Skip to main content
SpringerLink
Log in

Electro-viscoelastic behaviors of circular dielectric elastomer membrane actuator containing concentric rigid inclusion

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

The time-dependent electro-viscoelastic performance of a circular dielectric elastomer (DE) membrane actuator containing an inclusion is investigated in the context of the nonlinear theory for viscoelastic dielectrics. The membrane, a key part of the actuator, is centrally attached to a rigid inclusion of the radius a, and then connected to a fixed rigid ring of the radius b. When subject to a pressure and a voltage, the membrane inflates into an out-of-plane shape and undergoes an inhomogeneous large deformation. The governing equations for the large deformation are derived by means of non-equilibrium thermodynamics, and viscoelasticity of the membrane is characterized by a rheological spring-dashpot model. In the simulation, effects of the pressure, the voltage, and design parameters on the electromechanical viscoelastic behaviors of the membrane are investigated. Evolutions of the considered variables and profiles of the deformed membrane are obtained numerically and illustrated graphically. The results show that electromechanical loadings and design parameters significantly influence the electro-viscoelastic behaviors of the membrane. The design parameters can be tailored to improve the performance of the membrane. The approach may provide guidelines in designing and optimizing such DE devices.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pelrine, R., Kornbluh, R., Pei, Q. B., and Joseph, J. High-speed electrically actuated elastomers with strain greater than 100%. Science, 287, 836–839 (2000)

    Article  Google Scholar 

  2. Anderson, I. A., Gisby, T. A., McKay, T., O’Brien, B. M., and Calius, E. Multi-functional dielectric elastomer artificial muscles for soft and smart machines. Journal of Applied Physics, 112, 041101 (2012)

    Article  Google Scholar 

  3. Carpi, F., Chiarelli, P., Mazzoldi, A., and Rossi, D. D. Electromechanical characterization of dielectric elastomer planar actuators: comparative evaluation of different electrode materials and different counterloads. Sensors and Actuators A: Physical, 107, 85–95 (2003)

    Article  Google Scholar 

  4. Zhang, J. S., Tang, L. L., Li, B., Wang, Y. J., and Chen, H. L. Modeling of the dynamic characteristic of viscoelastic dielectric elastomer actuators subject to different conditions of mechanical load. Journal of Applied Physics, 117, 084902 (2015)

    Article  Google Scholar 

  5. Wang, H. M., Cai, S. Q., Carpi, F., and Suo, Z. G. Computational model of hydrostatically coupled dielectric elastomer actuators. Journal of Applied Mechanics, 79, 031008 (2012)

    Article  Google Scholar 

  6. Shankar, R., Ghosh, T. K., and Spontak, R. J. Dielectric elastomers as next-generation polymeric actuators. Soft Matter, 3, 1116–1129 (2007)

    Article  Google Scholar 

  7. Löwe, C., Zhang, X., and Kovacs, G. Dielectric elastomers in actuator technology. Advanced Engineering Materials, 7, 361–367 (2005)

    Article  Google Scholar 

  8. Lu, T. Q., Foo, C. C., Huang, J. S., Zhu, J., and Suo, Z. G. Highly deformable actuators made of dielectric elastomers clamped by rigid rings. Journal of Applied Physics, 115, 184105 (2014)

    Article  Google Scholar 

  9. He, X. Z., Yong, H. D., and Zhou, Y. H. The characteristics and stability of a dielectric elastomer spherical shell with a thick wall. Smart Materials and Structures, 20, 055016 (2011)

    Article  Google Scholar 

  10. He, T. H., Cui, L. L., Chen, C., and Suo, Z. G. Nonlinear deformation analysis of a dielectric elastomer membrane-spring system. Smart Materials and Structures, 19, 085017 (2009)

    Article  Google Scholar 

  11. Gisby, T. A., O’Brien, B. M., and Anderson, I. A. Self-sensing feedback for dielectric elastomer actuators. Applied Physics Letters, 102, 193703 (2013)

    Article  Google Scholar 

  12. Jung, K. M., Kim, K. J., and Choi, H. R. A novel self-sensing of dielectric elastomer actuator. Sensors and Actuators A: Physical, 143, 343–351 (2008)

    Article  Google Scholar 

  13. Kaltseis, R., Keplinger, C., Baumgartner, R., Kaltenbrunner, M., Li, T. F., Machler, P., Schwodiauer, R., Suo, Z. G., and Bauer, S. Method for measuring energy generation and efficiency of dielectric elastomer generators. Applied Physics Letters, 99, 4578–4586 (2011)

    Article  Google Scholar 

  14. Mckay, T., O’Brien, B., Calius, E., and Anderson, I. Self-priming dielectric elastomer generators. Smart Materials and Structures, 19, 055025 (2010)

    Article  Google Scholar 

  15. Choi, H. R., Jung, K., Ryew, S., Nam, J. D., Jeon, J., Koo, J. C., and Tanie, K. Biomimetic soft actuator: design, modeling, control, and applications. IEEE/ASME Transactions on Mechatronics, 10, 581–593 (2005)

    Article  Google Scholar 

  16. Carpi, F., Frediani, G., Turco, S., and De, R. D. Optics: bioinspired tunable lens with muscle-like electroactive elastomers. Advanced Functional Materials, 21, 4152–4158 (2011)

