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Dynamic pattern of wrinkles in a dielectric elastomer

Dielectric elastomers undergo phase transitions between thick and thin (wrinkled) states due to their electromechanical behaviour. In our experiments on a clamped circular dielectric elastomer membrane, we have observed that at a constant voltage close to the critical voltage for discontinuous phase transition, wrinkles are initiated at different locations on the membrane and they move across the membrane interchangeable with the co-existing flat states forming a dynamic pattern. At a different prestretch, we have also observed a similar co-existence and a dynamic pattern between wrinkled states of different wavelengths (wrinkle-wrinkle discontinuous transition). Analytical and finite element models have been developed to interpret the flat-wrinkle transitions and the effect of pre-stretch on them. A viscoelastic model considering rate dependant deformation may help to interpret the wrinkle-wrinkle transition.

Godaba, H., Zhang, Z.-Q., Gupta, U., Chiang Foo, C., Zhu, J., 2017. Dynamic pattern of wrinkles in a dielectric elastomer. Soft Matter. doi:10.1039/C7SM00198C

 

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Mike Ciavarella's picture

Patterns, forces, and metastable pathways in debonding of elastic filmsJ SarkarV ShenoyA Sharma - Physical review letters, 2004 - APSAbstract This Letter resolves several intriguing and fundamental aspects of debonding at soft 
interfaces, including the formation and persistence of regularly arranged nanocavities and 
bridges,“adhesion-debonding hysteresis,” and vastly lower adhesive strengths compared to 
the absence of pattern formation. The analysis shows the hysteresis to be caused by an 
energy barrier that separates the metastable patterned configuration during withdrawal, ...

Thank you very much for your comment. In these experiments, the membrane is a prestretched layer of dielectric elastomer and is not bonded onto any substrate. Unlike the surface instability you have pointed out to, the phenomenon we observe is wrinkling of the entire membrane after voltage induced loss of tension.

Mike Ciavarella's picture

Maybe a better reference is

 

Adhesion and debonding of soft elastic films: Crack patterns, metastable pathways, and forcesJ SarkarA SharmaV Shenoy - Langmuir, 2005 - ACS PublicationsWe study the phenomenon of debonding in a thin soft elastic film sandwiched between two 
rigid plates as one of the plates is brought into intimate contact and then pulled away from 
contact proximity by application of a normal force. Nonlinear simulations based on 
minimization of total energy (composed of stabilizing elastic strain energy and destabilizing 
adhesive interaction energy) are employed to address the problems of contact hysteresis, ...

Mike Ciavarella's picture

What I am trying to understand is the spacing with the electrodes.  If it is of the order of adhesion length scale, i.e. atomic size, you would not notice.

What is the spacing between wrinkles? In the adhesion instability one, it is governed by the thickness of the elastomer, namely about 3 H.

Dear Prof. Ciavarella. Thank you for your inputs. We haven't really looked in this direction and hence cannot really confirm anything now. But from my understanding, adhesion of electrode and polymer film may have little to do with the wrinkling instability we observed. For the electrode, we coat carbon grease, which is a dispersion of carbon black particles in silicone oil, on both sides of the membrane. This electrode is highly compliant and even at large stretches, there may be a dispersal of the conductive particles but we cannot effectively term it debonding. Debonding and adhesion energies may play a larger role in some of the solid electrodes people have come up with.

 

Also, the onset of wrinkling for different stretches is in line with the voltage for loss of tension we predict from the analytical model, for different initial prestretches of the membrane. Moreover, we can observe the same wrinkle pattern seeing from either side of the membrane, which means the membrane is wrinkled through the entire thickness. The wrinkles in the membrane are much more similar to lateral wrinkles one would see when they stretch an elastic sheet, due to poisson's effect. 

https://www.seas.harvard.edu/softmat/downloads/2003-03.pdf

The length scales of the wrinkle wavelength may be dependant on the stiffness and thickness of the membrane ( as pointed out in Cerda and Mahadevan) and is larger than 3H (H~0.1mm)

Mike Ciavarella's picture

so the wrinkles are indeed of the order of 3H=3 mm, as there are only few decades of wrinkles.  Please make some more precise estimates.

peppezurlo's picture

Dear Hareesh, 

Nice work! In your experiments you observe the coesxistence of thin/thick states under a given voltage. It's very interesting that you also report that the transition becomes "continous" with varying levels of prestretch. This reminds to me of the classical frameworks of phase transitions. There, a gradient term (or an interface energy) usually penalises the thick->thin transition. From your paper, it looks like this interface energy is lowered by prestretch. This energy term is explicitly calculated in: 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.078001

Indeed, it actually depends on the level of prestretch: it would be interesting to work more on this!!!

I would be also curious to ask: have you measured breakdown voltages associated to the thinning localisation? This is described in detail in the paper linked above. 

Kind regards, 

Giuseppe

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