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| Analyzing wrinkling instabilities in constrained dielectric elastomers: A symplectic eigenvalue approach |
| Received:November 08, 2023 Revised:November 24, 2023 |
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| DOI：10.7511/jslx20231110002 |
| KeyWord:symplectic dielectric elastomers wrinkling eigenvalue analysis |
| Author | Institution |
| 张腾 |
雪城大学 机械与航空系, 美国纽约, NY 13244 |
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| Abstract: |
| Symplectic elasticity has been widely used to find the exact solutions of various boundary value problems in elasticity, compute the surface wave modes, and predict surface wrinkles in multilayer hyper-elastic films.Here, we show that the symplectic analysis framework can also be applied to surface wrinkles in constrained dielectric elastomers, where the mechanical deformation is tightly coupled with the electric field.The critical voltage for wrinkles can be solved as a symplectic eigenvalue problem after introducing the dual variables to the primary variables of mechanical and electric displacement vectors.We employ the extended Wittrick-Williams (W-W) algorithm and precise integration method to solve the eigenvalues of the formulated symplectic eigenvalue problem accurately and efficiently.The symplectic analysis is validated by comparing the wrinkle voltage and wavenumber with benchmark results of wrinkles with and without surface energy.The symplectic framework is concise and applicable to other instability problems such as layered dielectric elastomers, magnetoelastic instabilities and the micro- and macro-instabilities of laminated composite structures. |