0
Research Papers

Electrostatically Driven Creep in Viscoelastic Dielectric Elastomers

[+] Author and Article Information
Jin Wang

Department of Mechanical Engineering,
Boston University,
Boston, MA 02215

Thao D. Nguyen

Department of Mechanical Engineering,
The Johns Hopkins University,
Baltimore, MD 21218

Harold S. Park

Department of Mechanical Engineering,
Boston University,
Boston, MA 02215
e-mail: parkhs@bu.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 20, 2013; final manuscript received November 4, 2013; accepted manuscript posted November 11, 2013; published online December 10, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(5), 051006 (Dec 10, 2013) (5 pages) Paper No: JAM-13-1437; doi: 10.1115/1.4025999 History: Received October 20, 2013; Revised November 04, 2013; Accepted November 11, 2013

We utilize a nonlinear, dynamic finite element model coupled with a finite deformation viscoelastic constitutive law to study the inhomogeneous deformation and instabilities resulting from the application of a constant voltage to dielectric elastomers. The constant voltage loading is used to study electrostatically driven creep and the resulting electromechanical instabilities for two different cases that have all been experimentally observed, i.e., electromechanical snap-through instability and bursting drops in a dielectric elastomer. We find that in general, increasing the viscoelastic relaxation time leads to an increase in time needed to nucleate the electromechanical instability. However, we find for these two cases that the time needed to nucleate the instability scales with the relaxation time.

FIGURES IN THIS ARTICLE
<>
Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Carpi, F., Bauer, S., and Rossi, D. D., 2010, “Stretching Dielectric Elastomer Performance,” Science, 330, pp. 1759–1761. [CrossRef] [PubMed]
Brochu, P., and Pei, Q., 2010, “Advances in Dielectric Elastomers for Actuators and Artificial Muscles,” Macromol. Rapid Commun., 31, pp. 10–36. [CrossRef] [PubMed]
Biddiss, E., and Chau, T., 2008, “Dielectric Elastomers As Actuators for Upper Limb Prosthetics: Challenges and Opportunities,” Med. Eng. Phys., 30, pp. 403–418. [CrossRef] [PubMed]
Bar-Cohen, Y., 2005, “Biomimetics: Mimicking and Inspired-by Biology,” Proc. SPIE, 5759, pp. 1–8. [CrossRef]
Mirfakhrai, T., Madden, J. D. W., and Baughman, R. H., 2007, “Polymer Artificial Muscles,” Mater. Today, 10(4), pp. 30–38. [CrossRef]
O'Halloran, A., O'Malley, F., and McHugh, P., 2008, “A Review on Dielectric Elastomer Actuators, Technology, Applications, and Challenges,” J. Appl. Phys., 104, p. 071101. [CrossRef]
Zhang, X., Wissler, C. L. M., Jaehne, B., and Kovacs, G., 2005, “Dielectric Elastomers in Actuator Technology,” Adv. Eng. Mater., 7(5), pp. 361–367. [CrossRef]
Zhang, X. Q., Wissler, M., Jaehne, B., Broennimann, R., and Kovacs, G., 2004, “Effects of Crosslinking, Prestrain and Dielectric Filler on the Electromechanical Response of a New Silicone and Comparison With Acrylic Elastomer,” Proc. SPIE, 5385, pp. 78–86. [CrossRef]
Plante, J.-S., and Dubowsky, S., 2006, “Large-Scale Failure Modes of Dielectric Elastomer Actuators,” Int. J. Solids Struct., 43, pp. 7727–7751. [CrossRef]
Keplinger, C., Kaltenbrunner, M., Arnold, N., and Bauer, S., 2008, “Capacitive Extensometry for Transient Strain Analysis of Dielectric Elastomer Actuators,” Appl. Phys. Lett., 92, p. 192903. [CrossRef]
Hong, W., 2011, “Modeling Viscoelastic Dielectrics,” J. Mech. Phys. Solids, 59, pp. 637–650. [CrossRef]
Zhao, X., Koh, S. J. A., and Suo, Z., 2011, “Nonequilibrium Thermodynamics of Dielectric Elastomers,” Int. J. Appl. Mech., 3(2), pp. 203–217. [CrossRef]
Foo, C. C., Cai, S., Koh, S. J. A., Bauer, S., and Suo, Z., 2012, “Model of Dissipative Dielectric Elastomers,” J. Appl. Phys., 111, p. 034102. [CrossRef]
Wang, H., Lei, M., and Cai, S., 2013, “Viscoelastic Deformation of a Dielectric Elastomer Membrane Subject to Electromechanical Loads,” J. Appl. Phys., 113, p. 213508. [CrossRef]
Tagarielli, V. L., Hildick-Smith, R., and Huber, J. E., 2012, “Electro-Mechanical Properties and Electrostriction Response of a Rubbery Polymer for EAP Applications,” Int. J. Solids Struct., 49, pp. 3409–3415. [CrossRef]
Park, H. S., and Nguyen, T. D., 2013, “Viscoelastic Effects on Electromechanical Instabilities in Dielectric Elastomers,” Soft Matter, 9, pp. 1031–1042. [CrossRef]
Buschel, A., Klinkel, S., and Wagner, W., 2013, “Dielectric Elastomers—Numerical Modeling of Nonlinear Visco-Electroelasticity,” Int. J. Numer. Methods Eng., 93, pp. 834–856. [CrossRef]
Khan, K. A., Wafai, H., and Sayed, T. E., 2013, “A Variational Constitutive Framework for the Nonlinear Viscoelastic Response of a Dielectric Elastomer,” Comput. Mech., 52, pp. 345–360. [CrossRef]
Pelrine, R., Kornbluh, R., Pei, Q., and Joseph, J., 2000, “High-Speed Electrically Actuated Elastomers With Strain Greater Than 100%,” Science, 287, pp. 836–839. [CrossRef] [PubMed]
Wang, Q., Suo, Z., and Zhao, X., 2012, “Bursting Drops in Solid Dielectrics Caused by High Voltages,” Nat. Commun., 3, p. 1157. [CrossRef] [PubMed]
Zhao, X., Hong, W., and Suo, Z., 2007, “Electromechanical Hysteresis and Coexistent States in Dielectric Elastomers,” Phys. Rev. B, 76, p. 134113. [CrossRef]
Suo, Z., Zhao, X., and Greene, W. H., 2008, “A Nonlinear Field Theory of Deformable Dielectrics,” J. Mech. Phys. Solids, 56, pp. 467–486. [CrossRef]
Park, H. S., Suo, Z., Zhou, J., and Klein, P. A., 2012, “A Dynamic Finite Element Method for Inhomogeneous Deformation and Electromechanical Instability of Dielectric Elastomer Transducers,” Int. J. Solids Struct., 49, pp. 2187–2194. [CrossRef]
Park, H. S., Wang, Q., Zhao, X., and Klein, P. A., 2013, “Electromechanical Instability on Dielectric Polymer Surface: Modeling and Experiment,” Comput. Methods Appl. Mech. Eng., 260, pp. 40–49. [CrossRef]
Suo, Z., 2010, “Theory of Dielectric Elastomers,” Acta Mech. Solida Sinica, 23(6), pp. 549–578. [CrossRef]
Vu, D. K., Steinmann, P., and Possart, G., 2007, “Numerical Modelling of Non-Linear Electroelasticity,” Int. J. Numer. Methods Eng., 70, pp. 685–704. [CrossRef]
Zhao, X., and Suo, Z., 2007, “Method to Analyze Electromechanical Instability of Dielectric Elastomers,” Appl. Phys. Lett., 91, p. 061921. [CrossRef]
Arruda, E. M., and Boyce, M. C., 1993, “A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials,” J. Mech. Phys. Solids, 41(2), pp. 389–412. [CrossRef]
Wissler, M., and Mazza, E., 2007, “Mechanical Behavior of an Acrylic Elastomer Used in Dielectric Elastomer Actuators,” Sensors Actuators A, 134, pp. 494–504. [CrossRef]
Reese, S., and Govindjee, S., 1998, “A Theory of Finite Viscoelasticity and Numerical Aspects,” Int. J. Solids Struct., 35(26–27), pp. 3455–3482. [CrossRef]
Hughes, T. J. R., 1987, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ.
Simo, J. C., Taylor, R. L., and Pister, K. S., 1985, “Variational and Projection Methods for the Volume Constraint in Finite Deformation Elasto-Plasticity,” Comput. Methods Appl. Mech. Eng., 51, pp. 177–208. [CrossRef]
Nguyen, T. D.2010, “A Comparison of a Nonlinear and Quasilinear Viscoelastic Anisotropic Model for Fibrous Tissues,” Proceedings of the IUTAM Symposium on Cellular, Molecular and Tissue Mechanics, Woods Hole, MA, June 18–21, K.Garikipati and E. M.Arruda, eds., Springer, New York, Vol. 16, pp. 19–29. [CrossRef]
Tahoe, 2013, SourceForge.net, http://sourceforge.net/projects/tahoe/

