Applied Physics A

, 124:2 | Cite as

Biaxial experimental and analytical characterization of a dielectric elastomer

  • Alexander Helal
  • Marc DoumitEmail author
  • Robert Shaheen


Electroactive polymers (EAPs) have emerged as a strong contender for use in low-cost efficient actuators in multiple applications especially related to biomimetic and mobile-assistive devices. Dielectric elastomers (DE), a subcategory of these smart materials, have been of particular interest due to their large achievable deformation and favourable mechanical and electro-mechanical properties. Previous work has been completed to understand the behaviour of these materials; however, their properties require further investigation to properly integrate them into real-world applications. In this study, a biaxial tensile experimental evaluation of 3M™ VHB 4905 and VHB 4910 is presented with the purpose of illustrating the elastomers’ transversely isotropic mechanical behaviours. These tests were applied to both tapes for equibiaxial stretch rates ranging between 0.025 and 0.300 s−1. Subsequently, a dynamic planar biaxial visco-hyperelastic constitutive relationship was derived from a Kelvin–Voigt rheological model and the general Hooke’s law for transversely isotropic materials. The model was then fitted to the experimental data to obtain three general material parameters for either tapes. The model’s ability to predict tensile stress response and internal energy dissipation, with respect to experimental data, is evaluated with good agreement. The model’s ability to predict variations in mechanical behaviour due to changes in kinematic variables is then illustrated for different conditions.


Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interest.


