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Modeling shape selection of buckled dielectric elastomers
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Langham, Jacob, Bense, Hadrien and Barkley, Dwight (2018) Modeling shape selection of buckled dielectric elastomers. Journal of Applied Physics, 123 (6). 065102. doi:10.1063/1.5012848 ISSN 0021-8979.
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Official URL: https://doi.org/10.1063/1.5012848
Abstract
A dielectric elastomer whose edges are held fixed will buckle, given sufficient 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 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 simulated equilibrium shapes with 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.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Library of Congress Subject Headings (LCSH): | Elastomers -- Mathematical models, Dielectrics, Buckling (Mechanics) -- Mathematical models, Strains and stresses -- Mathematical models, Electrostatics | ||||||||
Journal or Publication Title: | Journal of Applied Physics | ||||||||
Publisher: | American Institute of Physics | ||||||||
ISSN: | 0021-8979 | ||||||||
Official Date: | 14 February 2018 | ||||||||
Dates: |
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Volume: | 123 | ||||||||
Number: | 6 | ||||||||
Article Number: | 065102 | ||||||||
DOI: | 10.1063/1.5012848 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 15 February 2018 | ||||||||
Date of first compliant Open Access: | 15 February 2018 | ||||||||
RIOXX Funder/Project Grant: |
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