Figures

Grahic Jump Location
Fig. 1

Schematic of the two problems considered, with mechanical and electrostatic boundary conditions shown. (a) Single finite element for electromechanical snap-through problem. (b) Quarter symmetry model for bursting drop in a DE. Note that all schematics are shown in two dimensions as all z displacements are set to zero in this work to mimic a plane strain problem.

Grahic Jump Location
Fig. 2

Illustration of different stages of electromechanical snap-through instability. (a) Undeformed configuration. (b) Prior to snap-through instability. (c) Final configuration after snap-through instability has occurred. _D_VEC is the magnitude of the displacement vector.

Grahic Jump Location
Fig. 3

Time evolution of thickness-direction stretch λy for an applied normalized voltage of Φ = 0.7, or smaller than the critical voltage needed to cause the snap-through instability, for different viscosities η. (a) Not time normalized. (b) Normalized by the viscoelastic relaxation time τr.

Grahic Jump Location
Fig. 4

Time evolution of thickness-direction stretch λy for a constant normalized voltage of Φ = 0.8, or above the critical voltage needed to cause snap-through instability, for different viscosities η. (a) Not time normalized. (b) Normalized by the viscoelastic relaxation time τr.

Grahic Jump Location
Fig. 5

Illustration of electrostatically driven crack initiation and propagation in a DE containing a conductive drop. Note the formation and propagation of a crack from the top of the hole. _D_VEC is the magnitude of the displacement vector.

Grahic Jump Location
Fig. 6

(a) Crack propagation distance Δy as a function of time for different shear viscosities η. (b) Crack propagation distance Δy as a function of normalized time.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In