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Dynamic pull-in instability of a prestretched viscous dielectric elastomer under electric loading

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Abstract

The dynamic response of a pre-stretched elastomer membrane under electric loading was analysed. Thereby, two cases of voltage application, constant voltage and an incrementally increased voltage were regarded. The equation of motion (EOM) was derived from the Euler–Lagrange equation and the Rayleigh dissipation function. This allowed to include the influence of prestretch into the evolution equation of the viscous stretch. The critical values of pull-in instability under dynamic assumptions were determined at the initial state by an analytical model derived from the classical approaches of stability theory regarding geometric instabilities by using an energy criterion and were used to validate the numerical solution of the EOM. The results showed that both inertia and viscous effects have a notable influence on the pull-in stability behavior. In particular, at applied electric fields below the critical electric field the viscous behavior can still induce failure, which occurs time delayed. A non-monotonic dependence of the failure stretch on the magnitude of the applied electric fields below the critical value could be observed.

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Acknowledgements

The authors would like to gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG), who enables this work by supporting the Project XU 121/5-1.

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Authors and Affiliations

  1. Mechanics of Functional Materials, TU Darmstadt, Jovanka-Bontschits-Strasse 2, 64287, Darmstadt, Germany

    Dagmar Eder-Goy, Ying Zhao & Bai-Xiang Xu

  2. Graduate School of Computational Engineering, TU Darmstadt, Dolivostr. 15, 64293, Darmstadt, Germany

    Ying Zhao

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  1. Dagmar Eder-Goy
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Eder-Goy, D., Zhao, Y. & Xu, BX. Dynamic pull-in instability of a prestretched viscous dielectric elastomer under electric loading. Acta Mech 228, 4293–4307 (2017). https://doi.org/10.1007/s00707-017-1930-4

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  • DOI: https://doi.org/10.1007/s00707-017-1930-4

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