Research Papers

Electromechanical Instability of Dielectric Elastomer Actuators With Active and Inactive Electric Regions

[+] Author and Article Information
Atul Kumar Sharma

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India
e-mail: asharma4@me.iitr.ac.in

Pramod Kumar

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India

A. Singh

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India

D. M. Joglekar

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India
e-mail: dhanashri.joglekar.fme@iitr.ac.in

M. M. Joglekar

Department of Mechanical and Industrial Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247 667, India
e-mail: mmj81fme@iitr.ac.in

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received January 19, 2019; final manuscript received February 28, 2019; published online March 19, 2019. Assoc. Editor: Shaoxing Qu.

J. Appl. Mech 86(6), 061008 (Mar 19, 2019) (11 pages) Paper No: JAM-19-1030; doi: 10.1115/1.4042996 History: Received January 19, 2019; Accepted February 28, 2019

Electrically driven dielectric elastomers (DEs) suffer from an electromechanical instability (EMI) when the applied potential difference reaches a critical value. A majority of the past investigations address the mechanics of this operational instability by restricting the kinematics to homogeneous deformations. However, a DE membrane comprising both active and inactive electric regions undergoes inhomogeneous deformation, thus necessitating the solution of a complex boundary value problem. This paper reports the numerical and experimental investigation of such DE actuators with a particular emphasis on the EMI in quasistatic mode of actuation. The numerical simulations are performed using an in-house finite element framework developed based on the field theory of deformable dielectrics. Experiments are performed on the commercially available acrylic elastomer (VHB 4910) at varying levels of prestretch and proportions of the active to inactive areas. In particular, two salient features associated with the electromechanical response are addressed: the effect of the flexible boundary constraint and the locus of the dielectric breakdown point. To highlight the influence of the flexible boundary constraint, the estimates of the threshold value of potential difference on the onset of electromechanical instability are compared with the experimental observations and with those obtained using the lumped parameter models reported previously. Additionally, a locus of localized thinning, near the boundary of the active electric region, is identified using the numerical simulations and ascertained through the experimental observations. Finally, an approach based on the Airy stress function is suggested to justify the phenomenon of localized thinning leading to the dielectric breakdown.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Pelrine, R., Kornbluh, R., Pei, Q., and Joseph, J., 2000, “High-Speed Electrically Actuated Elastomers With Strain Greater Than 100%,” Science, 287(5454), pp. 836–839. [CrossRef] [PubMed]
Suo, Z., 2010, “Theory of Dielectric Elastomers,” Acta Mech. Solida Sin., 23(6), pp. 549–578. [CrossRef]
Carpi, F., Bauer, S., and De Rossi, D., 2010, “Stretching Dielectric Elastomer Performance,” Science, 330(6012), pp. 1759–1761. [CrossRef] [PubMed]
Gu, G.-Y., Zhu, J., Zhu, L.-M., and Zhu, X., 2017, “A Survey on Dielectric Elastomer Actuators for Soft Robots,” Bioinspir. Biomim., 12(1), p. 011003. [CrossRef] [PubMed]
McKay, T., O'Brien, B., Calius, E., and Anderson, I., 2010, “An Integrated, Self-Priming Dielectric Elastomer Generator,” Appl. Phys. Lett., 97(6), p. 062911. [CrossRef]
