An elaborated version of this paper has been accepted by Physical Review B. Please take a look at the second attachment.

XH

Hi Rui,

The case might be a little bit different here.

Both thick and thin regions may be stable under the same voltage. The reason why the thin region wrinkles is it expands a lot latterally, while constrained by the surrounding thick region at the same time. More like buckling of a constrained rod under thermal expansion.

Wei

In my paper on electrically induced surface instability, a linear perturbation analysis was performed to predict the critical condition for wrinkling, which could be applied to both the thin and thick states. The critical condition was obtained in terms of a dimensionless quantity combining the electrical voltage, dielectrics thickness, stiffness, and permititivity. Indeed, under the same voltage, a thinner region can become unstable (thus wrinkling) while a thicker region remains stable (thus flat).

RH

Thanks for the comment, Rui,

Due to the limit on the length of the paper, and as the focus of the
current paper is on the bi-stable states, we didn't elaborate on the
formation of the wrinkles. The wrinkle process we have in mind is first
having an instability from the homogeneous compression, resulting in
some localized "collapsed" area, which has very small thickness, but
very large lateral stretch; and then the mismatch in lateral stretch
between the surrounding thick state and the thin state causes the wrinkle.

The formation of the wrinkle might be similar as the cases all of us have
studied before (stiff film on compliant substrates), the difference is that
the constraint here is from the side instead of the substrate. Of course
a quantitative prediction of wrinkles needs full 2d, or actually 3d
analysis (to account for the constraint), which by itself might be
another interesting topic.

Wei

This is an interesting work. I read it very quickly, trying to understand the basic idea and approach. At the end, however, I find myself a little confused. If I understand it correctly, the most of the analysis presented in this paper is one-dimensional for both stretch and electrical field. The two states obtained from this analysis (as seen in Fig. 2) seem to be two states with different stretch or thickness. However, in the summary paragraph, the coexisting states are referred as flat and wrinkled states. Is this a far-reaching conclusion? Just as explained by the authors, wrinkling is not included explicitly in the present study. The coexistence of thick and thin states may correspond to one wrinkled state, which of course requires at least a two-dimensional analysis.

RH