    Article  Google Scholar 

  17. Shian, S., Diebold, R. M., and Clarke, D. R. Tunable lenses using transparent dielectric elastomer actuators. Optics Express, 21, 8669–8676 (2013)

    Article  Google Scholar 

  18. Li, T. F., Qu, S. X., and Yang, W. Energy harvesting of dielectric elastomer generators concerning inhomogeneous fields and viscoelastic deformation. Journal of Applied Physics, 112, 034119 (2012)

    Article  Google Scholar 

  19. Suo, Z. G. Theory of dielectric elastomers. Acta Mechanica Solida Sinica, 23, 549–578 (2010)

    Article  Google Scholar 

  20. Goulbourne, N., Mockenstrum, E., and Frecker, M. A nonlinear model for dielectric elastomer membranes. Journal of Applied Mechanics, 72, 899–907 (2005)

    Article  MATH  Google Scholar 

  21. He, T. H., Zhao, X. H., and Suo, Z. G. Dielectric elastomer membranes undergoing inhomogeneous deformation. Journal of Applied Physics, 106, 083522 (2009)

    Article  Google Scholar 

  22. Zhu, J., Cai, S. Q., and Suo, Z. G. Resonant behavior of a membrane of a dielectric elastomer. International Journal of Solids and Structures, 47, 3254–3262 (2010)

    Article  MATH  Google Scholar 

  23. Liu, L. W., Liu, Y. J., Li, B., Yang, K., Li, T. F., and Leng, J. S. Thermo-electro-mechanical instability of dielectric elastomers. Smart Materials and Structures, 20, 075004 (2011)

    Article  Google Scholar 

  24. McMeeking, R. M. and Landis, C. M. Electrostatic forces and stored energy for deformable dielectric materials. Journal of Applied Mechanics, 72, 581–590 (2005)

    Article  MATH  Google Scholar 

  25. Wissler, M. and Mazza, E. Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuator. Sensors and Actuators A: Physical, 134, 494–504 (2007)

    Article  Google Scholar 

  26. Lochmatter, P., Kovacs, G., and Wissler, M. Characterization of dielectric elastomer actuators based on a visco-hyperelastic film model. Smart Materials and Structures, 16, 477–486 (2007)

    Article  Google Scholar 

  27. Zhao, X. H., Koh, S. J. A., and Suo, Z. G. Nonequilibrium thermodynamics of dielectric elastomers. International Journal of Applied Mechanics, 3, 203–217 (2011)

    Article  Google Scholar 

  28. Foo, C. C., Koh, S. J. A., Keplinger, C., Kaltseis, R., Bauer, S., and Suo, Z. G. Performance of dissipative dielectric elastomer generators. Journal of Applied Physics, 111, 094107 (2012)

    Article  Google Scholar 

  29. Plante, J. and Dubowsky, S. Large-scale failure modes of dielectric elastomer actuators. International Journal of Solids and Structures, 43, 7727–7751 (2006)

    Article  MATH  Google Scholar 

  30. Bai, Y., Jiang, Y., Chen, B., Foo, C. C., Zhou, Y., Xiang, F., Zhou, J., Wang, H., and Suo, Z. G. Cyclic performance of viscoelastic dielectric elastomers with solid hydrogel electrodes. Applied Physics Letters, 104, 062902 (2014)

    Article  Google Scholar 

  31. Kollosche, M., Kofod, G., Suo, Z. G., and Zhu, J. Temporal evolution and instability viscoelastic dielectric elastomer. Journal of the Mechanics and Physics of Solids, 76, 47–64 (2015)

    Article  Google Scholar 

  32. Wang, H. M., Lei, M., and Cai, S. Q. Viscoelastic deformation of a dielectric elastomer membrane subject to electromechanical loads. Journal of Applied Physics, 113, 213508 (2013)

    Article  Google Scholar 

  33. Zhang, J., Chen, H., Sheng, J., Liu, L., Wang, Y., and Jia, S. Dynamic performance of dissipative dielectric elastomers under alternating mechanical load. Applied Physics A, 116, 59–67 (2013)

    Article  Google Scholar 

  34. Zhou, J., Jiang, L., and Khayat, R. Viscoelastic effects on frequency tuning of a dielectric elastomer membrane resonator. Journal of Applied Physics, 115, 124106 (2014)

    Article  Google Scholar 

  35. Li, T. F., Keplinger, C., Baumgartner, R., Bauer, S., Yang, W., and Suo, Z. G. Giant voltageinduced 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 

Download references

Acknowledgements

We would like to sincerely thank Huiming WANG, Professor of Zhejiang University, for his great help to the accomplishment of this paper.

Author information

Authors and Affiliations

  1. School of Science, Lanzhou University of Technology, Lanzhou, 730050, China

    Zhengang Wang & Tianhu He

Authors
  1. Zhengang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tianhu He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tianhu He.

Additional information

Project supported by the National Natural Science Foundation of China (No. 11372123)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., He, T. Electro-viscoelastic behaviors of circular dielectric elastomer membrane actuator containing concentric rigid inclusion. Appl. Math. Mech.-Engl. Ed. 39, 547–560 (2018). https://doi.org/10.1007/s10483-018-2318-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-018-2318-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation