Zeitschrift für angewandte Mathematik und Physik

, Volume 62, Issue 6, pp 1131–1142 | Cite as

Stability of anisotropic electroactive polymers with application to layered media

Article

Abstract

The stability of anisotropic electroactive polymers is investigated. A general criterion for the onset of instabilities under plane-strain conditions is introduced in terms of a sextic polynomial whose coefficients depend on the instantaneous electroelastic moduli. In a way of an example, the stable domains of layered neo-Hookean dielectrics are determined. It is found that depending on the direction of the electrostatic excitation field relative to the lamination direction, the critical stretch ratios at which instabilities may occur can be either larger or smaller than the ones for the purely mechanical case.

Mathematics Subject Classification (2000)

74B20 74G60 74F15 78A30 37C20 

Keywords

Electroactive polymers Dielectric elastomers Finite deformations Anisotropy Non-linear electroelasticity 

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References

  1. 1.
    Agoras M., Lopez-Pamies O., Castañeda P.P.: Onset of macroscopic instabilities in fiber-reinforced elastomers at finite strain. J. Mech. Phys. Solids 57, 1828–1850 (2009)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Bar-Cohen Y.: EAP history, current status, and infrastructure. In: Bar-Cohen, Y. (eds) Electroactive Polymer (EAP) Actuators as Artificial Muscles, chapter 1, pp. 3–44. SPIE Press, Bellingham, WA (2001)Google Scholar
  3. 3.
    Bertoldi K., Boyce M.C.: Wave propagation and instabilities in monolithic and periodically structured elastomeric materials undergoing large deformations. Phys. Rev. B 78, 184107 (2008)CrossRefGoogle Scholar
  4. 4.
    Bertoldi K., Gei M.: Instabilities in multilayered soft dielectrics. J. Mech. Phys. Solids 59, 18–42 (2011)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Bhattacharya K., Li J.Y., Xiao Y.: Electromechanical models for optimal design and effective behavior of electroactive polymers. In: Bar-Cohen, Y. (eds) Electroactive Polymer (EAP) Actuators as Artificial Muscles, chapter 12, pp. 309–330. SPIE press, Bellingham (2001)Google Scholar
  6. 6.
    Bustamante R.: Transversely isotropic non-linear electro-active elastomers. Acta Mech. 206, 237–259 (2009)MATHCrossRefGoogle Scholar
  7. 7.
    deBotton G.: Transversely isotropic sequentially laminated composites in finite elasticity. J. Mech. Phys. Solids 53, 1334–1361 (2005)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    deBotton, G., Tevet-Deree, L.: Electroactive polymer composites—analysis and simulation. In: Armstrong W.D. (eds.) Smart Structures and Materials 2006: Active Materials: Behavior and Mechanics, vol. 6170 of Proceedings of SPIE, pp. 2401–2410, San Diego, CA (2006)Google Scholar
  9. 9.
    deBotton G., Tevet-Deree L., Socolsky E.A.: Electroactive heterogeneous polymers: analysis and applications to laminated composites. Mech. Adv. Mater. Struct. 14, 13–22 (2007)CrossRefGoogle Scholar
  10. 10.
    Dorfmann A., Ogden R.W.: Nonlinear electroelasticity. Acta Mech. 174, 167–183 (2005)MATHCrossRefGoogle Scholar
  11. 11.
    Dorfmann A., Ogden R.W.: Nonlinear electroelastostatics: incremental equations and stability. Int. J. Eng. Sci. 48, 1–14 (2010)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Gei M., Roccabianca S., Bacca M.: Controlling band gap in electroactive polymer-based structures. IEEE-ASME Trans. Mechatron. 16, 102–107 (2011)CrossRefGoogle Scholar
  13. 13.
    Geymonat G., Müller S., Triantafyllidis N.: Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Arch. Ration. Mech. Anal. 122, 231–290 (1993)MATHCrossRefGoogle Scholar
  14. 14.
