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Voltage-driven torsion of electroactive thick tubes reinforced with helical fibers

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Abstract

This work studies the voltage-driven torsional deformation of a thick-walled circular cylindrical tube composed of a dielectric elastomer (DE) reinforced with a family of helical fibers. The Helmholtz free energy of the DE composite tube involves separate DE matrix and fiber contributions. Upon the application of an electrical voltage difference on its inner and outer surfaces, the DE matrix contracts through the thickness and expands in cylindrical surfaces due to the Maxwell stress. Since the composite is stiffened along the fiber direction, it preferentially expands in the direction orthogonal to the fiber within the cylindrical surfaces. As a result, voltage-driven torsional deformation will occur in the helical fiber-reinforced DE tube. Although membrane theory was usually adopted to model fiber-reinforced thin DE membranes, the finite deformation theory is utilized in the present work to model relatively thick DE composite tubes. It is found that the bending effect plays an important role in the voltage-driven torsional deformation. The reorientation of the fibers and the distribution of the stress carried by the fibers in the tubes are discussed in detail so as to provide an interpretation to some new voltage-driven torsional behaviors. The theoretical model and physical insights provided in this work will aid the design and optimization of soft electroactive actuators and soft robotics.

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References

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

    Article  Google Scholar 

  2. Suo, Z.: Theory of dielectric elastomers. Acta Mech. Solida Sin. 23, 549–578 (2010)

    Article  Google Scholar 

  3. Brochu, P., Pei, Q.: Advances in dielectric elastomers for actuators and artificial muscles. Macromol. Rapid Commun. 31, 10–36 (2010)

    Article  Google Scholar 

  4. O’Brien, B.M., McKay, T.G., Gisby, T.A., Anderson, I.A.: Rotating turkeys and self-commutating artificial muscle motors. Appl. Phys. Lett. 100, 074108 (2012)

    Article  Google Scholar 

  5. Pei, Q., Pelrine, R., Stanford, S., Kornbluh, R., Rosenthal, M.: Electroelastomer rolls and their application for biomimetic walking robots. Synth. Metals 135, 129–131 (2003)

    Article  Google Scholar 

  6. Kovacs, G., Düring, L., Michel, S., Terrasi, G.: Stacked dielectric elastomer actuator for tensile force transmission. Sens. Actuators A Phys. 155, 299–307 (2009)

    Article  Google Scholar 

  7. Kovacs, G., Lochmatter, P., Wissler, M.: An arm wrestling robot driven by dielectric elastomer actuators. Smart Mater. Struct. 16, S306–S317 (2007)

    Article  Google Scholar 

  8. Carpi, F., Frediani, G., Turco, S., De Rossi, D.: Bioinspired tunable lens with muscle-like electroactive elastomers. Adv. Funct. Mater. 21, 4152–4158 (2011)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Akbari, S., Shea, H.: Microfabrication and characterization of an array of dielectric elastomer actuators generating uniaxial strain to stretch individual cells. J. Micromech. Microeng. 22, 045020 (2012)

    Article  Google Scholar 

  11. McMeeking, R.M., Landis, C.M.: Electrostatic forces and stored energy for deformable dielectric materials. J. Appl. Mech. 72, 581–590 (2005)

    Article  MATH  Google Scholar 

  12. Suo, Z., Zhao, X., Greene, W.H.: A nonlinear field theory of deformable dielectrics. J. Mech. Phys. Solids 56, 467–486 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dorfmann, A., Ogden, R.: Nonlinear electroelasticity. Acta Mech. 174, 167–183 (2005)

    Article  MATH  Google Scholar 

  14. Liu, L.: An energy formulation of continuum magneto-electro-elasticity with applications. J. Mech. Phys. Solids 63, 451–480 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Li, T., Keplinger, C., Baumgartner, R., Bauer, S., Yang, W., Suo, Z.: Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability. J. Mech. Phys. Solids 61, 611–628 (2013)

    Article  Google Scholar 

  16. Koh, S.J.A., Li, T., Zhou, J., Zhao, X., Hong, W., Zhu, J., Suo, Z.: Mechanisms of large actuation strain in dielectric elastomers. J. Polym. Sci. Part B Polym. Phys. 49, 504–515 (2011)

