Modeling shape selection of buckled dielectric elastomers

Jake Langham, Hadrien Bense, Dwight Barkley

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)
236 Downloads (Pure)

Abstract

A dielectric elastomer whose edges are held fixed will buckle, given a sufficiently applied voltage, resulting in a nontrivial out-of-plane deformation. We study this situation numerically using a nonlinear elastic model which decouples two of the principal electrostatic stresses acting on an elastomer: normal pressure due to the mutual attraction of oppositely charged electrodes and tangential shear ("fringing") due to repulsion of like charges at the electrode edges. These enter via physically simplified boundary conditions that are applied in a fixed reference domain using a nondimensional approach. The method is valid for small to moderate strains and is straightforward to implement in a generic nonlinear elasticity code. We validate the model by directly comparing the simulated equilibrium shapes with the experiment. For circular electrodes which buckle axisymetrically, the shape of the deflection profile is captured. Annular electrodes of different widths produce azimuthal ripples with wavelengths that match our simulations. In this case, it is essential to compute multiple equilibria because the first model solution obtained by the nonlinear solver (Newton’s method) is often not the energetically favored state. We address this using a numerical technique known as "deflation." Finally, we observe the large number of different solutions that may be obtained for the case of a long rectangular strip.
Original languageEnglish
Article number065102
Number of pages11
JournalJournal of Applied Physics
Volume123
Issue number6
Early online date8 Feb 2018
DOIs
Publication statusPublished - 14 Feb 2018

Keywords

  • Smart materials
  • Polymers
  • Electrostatics
  • Elasticity
  • Euclidean geometries

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