Electromechanical Instability on Dielectric Polymer Surface: Modeling and Experiment

J. Wang, T.D. Nguyen and H.S. Park
Journal of Applied Mechanics 2014; 81:051006

Abstract

We utilize a nonlinear, dynamic finite element model coupled with a finite deformation viscoelastic constitutive law to study the inhomogeneous deformation and instabilities resulting from the application of a constant voltage to dielectric elastomers. The constant voltage loading is used to study electrostatically-driven creep and the resulting electromechanical instabilities for two different cases that have all been experimentally observed, i.e. electromechanical snap-through instability and bursting drops in a dielectric elastomer. We find that in general, increasing the viscoelastic relaxation time leads to an increase in time needed to nucleate the electromechanical instability. However, we find for these two cases that the time needed to nucleate the instability scales with the relaxation time.

This paper is available in PDF form .


Electromechanical Instability on Dielectric Polymer Surface: Modeling and Experiment

H.S. Park, Q. Wang, X. Zhao and P.A. Klein
Computer Methods in Applied Mechanics and Engineering 2013; 260:40-49

Abstract

We present a dynamic finite element formulation for dielectric elastomers that significantly alleviates the problem of volumetric locking that occurs due to the incompressible nature of the elastomers. We accomplish this by modifying the Q1P0 formulation of Simo et al. [1], and adapting it to the electromechanical coupling that occurs in dielectric elastomers. We demonstrate that volumetric locking has a significant impact on the critical electric fields that are necessary to induce electromechanical instabilities such as creasing and cratering in dielectric elastomers, and that the locking effects are most severe in problems related to recent experiments that involve significant constraints upon the deformation of the elastomers. We then compare the results using the new Q1P0 formulation to that obtained using standard 8-node linear and 27-node quadratic hexahedral elements to demonstrate the capability of the proposed approach. Finally, direct comparison to the recent experimental work on the creasing instability on dielectric polymer surface by Wang et al. [2] is presented. The present formulation demonstrates good agreement to experiment for not only the critical electric field for the onset of the creasing instability, but also the experimentally observed average spacing between the creases.

This paper is available in PDF form .


Viscoelastic Effects on Electromechanical Instabilities in Dielectric Elastomers

H.S. Park and T.D. Nguyen
Soft Matter 2013; 9:1031-1042

Abstract

We present a computational study of the effect of viscoelasticity on the electromechanical behavior of dielectric elastomers. A dynamic, finite deformation finite element formulation for dielectric elastomers is developed that incorporates the effects of viscoelasticity using the nonlinear viscoelasticity theory previously proposed by Reese and Govindjee (IJSS, 1998). The finite element model features a three-field Q1P0 formulation to alleviate volumetric locking effects caused by material incompressibility. We apply the formulation to first perform a fundamental examination of the effects of the viscoelastic deviatoric and volumetric response on dielectric elastomers undergoing homogeneous deformation. Specifically, we evaluate the effects of the shear and bulk relaxation times on the electromechanical instability, and demonstrate that while the bulk relaxation time has a negligible impact, the shear relaxation time substantially increases the critical electric field needed to induce electromechanical instability. We also demonstrate a significant increase in the critical voltage needed to induce electromechanical instability in the presence of a distribution of relaxation times, compared to a single relaxation time, where the former is more representative of viscoelastic behavior of polymers. We then study the effects of viscoelasticity on crack-like electromechanical instabilities that have recently been observed in constrained dielectric films with a small hole containing a conductive liquid. Viscoelasticity is shown again to not only significantly increase the critical electric field to induce the electromechanical instability, but also to substantially reduce the crack propagation speeds in the elastomer.

This paper is available in PDF form .


A Dynamic Finite Element Method for Inhomogeneous Deformation and Electromechanical Instability of Dielectric Elastomer Transducers

H.S. Park, Z. Suo, J.X. Zhou and P.A. Klein
International Journal of Solids and Structures 2012; 49:2187-2194.

Abstract

We present a three-dimensional nonlinear finite element formulation for dielectric elastomers. The mechanical and electrical governing equations are solved monolithically using an implicit time integrator, where the governing finite element equations are given for both static and dynamic cases. By accounting for inertial terms in conjunction with the Arruda-Boyce rubber hyperelastic constitutive model, we demonstrate the ability to capture the various modes of inhomogeneous deformation, including pull-in instability and wrinkling, that may result in dielectric elastomers that are subject to various forms of electrostatic loading. The formulation presented here forms the basis for needed computational tools that can elucidate the electromechanical behavior and properties of dielectric elastomers that are used for engineering applications.

This paper is available in PDF form .