Li, B., Zhang, J., Liu, L., Chen, H., Jia, S., and Li, D., 2014, “Modeling of Dielectric Elastomer as Electromechanical Resonator,” J. Appl. Phys., 116(12), p. 124509. [CrossRef]
Brochu, P., and Pei, Q., 2010, “Advances in Dielectric Elastomers for Actuators and Artificial Muscles,” Macromol. Rapid Commun., 31(1), pp. 10–36. [CrossRef] [PubMed]
Anderson, I. A., Gisby, T. A., McKay, T. G., O'Brien, B. M., and Calius, E. P., 2012, “Multi-Functional Dielectric Elastomer Artificial Muscles for Soft and Smart Machines,” J. Appl. Phys., 112(4), p. 041101. [CrossRef]
Lu, T., Shi, Z., Shi, Q., and Wang, T., 2016, “Bioinspired Bicipital Muscle With Fiber-Constrained Dielectric Elastomer Actuator,” Extreme Mech. Lett., 6, pp. 75–81. [CrossRef]
Xu, B.-X., Mueller, R., Klassen, M., and Gross, D., 2010, “On Electromechanical Stability Analysis of Dielectric Elastomer Actuators,” Appl. Phys. Lett., 97(16), p. 162908. [CrossRef]
Zhao, X., Hong, W., and Suo, Z., 2007, “Electromechanical Hysteresis and Coexistent States in Dielectric Elastomers,” Phys. Rev. B, 76(13), p. 134113. [CrossRef]
Zhao, X., and Wang, Q., 2014, “Harnessing Large Deformation and Instabilities of Soft Dielectrics: Theory, Experiment, and Application,” Appl. Phys. Rev., 1(2), p. 021304. [CrossRef]
Mao, G., Huang, X., Diab, M., Liu, J., and Qu, S., 2016, “Controlling Wrinkles on the Surface of a Dielectric Elastomer Balloon,” Extreme Mech. Lett., 9, pp. 139–146. [CrossRef]
Liu, X., Li, B., Chen, H., Jia, S., and Zhou, J., 2016, “Voltage-Induced Wrinkling Behavior of Dielectric Elastomer,” J. Appl. Polym. Sci. 133(14), p. 43258. [CrossRef]
Mao, G., Xiang, Y., Huang, X., Hong, W., Lu, T., and Qu, S., 2018, “Viscoelastic Effect on the Wrinkling of an Inflated Dielectric-Elastomer Balloon,” J. Appl. Mech., 85(7), p. 071003. [CrossRef]
Li, B., Chen, H., Qiang, J., Hu, S., Zhu, Z., and Wang, Y., 2011, “Effect of Mechanical Pre-Stretch on the Stabilization of Dielectric Elastomer Actuation,” J. Phys. D Appl. Phys., 44(15), p. 155301. [CrossRef]
Sharma, A. K., Bajpayee, S., Joglekar, D. M., and Joglekar, M. M., 2017, “Dynamic Instability of Dielectric Elastomer Actuators Subjected to Unequal Biaxial Prestress,” Smart Mater. Struct., 26(11), p. 115019. [CrossRef]
Sharma, A. K., Arora, N., and Joglekar, M. M., 2018, “DC Dynamic Pull-In Instability of a Dielectric Elastomer Balloon: An Energy-Based Approach,” Proc. R. Soc. A, 474(2211), p. 20170900. [CrossRef]
Xu, B.-X., Mueller, R., Theis, A., Klassen, M., and Gross, D., 2012, “Dynamic Analysis of Dielectric Elastomer Actuators,” Appl. Phys. Lett., 100(11), p. 112903. [CrossRef]
Joglekar, M. M., 2014, “An Energy-Based Approach to Extract the Dynamic Instability Parameters of Dielectric Elastomer Actuators,” J. Appl. Mech. Trans. ASME, 81(9), p. 091010. [CrossRef]
Joglekar, M. M., 2015, “Dynamic-Instability Parameters of Dielectric Elastomer Actuators With Equal Biaxial Prestress,” AIAA J., 53(10), pp. 3129–3133. [CrossRef]
Arora, N., Kumar, P., and Joglekar, M., 2018, “A Modulated Voltage Waveform for Enhancing the Travel Range of Dielectric Elastomer Actuators,” J. Appl. Mech., 85(11), p. 111009. [CrossRef]
Sharma, A. K., and Joglekar, M., 2018, “Effect of Anisotropy on the Dynamic Electromechanical Instability of a Dielectric Elastomer Actuator,” Smart Mater. Struct., 28(1), p. 015006. [CrossRef]
Sharma, A. K., and Joglekar, M., 2019, “A Numerical Framework for Modeling Anisotropic Dielectric Elastomers,” Comput. Methods Appl. Mech. Eng., 344, pp. 402–420. [CrossRef]
