We present a new finite deformation, dynamic finite element model that incorporates surface tension to capture elastocapillary effects on the electromechanical deformation of dielectric elastomers. We demonstrate the significant effect that surface tension can have on the deformation of dielectric elastomers through three numerical examples: (1) surface tension effects on the deformation of single finite elements with homogeneous and inhomogeneous boundary conditions; (2) surface tension effects on instabilities in constrained dielectric elastomer films, and (3) surface tension effects on bursting drops in solid dielectrics. Generally, we find that surface tension creates a barrier to instability nucleation. Specifically, we find in agreement with recent experimental studies of constrained dielectric elastomer films a transition in the surface instability mechanism depending on the elastocapillary length. The present results indicate that the proposed methodology may be beneficial in studying the electromechanical deformation and instabilities for dielectric elastomers in the presence of surface tension.

We demonstrate, using both finite element simulations and a linear stability analysis, the emergence of an electro-elastocapillary Rayleigh-plateau instability in dielectric elastomer (DE) films under 2D, plane strain conditions. When subject to an electric field, the DEs exhibit a buckling instability for small elastocapillary numbers. For larger elastocapillary numbers, the DEs instead exhibit the Rayleigh-plateau instability. The stability analysis demonstrates the critical effect of the electric field in causing the Rayleigh-plateau instability, which cannot be induced solely by surface tension in DE films. Overall, this work demonstrates the effects of geometry, boundary conditions, and multi-physical coupling on a new example of Rayleigh-plateau instability in soft solids.

Electroactive polymers such as dielectric elastomers (DEs) have attracted significant attention in recent years. Computational techniques to solve the coupled electromechanical system of equations for this class of materials have universally centered around fully coupled monolithic formulations, which while generating good accuracy requires significant computational expense. However, this has significantly hindered the ability to solve large scale, fully three-dimensional problems involving complex deformations and electromechanical instabilities of DEs. In this work, we provide theoretical basis for the effectiveness and accuracy of staggered explicit-implicit finite element formulations for this class of electromechanically coupled materials, and elicit the simplicity of the resulting staggered formulation. We demonstrate the stability and accuracy of the staggered approach by solving complex electromechanically coupled problems involving electroactive polymers, where we focus on problems involving electromechanical instabilities such as creasing, wrinkling, and bursting drops. In all examples, essentially identical results to the fully monolithic solution are obtained, showing the accuracy of the staggered approach at a significantly reduced computational cost.

Dielectric elastomer transducers (DETs) have attracted interest as generators, actuators, sensors, and even as self-sensing actuators for applications in medicine, soft robotics, and microfluidics. Their performance crucially depends on the elastic properties of the electrode-elastomer sandwich structure. The compressive displacement of a single-layer DET can be easily measured using atomic force microscopy (AFM) in the contact mode. While polymers used as dielectric elastomers are known to exhibit significant mechanical stiffening for large strains, their mechanical properties when subjected to voltages are not well understood. To examine this effect, we measured the depths of 400 nanoindentations as a function of the applied electric field using a spherical AFM probe with a radius of (522 ± 4) nm. Employing a field as low as 20 V/μm, the indentation depths increased by 42% at a load of 100 nN with respect to the field-free condition, implying an electromechanically driven elastic softening of the DET. This at-a-glance surprising experimental result agrees with related nonlinear, dynamic finite element model simulations. Furthermore, the pull-off forces rose from (23.0 ± 0.4) to (49.0 ± 0.7) nN implying a nanoindentation imprint after unloading. This embossing effect is explained by the remaining charges at the indentation site. The root-mean-square roughness of the Au electrode raised by 11% upon increasing the field from zero to 12 V/μm, demonstrating that the electrode's morphology change is an undervalued factor in the fabrication of DET structures.