  1. 1.
    P. Lochmatter, Development of a Shell-like Electroactive Polymer (EAP) Actuator, Zurich. Swiss Federal Institute of Technology Zurich (2007)Google Scholar
  2. 2.
    J. Madden, Dielectric Elastomers as High-Performance Electroactive Polymers, in Dielectric Elastomers as Electromechanical Transducers, (Elsevier, Oxford, 2008), pp. 13–21CrossRefGoogle Scholar
  3. 3.
    Y. Bar-Cohen, E.A.P. History, Current status, and infrastructure” in Electroactive Polymer (EAP) Actuators as Artificial Muscles: Reality, Potential, and Challenges, 2nd edn, (Bellingham, SPIE—The International Society for Optical Engineering, 2004), pp. 3–52Google Scholar
  4. 4.
    R. Kornbluh, R. Pelrine, Q. Pei, M. Rosenthal, S. Stanford, N. Bonwit, R. Heydt, H. Prahlad, S.V. Shastri, Application of Dielectric Elastomer EAP Actuators, in Electroactive Polymer (EAP) Actuators as Artificial Muscles (The Society of Photo-Optical Instrumentation Engineers, Bellingham, 2004), pp. 529–580Google Scholar
  5. 5.
    R. Kornbluh, R. Heydt, R. Pelrine, “Dielectric Elastomer Actuators: Fundementals” in Biomedical Applications of Electroactive Polymer Actuators, (Wiley, West Sussex, 2009), pp. 387–393Google Scholar
  6. 6.
    I.A. Anderson, T.A. Gisby, T.G. McKay, B.M. O’Brien, E.P. Calius, Multi-functional dielectric elastomer artificial muscles for soft and smart machines. J. Appl. Phys 112(4), 1–20 (2012)CrossRefGoogle Scholar
  7. 7.
    S. Rosset, H.R. Shea, Small, fast, and tough: Shrinking down integrated elastomer transducers. Appl. Phys. Rev. 3, 3 (2016)Google Scholar
  8. 8.
    R. Kornbluh, R. Pelrine, “High-Performance Acrylic and Silicone Elastomers” in Dielectric Elastomers as Electromechanical Transducers, (Elsevier, Oxford, 2008), pp. 33–42CrossRefGoogle Scholar
  9. 9.
    R. Pelrine, R. Kornbluh, Q. Pei, S. Stanford, S. Oh, J. Eckerle, R. Full, M. Rosenthal, K. Meijer, Dielectric elastomer artificial muscle actuators: toward biomimetic motion, in Proc. of SPIE Vol. 4695 (2002) (2000)Google Scholar
  10. 10.
    P. Steinmann, M. Hossain, G. Possart, Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for Treloar’s data. Arch. Appl. Mech 82(9), 1183–1217 (2012)ADSCrossRefzbMATHGoogle Scholar
  11. 11.
    M. Hossain, P. Steinmann, More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study. J. Mech. Behavior Mat 22(1–2), 27–50 (2013)Google Scholar
  12. 12.
    G. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering. (Wiley, Chichester, 2000)zbMATHGoogle Scholar
  13. 13.
    R. Ogden, Large deformation isotropic elasticity - on the correlation of theory and experiment for incompressible rubberlike solids,” in Proc. of the R. Soc. of London. Series A, Math. and Phys. Sci, pp. 565–584 (1972)Google Scholar
  14. 14.
    O. Yeoh, Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber Chem. Technol 63(5), 792–805 (1990)CrossRefGoogle Scholar
  15. 15.
    N. Goulbourne, E. Mockensturm, M. Frecker, A nonlinear model for dielectric elastomer membranes. J. Appl. Mech 72(6), 899–906 (2005)ADSCrossRefzbMATHGoogle Scholar
  16. 16.
    G. Kofod, Dielectric Elastomer Actuators. (The Technical University of Denmark, Denmark, 2001)Google Scholar
  17. 17.
    M. Wissler, E. Mazza, Modeling of a pre-strained circular actuator made of dielectric elastomers. Sens. Actuators A: Phys 120(1), 184–192 (2005)CrossRefGoogle Scholar
  18. 18.
    G. Kofod, P. Sommer-Larsen, Silicone dielectric elastomer actuators: finite-elasticity model of actuation. Sens. Actuators A: Phys 122(26), 273–283 (2005)CrossRefGoogle Scholar
  19. 19.
    P. Lochmatter, G. Kovacs, M. Silvain, Characterization of dielectric elastomer actuators based on a hyperelastic film model. Sens. Actuators A 135(2), 748–757 (2007)CrossRefGoogle Scholar
  20. 20.
    M. Mansouri, H. Darijani, “Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach. Int. J. Solids Struct 51, 4316–4326 (2014)CrossRefGoogle Scholar
  21. 21.
    M. Wissler, E. Mazza, Mechanical behavior of an acrylic elastomer used in dielectric elastomer actuators. Sens. Actuators A: Phys 134(2), 494–504 (2007)CrossRefGoogle Scholar
  22. 22.
    M. Hossain, D. Vu, P. Steinmann, Experimental study and numerical modelling of VHB 4910 polymer. Comput. Mater. Sci 59, 65–74 (2012)CrossRefGoogle Scholar
  23. 23.
    C. Foo, S. Cai, S. Koh, S. Bauer, Z. Suo, Model of dissipative dielectric elastomers. J. Appl. Phys. 111, 034102 (2012)Google Scholar
