Analysis of axisymmetric necking of a circular dielectric membrane based on a one-dimensional model

Yu, Xiang; Fu, Yibin

Abstract

To facilitate the understanding of the mechanisms underlying the electric breakdown of dielectric elastomers, we derive a one-dimensional (1d) model for axisymmetric necking in a dielectric membrane subjected to equibiaxial stretching and an electric field, starting from the three-dimensional (3d) nonlinear electroelasticity theory. Our reduction is built on the variational asymptotic method, so that the resulting 1d model is asymptotically self-consistent. The 1d model offers an easier and more efficient way to analyze axisymmetric necking in a dielectric membrane in the linear, weakly nonlinear and fully nonlinear regimes. It delivers results identical to the 3d theory in the linear and weakly nonlinear regimes, and near-identical results in the fully nonlinear regime due to its asymptotic self-consistency. We demonstrate the straightforward implementation of this 1d model by solving it using the Rayleigh–Ritz method and validate it by comparison with finite-element simulations. The 1d model enables a precise calculation of the minimum thickness that a dielectric membrane can reach when necking instability occurs and quantitative assessment of the effects of imperfections so that the integrity of a dielectric elastomer actuator can be evaluated with respect to electric breakdown.
The developed methodology is not problem-specific and can also be applied to analyze similar phenomena in other soft materials subjected to any fields (e.g., the axisymmetric necking of stretched plastic membranes).

Citation

Yu, X., & Fu, Y. (2025). Analysis of axisymmetric necking of a circular dielectric membrane based on a one-dimensional model. Journal of the Mechanics and Physics of Solids, 198, Article 106071. https://doi.org/10.1016/j.jmps.2025.106071

• Journal Article Type: Article
• Acceptance Date: Feb 2, 2025
• Online Publication Date: Feb 10, 2025
• Publication Date: 2025-05
• Deposit Date: Mar 4, 2025
• Publicly Available Date: Mar 6, 2025
• Journal: Journal of the Mechanics and Physics of Solids
• Print ISSN: 0022-5096
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 198
• Article Number: 106071
• DOI: https://doi.org/10.1016/j.jmps.2025.106071
• Keywords: Nonlinear electroleasticity; Dielectric membranes; Stability and bifurcation; Localization; Variational asymptotic method
• Public URL: https://keele-repository.worktribe.com/output/1103851
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S002250962500047X?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Analysis of axisymmetric necking of a circular dielectric membrane based on a one-dimensional model; Journal Title: Journal of the Mechanics and Physics of Solids; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.jmps.2025.106071; Content Type: article; Copyright: © 2025 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.