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Creasing to cratering instability in polymers under ultrahigh electric fields
Creasing to cratering instability in polymers under ultrahigh electric fields
Qiming Wang, Lin Zhang, and Xuanhe Zhao*
Physical Review Letters, In press
Abstract: We report a new type of instability in a substrate-bonded elastic polymer subject to an ultrahigh electric field. Once the electric field reaches a critical value, the initially flat surface of the polymer locally folds against itself to form a pattern of creases. As the electric field further rises, the creases increase in size and decrease in density, and strikingly evolve into craters in the polymer. The critical field for the electro-creasing instability scales with the square root of the polymer’s modulus. Linear stability analysis overestimates the critical field for the electro-creasing instability. A theoretical model has been developed to predict the critical field by comparing the potential energies in the creased and flat states. The theoretical prediction matches consistently with the experimental results.
* To whom correspondence should be addressed. E-mail: xz69@duke.edu
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Dear Qiming, It's really a
Dear Qiming, It's really a neat job. Can you propose any mechanism for cratering? qualitative or quantitative
Reply to Shengqiang: the mechanism of cratering instability
Dear Shengqiang, thank you so much for your comments.
Let us have a look at Fig. 2(g-i) in the paper. When creases form, on the contact surface of the crease, the electric field is perpendicular to the surface, thus developing a tensile stress (Fig. 2(H)). At a critical point, the tensile stress pulls open the contact surface to form craters. With the increasing electric field, the craters become larger and deeper. We can just imagine a competition between the electrostatic energy and elastic energy. This is a qualitative explanation, while the quantitative analysis for the critical point for the cratering is still under study.
how to understand tensile stress on the free surface
Hi Qiming, thanks for your response. I am a little confused about the tensile stress. No matter crease or crater, should not the normal stress near the crease/crater surface be either compressive or zero? I saw your numerical results in the paper, is that possible to get craters? and what is the normal stress around crease/crater in the simulation? The last question, in the experiments, are all creasing and cratering reversible or not? Hope not bother you too much.
Reply to Shengqiang's three good points
Dear Shengqiang, you raised very good points.
First, you are absolutely right that the total stress is zero on a crater surface and either compressive or zero on crease surface. As the polymer is regarded as an ideal dielectric, the total stress in the polymer is the sum of the mechanical stress and the electrical stress. The mechanical stress normal to the crease surface is compressive, but the electrical stress is tensile becausethe electric field is normal to the crease surface as illustrated on Fig 2(h). Once the tensile electrical stress is high enough, the total stress on a crease surface reduces to 0 and the crease opens into a crater.
Second, We used ABAQUS for analyzing the electro-creasing instability. However, ABAQUS fails to converge in simulating the creasing to cratering transition.
Third, not all the instabilities are reversible. In some cases, we can observe fracture of the polymer especially in the cratering instability as mentioned in the paper.