  24. 24.
    J. Zhang, H. Chen, J. Sheng, L. Liu, Y. Wang, S. Jia, Constitutive relation of viscoelastic dielectric elastomer. Theor. Appl. Mech. Lett. 3, 5 (2013)Google Scholar
  25. 25.
    K. Patra, R. Sahu, A visco-hyperelastic approach to modelling rate-dependent large deformation of a dielectric acrylic elastomer. Int. J. Mech. Mat. Des 11, 79–90 (2015)CrossRefGoogle Scholar
  26. 26.
    A. Gent, A new constitutive relation for rubber. Rubber Chem. Technol 69(1), 59–61 (1996)CrossRefGoogle Scholar
  27. 27.
    J. Bergström, M. Boyce, Constitutive modeling of the large strain time-dependent behavior of elastomers. J. Mech. Phys. Solids 46(5), 931–954 (1998)ADSCrossRefzbMATHGoogle Scholar
  28. 28.
    P. Lochmatter, G. Kovacs, M. Wissler, Characterization of dielectric elastomer actuators based on a visco-hyperelastic film model. Smart Mat. Struct. 16, 2 (2007)Google Scholar
  29. 29.
    Y. Wang, H. Xue, H. Chen, J. Qiang, A dynamic visco-hyperelastic model of dielectric elastomers and their energy dissipation characteristics. Appl. Phys. A 112, 339–347 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    X. Zhao, S.J.A. Koh, Z. Suo, Nonequilibrium thermodynamics of dielectric elastomers. Int. J. Appl. Mech 3(2), 203–217 (2011)CrossRefGoogle Scholar
  31. 31.
    W. Hong, Modeling viscoelastic dielectrics. J. Mech. Phys. Solids 59(3), 637–650 (2011)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Y. Wang, H. Chen, Y. Wang, D. Li, A general visco-hyperelastic model for dielectric elastomers and its efficient simulation based on complex frequency representation. Int. J. Appl. Mech. 7, 1 (2015)Google Scholar
  33. 33.
    G. Berselli, R. Vertechy, M. Babic, V. Parenti Castelli, Dynamic modeling and experimental evaluation of a constant-force dielectric elastomer actuator. J. Intelligent Mat. Syst 24(6), 779–791 (2012)CrossRefGoogle Scholar
  34. 34.
    R. Sarban, B. Lassen, M. Willatzen, Dynamic electromechanical modeling of dielectric elastomer actuators with metallic electrodes. IEEE/ASME Trans. Mechatron., 17(5), 960–967 (2012)CrossRefGoogle Scholar
  35. 35.
    J. Zhang, L. Tang, B. Li, Y. Wang, Modeling of the dynamic characteristic of viscoelastic dielectric elastomer actuators subject to different conditions of mechanical load. J. Appl. Phys. 117, 8 (2015)Google Scholar
  36. 36.
    R. Pelrine, P. Sommer-Larsen, R. Kornbluh, R. Heydt, G. Kofod, Q. Pei, Applications of dielectric elastomer actuators. Proc SPIE 4329, 335, Newport Beach (2001)Google Scholar
  37. 37.
    J. Plante, Dielectric Elastomer Actuators for Binary Robotics and Mechatronics (Massachusetts Institute of Technology, Cambridge, 2006)Google Scholar
  38. 38.
    CellScale, BioTester Biaxial Test System—User Manual (2016)Google Scholar
  39. 39.
    J.-D. Nam, H. Choi, J. Koo, Y. Lee, K. Kim, Dielectric Elastomers for Artificial Muscles in Electroactive Polymers for Robotic Applications: Artificial Muscles and Sensors, (Springer-Verlag, London, 2007), pp. 37–48CrossRefGoogle Scholar
  40. 40.
    C. Chiang Foo, S.J.A. Koh, C. Keplinger, R. Kaltseis, S. Bauer, Z. Suo, Performance of dissipative dielectric elastomer generators. J. Appl. Phys 111, 9 (2012)Google Scholar
  41. 41.
    M. Labrosse, R. Jafar, J. Ngu, M. Boodhwani, Planar biaxial testing of heart valve cusp replacement biomaterials: experiments, theory and material constants. Acta Biomed 45, 303–320 (2016)Google Scholar
  42. 42.
    J. Humphrey, R. Vawter, R. Vito, Quantification of strains in biaxially tested soft tissues. J. Biomechanics 20(1), 56–65 (1987)CrossRefGoogle Scholar
  43. 43.
    J. Humphrey, Cardiovascular Solid Mechanics: Cells, Tissues, and Organs. (Springer, New York, 2002)CrossRefGoogle Scholar
  44. 44.
    M. Labrosse, MCG4102/5108 Finite Element Analysis. (University of Ottawa, Ottawa, 2014)Google Scholar
  45. 45.
    M. Carfagni, E. Lenzi, M. Pierini, The loss factor as a measure of mechanical damping. Proc. SPIE 3243, 580C (1998)Google Scholar
  46. 46.
    M.I. Adhesives, T. Division, VHB Tape Specialty Tapes. (3M Industrial Adhesives and Tapes Division, St Paul, 2015)Google Scholar
  47. 47.
    J. Cowie, V. Arrighi, Polymers: Chemistry and Physics of Modern Materials. (CRC Press, Third Edition, 2007)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of OttawaOttawaCanada

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