Wrinkles in soft dielectric plates

TL;DR

This paper investigates the wrinkling phenomena in soft dielectric plates under voltage actuation, providing explicit models and expressions for different thickness regimes, and linking to classical instability criteria.

Contribution

It offers a detailed analysis of wrinkling onset in dielectric plates, including explicit formulas and comparisons with classical buckling and instability theories.

Findings

Wrinkling occurs before large stretch can be achieved in voltage-actuated dielectric plates.

Explicit expressions for wrinkling thresholds are derived for thin and thick plates.

The study connects wrinkling with classical electro-mechanical instability and buckling theories.

Abstract

We show that a smooth giant voltage actuation of soft dielectric plates is not easily obtained in practice. In principle one can exploit, through pre-deformation, the snap-through behavior of their loading curve to deliver a large stretch prior to electric breakdown. However, we demonstrate here that even in this favorable scenario, the soft dielectric is likely to first encounter the plate wrinkling phenomenon, as modeled by the onset of small-amplitude sinusoidal perturbations on its faces. We provide an explicit treatment of this incremental boundary value problem. We also derive closed-form expressions for the two limit cases of very thin membranes (with vanishing thickness) and of thick plates (with thickness comparable to or greater than the wavelength of the perturbation). We treat explicitly examples of ideal dielectric free energy functions (where the mechanical part is of the neo-Hookean, Mooney-Rivlin or Gent form) and of dielectrics exhibiting polarization saturation. Finally we make the link with the classical results of the Hessian electro-mechanical instability criterion and of Euler buckling for an elastic column.