The effect of an exterior electric field on the instability of dielectric plates

TL;DR

This paper explores how an external electric field influences the stability and wrinkling behavior of dielectric plates immersed in silicone oil, revealing voltage-induced thinning or thickening effects and conditions for instability.

Contribution

It provides a theoretical analysis of nonlinear response and bifurcation behavior of dielectric plates under electric fields, including new insights into stability and wrinkling mechanisms.

Findings

Electric fields can cause dielectric plates to thin or thicken depending on parameters.

Voltage can induce spontaneous instability and wrinkling bifurcation.

Different modes of instability are decoupled and analyzed separately.

Abstract

We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and bottom of the tank, and an electric field is generated by a potential difference between the electrodes. We solve the associated incremental boundary value problem of superimposed, inhomogeneous small-amplitude wrinkles, signalling the onset of instability. We decouple the resulting bifurcation equation into symmetric and antisymmetric modes. For a neo-Hookean dielectric plate, we show that a potential difference between the electrodes can induce a thinning of the plate and thus an increase of its planar area, similar to the scenarios encountered when there is no silicone oil. However, we also find that, depending on the material and geometric parameters, an increasing applied voltage can also lead to a thickening of the plate, and thus a shrinking of its area. In that scenario, Hessian instability and wrinkling bifurcation may then occur spontaneously once some critical voltages are reached.