    Huang C., Zhang Q.M., deBotton G., Bhattacharya K.: All-organic dielectric-percolative three-component composite materials with high electromechanical response. Appl. Phys. Lett. 84, 4391–4393 (2004)CrossRefGoogle Scholar
  15. 15.
    Kofod G., Sommer-Larsen P., Kornbluh R., Pelrine R.: Actuation response of polyacrylate dielectric elastomers. J. Intell. Mater. Syst. Struct. 14, 787–793 (2003)CrossRefGoogle Scholar
  16. 16.
    McMeeking R.M., Landis C.M.: Electrostatic forces and stored energy for deformable dielectric materials. J. Appl. Mech. Trans. ASME 72, 581–590 (2005)MATHCrossRefGoogle Scholar
  17. 17.
    Mockensturm E.M., Goulbourne N.: Dynamic response of dielectric elastomers. Int. J. Nonlinear Mech. 41, 388–395 (2006)CrossRefGoogle Scholar
  18. 18.
    Nestorovic M.D., Triantafyllidis N.: Onset of failure in finitely strained layered composites subjected to combined normal and shear loading. J. Mech. Phys. Solids 52, 941–974 (2004)MATHCrossRefGoogle Scholar
  19. 19.
    O’Halloran A., O’Malley F., McHugh P.: A review on dielectric elastomer actuators, technology, applications, and challenges. J. Appl. Phys. 104, 071101 (2008)CrossRefGoogle Scholar
  20. 20.
    Pelrine R., Kornbluh R., Joseph J., Heydt R., Pei Q.-B., A. C.: High-field deformation of elastomeric dielectrics for actuators. Mater. Sci. Eng. 11, 89–100 (2000)CrossRefGoogle Scholar
  21. 21.
    Plante J.-S., Dubowsky S.: Large-scale failure modes of dielectric elastomer actuators. Int. J. Solids Struct. 43, 7727–7751 (2006)MATHCrossRefGoogle Scholar
  22. 22.
    Rudykh, S., deBotton, G.: Instabilities of hyperelastic fiber composites: micromechanical versus numerical analyses. J. Elast. doi:10.1007/s10659-011-9313-x (2011)
  23. 23.
    Rudykh, S., Bhattacharya, K., deBotton, G.: Snap-through actuation of thick-wall electroactive balloons. To appear in Int. J. Nonlinear Mech. doi:10.1016/j.ijnonlinmec.2011.05.006 (2011)
  24. 24.
    Rudykh, S., Lewinstein, A., Uner, G., deBotton, G.: Giant enhancement of the electromechanical coupling in soft heterogeneous dielectrics. Submitted for publication. http://arxiv.org/abs/1105.4217v1 (2011)
  25. 25.
    Shmuel G., deBotton G.: Out-of-plane shear of fiber composites at moderate stretch levels. J. Eng. Math. 68, 85–97 (2010)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Tevet-Deree, L.: Electroactive Polymer Composites—Analysis and Simulation. PhD thesis, Ben-Gurion University (2008)Google Scholar
  27. 27.
    Tian, L., Tevet-Deree, L., deBotton, G., Bhattacharya, K.: Dielectric elastomer composites. Submitted for publication (2010)Google Scholar
  28. 28.
    Toupin R.A.: The elastic dielectric. Arch. Ration. Mech. Anal. 5, 849–915 (1956)MathSciNetMATHGoogle Scholar
  29. 29.
    Triantafyllidis N., Maker B.N.: On the comparison between microscopic and macroscopic instability mechanisms in a class of fiber-reinforced composites. J. Appl. Mech. Trans. ASME 52, 794–800 (1985)MATHCrossRefGoogle Scholar
  30. 30.
    Triantafyllidis N., Nestorovic M.D., Schraad M.W.: Failure surfaces for finitely strained two-phase periodic solids under general in-plane loading. J. Appl. Mech. Trans. ASME 73(3), 505–515 (2006)MATHCrossRefGoogle Scholar
  31. 31.
    Vu D.K., Steinmann P.: Nonlinear electro- and magneto-elastostatics: material and spatial settings. Int. J. Solids Struct. 44(24), 7891–7905 (2007)MATHCrossRefGoogle Scholar
  32. 32.
    Zhang S., Huang C., Klein R.J., Xia F., Zhang Q.M., Cheng Z.-Y.: High performance electroactive polymers and nano-composites for artificial muscles. J. Intell. Mater. Syst. Struct. 18, 133–145 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.The Pearlstone Center for Aeronautical Studies, Department of Mechanical EngineeringBen-Gurion UniversityBeer-ShevaIsrael
  2. 2.Department of Biomedical EngineeringBen-Gurion UniversityBeer-ShevaIsrael

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