., JIA, Z., ZHOU, H., LI, T., QU, S., XU, Z., HUANG, Z., LUO, Y., XIE, T., GU, J., ZHU, S., and YANG, W. Self-powered soft robot in the mariana trench. Nature, 591, 66–71 (2021)

    Article  Google Scholar 

  7. LI, T., LI, G., LIANG, Y., CHENG, T., DAI, J., YANG, X., LIU, B., ZENG, Z., HUANG, Z., LUO, Y., XIE, T., and YANG, W. Fast-moving soft electronic fish. Science Advances, 3, e1602045 (2017)

    Article  Google Scholar 

  8. MAFFLI, L., ROSSET, S., GHILARDI, M., CARPI, F., and SHEA, H. Ultrafast all-polymer electrically tunable silicone lenses. Advanced Functional Materials, 25, 1656–1665 (2015)

    Article  Google Scholar 

  9. CHEN, B., SUN, W., LU, J., YANG, J., CHEN, Y., ZHOU, J., and SUO, Z. All-solid ionic eye. Journal of Applied Mechanics, 88, 1–25 (2020)

    Google Scholar 

  10. KEPLINGER, C., SUN, J. Y., FOO, C. C., ROTHEMUND, P., WHITESIDES, G. M., and SUO, Z. Stretchable, transparent, ionic conductors. Science, 341, 984–987 (2013)

    Article  Google Scholar 

  11. WISSLER, M. and MAZZA, E. Electromechanical coupling in dielectric elastomer actuators. Sensors and Actuators A: Physical, 138, 384–393 (2007)

    Article  Google Scholar 

  12. ZHAO, X., HONG, W., and SUO, Z. Electromechanical hysteresis and coexistent states in dielectric elastomers. Physical Review B, 76, 134113 (2007)

    Article  Google Scholar 

  13. SUO, Z. Theory of dielectric elastomers. Acta Mechanica Solida Sinica, 23, 549–578 (2010)

    Article  Google Scholar 

  14. ZHAO, X. and SUO, Z. Method to analyze electromechanical stability of dielectric elastomers. Applied Physics Letters, 91, 061921 (2007)

    Article  Google Scholar 

  15. LENG, J., LIU, L., LIU, Y., YU, K., and SUN, S. Electromechanical stability of dielectric elastomer. Applied Physics Letters, 94, 211901 (2009)

    Article  Google Scholar 

  16. KOLLOSCHE, M., KOFOD, G., SUO, Z., and ZHU, J. Temporal evolution and instability in a viscoelastic dielectric elastomer. Journal of the Mechanics and Physics of Solids, 76, 47–64 (2015)

    Article  Google Scholar 

  17. ZHU, J., KOLLOSCHE, M., LU, T., KOFOD, G., and SUO, Z. Two types of transitions to wrinkles in dielectric elastomers. Soft Matter, 8, 8840–8846 (2012)

    Article  Google Scholar 

  18. HE, T., ZHAO, X., and SUO, Z. Dielectric elastomer membranes undergoing inhomogeneous deformation. Journal of Applied Physics, 106, 083522 (2009)

    Article  Google Scholar 

  19. CAO, C., CHEN, L., DUAN, W., HILL, T. L., LI, B., CHEN, G., LI, H., LI, Y., WANG, L., and GAO, X. On the mechanical power output comparisons of cone dielectric elastomer actuators. IEEE/ASME Transactions on Mechatronics, 26, 3151–3162 (2020)

    Article  Google Scholar 

  20. LI, B., LIU, L., and SUO, Z. Extension limit, polarization saturation, and snap-through instability of dielectric elastomers. International Journal of Smart and Nano Materials, 2, 59–67 (2011)

    Article  Google Scholar 

  21. HUANG, J., LI, T., FOO, C. C., ZHU, J., CLARKE, D. R., and SUO, Z. Giant, voltage-actuated deformation of a dielectric elastomer under dead load. Applied Physics Letters, 100, 041911 (2012)

    Article  Google Scholar 

  22. LI, T., KEPLINGER, C., BAUMGARTNER, R., BAUER, S., YANG, W., and SUO, Z. Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability. Journal of the Mechanics and Physics of Solids, 61, 611–628 (2013)

    Article  Google Scholar 

  23. O’HALLORAN, A., O’MALLEY, F., and MCHUGH, P. A review on dielectric elastomer actuators, technology, applications, and challenges. Journal of Applied Physics, 104, 071101 (2008)

    Article  Google Scholar 

  24. ZHAO, H., HUSSAIN, A. M., DUDUTA, M., VOGT, D. M., WOOD, R. J., and CLARKE, D. R. Compact dielectric elastomer linear actuators. Advanced Functional Materials, 28, 1804328 (2018)

    Article  Google Scholar 

  25. HAJIESMAILI, E. and CLARKE, D. R. Reconfigurable shape-morphing dielectric elastomers using spatially varying electric fields. Nature Communications, 10, 183 (2019)

    Article  Google Scholar 

  26. SUN, W., LIU, F., MA, Z., LI, C., and ZHOU, J. Soft mobile robots driven by foldable dielectric elastomer actuators. Journal of Applied Physics, 120, 084901 (2016)

    Article  Google Scholar 

  27. WISSLER, M. and MAZZA, E. Modeling and simulation of dielectric elastomer actuators. Smart Materials and Structures, 14, 1396–1402 (2005)

    Article  Google Scholar 

  28. ZHAO, X. and SUO, Z. Method to analyze programmable deformation of dielectric elastomer layers. Applied Physics Letters, 93, 251902 (2008)

    Article  Google Scholar 

  29. HENANN, D. L., CHESTER, S. A., and BERTOLDI, K. Modeling of dielectric elastomers: design of actuators and energy harvesting devices. Journal of the Mechanics and Physics of Solids, 61, 2047–2066 (2013)

    Article  MathSciNet  Google Scholar 

  30. FOO, C. C. and ZHANG, Z. Q. A finite element method for inhomogeneous deformation of viscoelastic dielectric elastomers. International Journal of Applied Mechanics, 7, 1550069 (2015)

    Article  Google Scholar 

  31. QU, S. and SUO, Z. A finite element method for dielectric elastomer transducers. Acta Mechanica Solida Sinica, 25, 459–466 (2012)

    Article  Google Scholar 

  32. O’BRIEN, B., MCKAY, T., CALIUS, E., XIE, S., and ANDERSON, I. Finite element modelling of dielectric elastomer minimum energy structures. Applied Physics A, 94, 507–514 (2008)

    Article  Google Scholar 

  33. LIU, J., FOO, C. C., and ZHANG, Z. Q. A 3D multi-field element for simulating the electromechanical coupling behavior of dielectric elastomers. Acta Mechanica Solida Sinica, 30, 374–389 (2017)

    Article  Google Scholar 

  34. GENT, A. N. A new constitutive relation for rubber. Rubber Chemistry and Technology, 69, 59–61 (1996)

    Article  Google Scholar 

  35. LI, B., CHEN, H., QIANG, J., HU, S., ZHU, Z., and WANG, Y. Effect of mechanical pre-stretch on the stabilization of dielectric elastomer actuation. Journal of Physics D: Applied Physics, 44, 155301 (2011)

    Article  Google Scholar 

  36. ZHOU, L., WANG, S., LI, L., and FU, Y. An evaluation of the Gent and Gent-Gent material models using inflation of a plane membrane. International Journal of Mechanical Sciences, 146, 39–48 (2018)

    Article  Google Scholar 

  37. ALIBAKHSHI, A. and HEIDARI, H. Nonlinear dynamics of dielectric elastomer balloons based on the Gent-Gent hyperelastic model. European Journal of Mechanics-A/Solids, 82, 103986 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  38. PATRICK, L., GABOR, K., and SILVAIN, M. Characterization of dielectric elastomer actuators based on a hyperelastic film model. Sensors and Actuators A: Physical, 135, 748–757 (2007)

    Article  Google Scholar 

  39. HAJIESMAILI, E. and CLARKE, D. R. Dielectric elastomer actuators. Journal of Applied Physics, 129, 151102 (2021)

    Article  Google Scholar 

  40. HOSOYA, N., MASUDA, H., and MAEDA, S. Balloon dielectric elastomer actuator speaker. Applied Acoustics, 148, 238–245 (2019)

    Article  Google Scholar 

  41. CAO, C., GAO, X., and CONN, A. T. A magnetically coupled dielectric elastomer pump for soft robotics. Advanced Materials Technologies, 4, 1900128 (2019)

    Article  Google Scholar 

  42. KEPLINGER, C., LI, T., BAUMGARTNER, R., SUO, Z., and BAUER, S. Harnessing snap-through instability in soft dielectrics to achieve giant voltage-triggered deformation. Soft Matter, 8, 285–288 (2011)

    Article  Google Scholar 

  43. WANG, Y., LI, Z., QIN, L., CADDY, G., YAP, C. H., and ZHU, J. Dielectric elastomer fluid pump of high pressure and large volume via synergistic snap-through. Journal of Applied Mechanics, 85, 101003 (2018)

    Article  Google Scholar 

  44. MCCOUL, D. and PEI, Q. Tubular dielectric elastomer actuator for active fluidic control. Smart Materials and Structures, 24, 105016 (2015)

    Article  Google Scholar 

  45. CHAKRABORTI, P., TOPRAKCI, H. A. K., YANG, P., SPIGNA, N. D., FRANZON, P., and GHOSH, T. A compact dielectric elastomer tubular actuator for refreshable braille displays. Sensors and Actuators A: Physical, 179, 151–157 (2012)

    Article  Google Scholar 

  46. NASAB, A. M., SABZEHZAR, A., TATARI, M., MAJIDI, C., and SHAN, W. A soft gripper with rigidity tunable elastomer strips as ligaments. Soft Robotics, 4, 411–420 (2017)

    Article  Google Scholar 

  47. LI, J., LIU, L., LIU, Y., and LENG, J. Dielectric elastomer spring-roll bending actuators: applications in soft robotics and design. Soft Robotics, 6, 69–81 (2018)

    Article  Google Scholar 

  48. LU, T., AN, L., LI, J., YUAN, C., and WANG, T. J. Electro-mechanical coupling bifurcation and bulging propagation in a cylindrical dielectric elastomer tube. Journal of the Mechanics and Physics of Solids, 85, 160–175 (2015)

    Article  MathSciNet  Google Scholar 

  49. ROTHEMUND, P., AINLA, A., BELDING, L., PRESTON, D. J., KURIHARA, S., SUO, Z., and WHITESIDES, G. M. A soft, bistable valve for autonomous control of soft actuators. Science Robotics, 3, eaar7986 (2018)

    Article  Google Scholar 

  50. ZHANG, Z., NI, X., WU, H., SUN, M., BAO, G., WU, H., and JIANG, S. Pneumatically actuated soft gripper with bistable structures. Soft Robotics, 9, 57–71 (2022)

    Article  Google Scholar 

  51. PRESTON, D. J., ROTHEMUND, P., JIANG, H. J., NEMITZ, M. P., RAWSON, J., SUO, Z., and WHITESIDES, G. M. Digital logic for soft devices. Proceedings of the National Academy of Sciences, 116, 7750–7759 (2019)

    Article  Google Scholar 

  52. HINES, L., PETERSEN, K., and SITTI, M. Inflated soft actuators with reversible stable deformations. Advanced Materials, 28, 3690–3696 (2016)

    Article  Google Scholar 

  53. BAUMGARTNER, R., KOGLER, A., STADLBAUER, J. M., FOO, C. C., KALTSEIS, R., BAUMGARTNER, M., MAO, G., KEPLINGER, C., KOH, S. J. A., ARNOLD, N., SUO, Z., KALTENBRUNNER, M., and BAUER, S. A lesson from plants: high-speed soft robotic actuators. Advanced Science, 7, 1903391 (2020)

    Article  Google Scholar 

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Funding

Project supported by the National Key Research and Development Program of China (No. 2019YFB1311600), the National Natural Science Foundation of China (Nos. 11902248 and 52075411), the Shaanxi Key Research and Development Program of China (No. 2020ZDLGY06-11), and the State Key Laboratory for Strength and Vibration of Mechanical Structures of China (No. SV2018-KF-08)

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Correspondence to Bo Li.

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Citation: SUN, W. J., MA, W. T., ZHANG, F., HONG, W., and LI, B. Snap-through path in a bistable dielectric elastomer actuator. Applied Mathematics and Mechanics (English Edition), 43(8), 1159–1170 (2022) https://doi.org/10.1007/s10483-022-2888-6

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Sun, W., Ma, W., Zhang, F. et al. Snap-through path in a bistable dielectric elastomer actuator. Appl. Math. Mech.-Engl. Ed. 43, 1159–1170 (2022). https://doi.org/10.1007/s10483-022-2888-6

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  • DOI: https://doi.org/10.1007/s10483-022-2888-6

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