Eder-Goy, D., Zhao, Y., and Xu, B.-X., 2017, “Dynamic Pull-In Instability of a Prestretched Viscous Dielectric Elastomer Under Electric Loading,” Acta Mech., 228(12), pp. 4293–4307. [CrossRef]
Zhang, J., Chen, H., and Li, D., 2017, “Loss of Tension in Electromechanical Actuation of Fiber-Constrained Viscoelastic Dielectric Elastomers,” Europhys. Lett., 117(6), p. 67004. [CrossRef]
Patra, K., and Sahu, R. K., 2015, “A Visco-Hyperelastic Approach to Modelling Rate-Dependent Large Deformation of a Dielectric Acrylic Elastomer,” Int. J. Mech. Mater. Des., 11(1), pp. 79–90. [CrossRef]
Zhao, X., and Suo, Z., 2007, “Method to Analyze Electromechanical Stability of Dielectric Elastomers,” Appl. Phys. Lett., 91(6), p. 061921. [CrossRef]
Huang, J., Li, T., Chiang, F., Clarke, D. R., and Suo, Z., 2012, “Giant, Voltage-Actuated Deformation of a Dielectric Elastomer Under Dead Load,” Appl. Phys. Lett., 100(4), p. 041911. [CrossRef]
Bense, H., Trejo, M., Reyssat, E., Bico, J., and Roman, B., 2017, “Buckling of Elastomer Sheets Under Non-Uniform Electro-Actuation,” Soft Matter, 13(15), pp. 2876–2885. [CrossRef] [PubMed]
Rasti, P., Hous, H., Schlaak, H. F., Kiefer, R., and Anbarjafari, G., 2015, “Dielectric Elastomer Stack Actuator-Based Autofocus Fluid Lens,” Appl. Optics, 54(33), pp. 9976–9980. [CrossRef]
Koh, S. J. A., Li, T., Zhou, J., Zhao, X., Hong, W., Zhu, J., and Suo, Z., 2011, “Mechanisms of Large Actuation Strain in Dielectric Elastomers,” J. Polym. Sci. Part B Polym. Phys., 49(7), pp. 504–515. [CrossRef]
Sahu, R. K., Saini, A., Ahmad, D., Patra, K., and Szpunar, J., 2016, “Estimation and Validation of Maxwell Stress of Planar Dielectric Elastomer Actuators,” J. Mech. Sci. Technol., 30(1), pp. 429–436. [CrossRef]
McCoul, D., and Pei, Q., 2015, “Tubular Dielectric Elastomer Actuator for Active Fluidic Control,” Smart Mater. Struct., 24(10), p. 105016. [CrossRef]
Zhao, J., Wang, S., McCoul, D., Xing, Z., Huang, B., Liu, L., and Leng, J., 2016, “Bistable Dielectric Elastomer Minimum Energy Structures,” Smart Mater. Struct., 25(075016), p. 075016. [CrossRef]
Zhou, J., Hong, W., Zhao, X., Zhang, Z., and Suo, Z., 2008, “Propagation of Instability in Dielectric Elastomers,” Int. J. Solids Struct., 45(13), pp. 3739–3750. [CrossRef]
Bozlar, M., Punckt, C., Korkut, S., Zhu, J., Chiang, F., and Aksay, I. A., 2012, “Dielectric Elastomer Actuators With Elastomeric Electrodes,” Appl. Phys. Lett., 101(9), p. 091907. [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(15), pp. 2187–2194. [CrossRef]
Qu, S., and Suo, Z., 2012, “A Finite Element Method for Dielectric Elastomer Transducers,” Acta Mech. Solida Sin., 25(5), pp. 459–466. [CrossRef]
Henann, D. L., Chester, S. A., and Bertoldi, K., 2013, “Modeling of Dielectric Elastomers: Design of Actuators and Energy Harvesting Devices,” J. Mech. Phys. Solids, 61(10), pp. 2047–2066. [CrossRef]
Toupin, R. A., 1956, “The Elastic Dielectric,” J. Ratio. Mech. Anal., 5(6), pp. 849–915.
McMeeking, R. M., and Landis, C. M., 2005, “Electrostatic Forces and Stored Energy for Deformable Dielectric Materials,” J. Appl. Mech. Trans. ASME, 72(4), pp. 581–590. [CrossRef]
Suo, Z., Zhao, X., and Greene, W. H., 2008, “A Nonlinear Field Theory of Deformable Dielectrics,” J. Mech. Phys. Solids, 56(2), pp. 467–486. [CrossRef]
Klinkel, S., Zwecker, S., and Müller, R., 2013, “A Solid Shell Finite Element Formulation for Dielectric Elastomers,” J. Appl. Mech., 80(2), p. 021026. [CrossRef]
Gao, Z., Tuncer, A., and Cuitiño, A. M., 2011, “Modeling and Simulation of the Coupled Mechanical–Electrical Response of Soft Solids,” Int. J. Plasticity, 27(10), pp. 1459–1470. [CrossRef]