    Article  Google Scholar 

  17. Lu, T., An, L., Li, J., Yuan, C., Wang, T.: Electro-mechanical coupling bifurcation and bulging propagation in a cylindrical dielectric elastomer tube. J. Mech. Phys. Solids 85, 160–175 (2015)

    Article  MathSciNet  Google Scholar 

  18. Zhao, X., Suo, Z.: Method to analyze electromechanical stability of dielectric elastomers. Appl. Phys. Lett. 91, 061921 (2007)

    Article  Google Scholar 

  19. Rudykh, S., Bhattacharya, K.: Snap-through actuation of thick-wall electroactive balloons. Int. J. Nonlinear Mech. 47, 206–209 (2012)

    Article  Google Scholar 

  20. Zhou, J., Hong, W., Zhao, X., Zhang, Z., Suo, Z.: Propagation of instability in dielectric elastomers. Int. J. Solids Struct. 45, 3739–3750 (2008)

    Article  MATH  Google Scholar 

  21. Zhao, X., Suo, Z.: Theory of dielectric elastomers capable of giant deformation of actuation. Phys. Rev. Lett. 104, 178302 (2010)

    Article  Google Scholar 

  22. Zhu, J., Cai, S., Suo, Z.: Resonant behavior of a membrane of a dielectric elastomer. Int. J. Solids Struct. 47, 3254–3262 (2010)

    Article  MATH  Google Scholar 

  23. Zhu, J., Cai, S., Suo, Z.: Nonlinear oscillation of a dielectric elastomer balloon. Polym. Int. 59, 378–383 (2010)

    Article  Google Scholar 

  24. Lu, T., Huang, J., Jordi, C., Kovacs, G., Huang, R., Clarke, D.R., Suo, Z.: Dielectric elastomer actuators under equal-biaxial forces, uniaxial forces, and uniaxial constraint of stiff fibers. Soft Matter 8, 6167–6173 (2012)

    Article  Google Scholar 

  25. Huang, J., Lu, T., Zhu, J., Clarke, D.R., Suo, Z.: Large uni-directional actuation in dielectric elastomers achieved by fiber stiffening. Appl. Phys. Lett. 100, 211901 (2012)

    Article  Google Scholar 

  26. Lu, T., Shi, Z., Shi, Q., Wang, T.: Bioinspired bicipital muscle with fiber-constrained dielectric elastomer actuator. Extrem. Mech. Lett. 6, 75–81 (2016)

    Article  Google Scholar 

  27. Shian, S., Bertoldi, K., Clarke, D.R.: Dielectric elastomer based "grippers" for soft robotics. Adv. Mater. 27, 6814–6819 (2015)

    Article  Google Scholar 

  28. He, L., Lou, J., Du, J., Wang, J.: Finite bending of a dielectric elastomer actuator and pre-stretch effects. Int. J. Mech. Sci. 122, 120–128 (2017)

    Article  Google Scholar 

  29. Shian, S., Bertoldi, K., Clarke, D.R.: Use of aligned fibers to enhance the performance of dielectric elastomer inchworm robots. In: SPIE Smart Structures and Materials & Nondestructive Evaluation and Health Monitoring, International Society for Optics and Photonics, pp. 94301–94309 (2015)

  30. Lee, K., Tawfick, S.: Fiber micro-architected electro-elasto-kinematic muscles. Extrem. Mech. Lett. 8, 64–69 (2016)

    Article  Google Scholar 

  31. Goulbourne, N., Son, S., Fox, J.: Self-sensing McKibben actuators using dielectric elastomer sensors. In: The 14th International Symposium on: Smart Structures and Materials & Nondestructive Evaluation and Health Monitoring, International Society for Optics and Photonics, pp. 652414–652412 (2007)

  32. Son, S., Goulbourne, N.: Finite deformations of tubular dielectric elastomer sensors. J. Intell. Mater. Syst. Struct. 20, 2187–2199 (2009)

    Article  Google Scholar 

  33. He, L., Lou, J., Du, J., Wu, H.: Voltage-induced torsion of a fiber-reinforced tubular dielectric elastomer actuator. Compos. Sci. Technol. 140, 106–115 (2017)