Park, H. S., and Nguyen, T. D., 2013, “Viscoelastic Effects on Electromechanical Instabilities in Dielectric Elastomers,” Soft Matter, 9(4), pp. 1031–1042. [CrossRef]
Vogel, F., Göktepe, S., Steinmann, P., and Kuhl, E., 2014, “Modeling and Simulation of Viscous Electro-Active Polymers,” Eur. J. Mech. A Solids, 48, pp. 112–128. [CrossRef] [PubMed]
Schlögl, T., and Leyendecker, S., 2016, “Electrostatic–Viscoelastic Finite Element Model of Dielectric Actuators,” Comput. Methods Appl. Mech. Eng., 299, pp. 421–439. [CrossRef]
Vogan, J. D., 2004, “Development of Dielectric Elastomer Actuators for MRI Devices,” Master’s thesis, Massachusetts Institute of Technology, Cambridge, MA.
Plante, J.-S., and Dubowsky, S., 2006, “Large-Scale Failure Modes of Dielectric Elastomer Actuators,” Int. J. Solids Struct., 43(25–26), pp. 7727–7751. [CrossRef]
Orita, A., and Cutkosky, M. R., 2016, “Scalable Electroactive Polymer for Variable Stiffness Suspensions,” IEEE ASME Trans. Mechatron., 21(6), pp. 2836–2846. [CrossRef]
Zurlo, G., Destrade, M., DeTommasi, D., and Puglisi, G., 2017, “Catastrophic Thinning of Dielectric Elastomers,” Phys. Rev. Lett., 118(7), p. 078001. [CrossRef] [PubMed]
Dorfmann, A., and Ogden, R., 2005, “Nonlinear Electroelasticity,” Acta Mech., 174(3–4), pp. 167–183. [CrossRef]
Patil, R. U., Mishra, B. K., and Singh, I. V., 2018, “A Local Moving Extended Phase Field Method (lmxpfm) for Failure Analysis of Brittle Materials,” Comput. Methods Appl. Mech. Eng., 342, pp. 674–709. [CrossRef]
Jog, C. S., and Patil, K. D., 2016, “A Hybrid Finite Element Strategy for the Simulation of MEMS Structures,” Int. J. Numer. Methods Eng., 106(7), pp. 527–555. [CrossRef]
Kumar, M., Singh, I. V., Mishra, B. K., Ahmad, S., Rao, A. V., and Kumar, V., 2018, “Mixed Mode Crack Growth in Elasto-Plastic-Creeping Solids Using XFEM,” Eng. Fract. Mech., 199, pp. 489–517. [CrossRef]
Zhao, X., and Suo, Z., 2008, “Method to Analyze Programmable Deformation of Dielectric Elastomer Layers,” Appl. Phys. Lett., 93(25), p. 251902. [CrossRef]
Gent, A. N., 1996, “A New Constitutive Relation for Rubber,” Rubber Chem. Technol., 69(1), pp. 59–61. [CrossRef]
Godaba, H., Zhang, Z.-Q., Gupta, U., Foo, C. C., and Zhu, J., 2017, “Dynamic Pattern of Wrinkles in a Dielectric Elastomer,” Soft Matter, 13(16), pp. 2942–2951. [CrossRef] [PubMed]
Kofod, G., 2008, “The Static Actuation of Dielectric Elastomer Actuators: How Does Pre-Stretch Improve Actuation?,” J. Phys. D Appl. Phys., 41(21), p. 215405. [CrossRef]
Malkus, D. S., and Hughes, T. J., 1978, “Mixed Finite Element Methods—Reduced and Selective Integration Techniques: A Unification of Concepts,” Comput. Methods Appl. Mech. Eng., 15(1), pp. 63–81. [CrossRef]
Jiang, L., Zhou, Y., Chen, S., Ma, J., Betts, A., and Jerrams, S., 2018, “Electromechanical Instability in Silicone- and Acrylate-Based Dielectric Elastomers,” J. Appl. Polym. Sci., 135(9), p. 45733. [CrossRef]
Yeoh, O. H., and Fleming, P., 1997, “A New Attempt to Reconcile the Statistical and Phenomenological Theories of Rubber Elasticity,” J. Polym. Sci. Part B Polym. Phys., 35(12), pp. 1919–1931. [CrossRef]
Mihai, L. A., and Goriely, A., 2017, “How to Characterize a Nonlinear Elastic Material? A Review on Nonlinear Constitutive Parameters in Isotropic Finite Elasticity,” Proc. R. Soc. A, 473(2207), p. 20170607. [CrossRef]
Huang, J., Shian, S., Diebold, R. M., Suo, Z., and Clarke, D. R., 2012, “The Thickness and Stretch Dependence of the Electrical Breakdown Strength of an Acrylic Dielectric Elastomer,” Appl. Phys. Lett., 101(12), p. 122905. [CrossRef]
Doghri, I., 2000, Mechanics of Deformable Solids, Springer-Verlag, Berlin, Heidelberg.


Grahic Jump Location
Fig. 1

An arbitrary continuum dielectric body in undeformed and deformed states

Grahic Jump Location
Fig. 2

(a) Schematic of a dielectric elastomer in the reference state. (b) Prestretched DE actuator with clamped boundaries and square-shaped electrodes (LAP × LAP) deposited on the top and bottom surfaces.

Grahic Jump Location
Fig. 3

A representative specimen used for experimentation

Grahic Jump Location
Fig. 4

(a) Schematic and (b) FE mesh of the (1/8)th symmetric model of DEA used in finite element simulations

Grahic Jump Location
Fig. 5

Electromechanical response of the dielectric elastomer actuator for varying proportions of active to inactive area and the applied prestretch: (a) λP = 2.0, (b) λP = 2.5, and (c) λP = 3.0., finite element analysis; o, experiment.

Grahic Jump Location
Fig. 6

Evolution of the total thickness stretch at the breakdown point with the applied potential difference for (a) λP = 2.0, (b) λP = 2.5, and (c) λP = 3.0

Grahic Jump Location
Fig. 7

(a) and (b) Experimental evidences of the location of the breakdown point. (c) Contour plot of the top surface of the DE actuator obtained from the FE analysis [λP = 2.0, Φ = 6 kV].

Grahic Jump Location
Fig. 8

(a) Beam configuration, dimensions, material, and geometric parameters. (b) Variation of the point of maximum deformation with the slenderness ratio of the beam (the slenderness ratio pertaining to λP = 2 is marked by X). (c) Deformation profile for thin (d = 1 mm) and thick (d = 20 mm) beams obtained using the Airy function method and FE analysis.

Grahic Jump Location
Fig. 9

Schematic of a homogeneously deforming dielectric elastomer in the (a) reference state, (b) prestretched state, and (c) actuated state



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