    Article  Google Scholar 

  34. He, L., Lou, J., Du, J.: Analytical solutions for inextensible fiber-reinforced dielectric elastomer torsional actuators. J. Appl. Mech. 84, 051003 (2017)

    Article  Google Scholar 

  35. He, L., Lou, J., Du, J., Wu, H.: Voltage-driven axisymmetric torsion of a tubular dielectric elastomer actuator reinforced with one family of inextensible fibers. Eur. J. Mech. A Solids (2017) (under review)

  36. Demirkoparan, H., Pence, T.J.: Torsional swelling of a hyperelastic tube with helically wound reinforcement. J. Elast. 92, 61–90 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  37. Goriely, A., Tabor, M.: Rotation, inversion and perversion in anisotropic elastic cylindrical tubes and membranes. Proc. R. Soc. A 469, 20130011 (2013). https://doi.org/10.1098/rspa.2013.0011

    Article  MathSciNet  MATH  Google Scholar 

  38. Connolly, F., Walsh, C.J., Bertoldi, K.: Automatic design of fiber-reinforced soft actuators for trajectory matching. Proc. Natl. Acad. Sci. 114, 51–56 (2017)

    Article  Google Scholar 

  39. Zhu, J., Stoyanov, H., Kofod, G., Suo, Z.: Large deformation and electromechanical instability of a dielectric elastomer tube actuator. J. Appl. Phys. 108, 074113 (2010)

    Article  Google Scholar 

  40. Goulbourne, N.C.: A mathematical model for cylindrical, fiber reinforced electro-pneumatic actuators. Int. J. Solids Struct. 46, 1043–1052 (2009)

    Article  MATH  Google Scholar 

  41. Melnikov, A., Ogden, R.W.: Finite deformations of an electroelastic circular cylindrical tube. Z. Angew. Math. Phys. 67, 1–20 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  42. Spencer, A.J.M.: Theory of invariants. In: Eringen, A. (ed.) Continuum Physics, pp. 239–353. Academic Press, New York (1971)

    Google Scholar 

  43. Zheng, Q.S.: Theory of representations for tensor functions. Appl. Mech. Rev. 47, 545–587 (1994)

    Article  Google Scholar 

  44. Bustamante, R.: Transversely isotropic non-linear electro-active elastomers. Acta Mech. 206, 237–259 (2009)

    Article  MATH  Google Scholar 

  45. Bustamante, R., Merodio, J.: Constitutive structure in coupled non-linear electro-elasticity: invariant descriptions and constitutive restrictions. Int. J. Nonlinear Mech. 46, 1315–1323 (2011)

    Article  Google Scholar 

  46. Murphy, J.: Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants. Eur. J. Mech. A Solids 42, 90–96 (2013)

    Article  MathSciNet  Google Scholar 

  47. Horgan, C.O., Smayda, M.G.: The importance of the second strain invariant in the constitutive modeling of elastomers and soft biomaterials. Mech. Mater. 51, 43–52 (2012)

    Article  Google Scholar 

  48. Singh, M., Pipkin, A.: Controllable states of elastic dielectrics. Arch. Ration. Mech. Anal. 21, 169–210 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  49. Lu, T.-Q., Suo, Z.-G.: Large conversion of energy in dielectric elastomers by electromechanical phase transition. Acta Mech. Sin. 28, 1106–1114 (2012)

    Article  MATH  Google Scholar 

  50. Xiao, R., Gou, X., Chen, W.: Suppression of electromechanical instability in fiber-reinforced dielectric elastomers. AIP Adv. 6, 035321 (2016)

    Article  Google Scholar 

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Authors and Affiliations

  1. Piezoelectric Device Laboratory, Department of Mechanics and Engineering Science, Ningbo University, Ningbo, 315211, Zhejiang, China

    Liwen He, Jia Lou & Jianke Du

Authors
  1. Liwen He
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  2. Jia Lou
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  3. Jianke Du
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Correspondence to Liwen He or Jia Lou.

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He, L., Lou, J. & Du, J. Voltage-driven torsion of electroactive thick tubes reinforced with helical fibers. Acta Mech 229, 2117–2131 (2018). https://doi.org/10.1007/s00707-017-2103-1

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  • DOI: https://doi.org/10.1007/s00707-017-2103-1

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