Computational modeling of electro-elasto-capillary phenomena in dielectric elastomers

Abstract

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.

Nanomechanical probing of thin-film dielectric elastomer transducers

“…111, 093104-1 methods and simulations including finite element (FE) analysis. [23][24][25][26] In this communication, we elucidate that probing a DC-powered thin-film DET with a spherical AFM tip leads to increased indentation depths by several tens of percent, as verified by dynamic FE models. Furthermore, we investigate how far the roughness of the Au electrode increases owing to the actuation.…”

A staggered explicit–implicit finite element formulation for electroactive polymers

“…From a historical perspective, our algorithm may be akin to a node-by-node partition of Belytschko and Mullen [25], although both the structural system and the dielectric field equations occupy the same spatial domain. We demonstrate the robustness of the present algorithm in solving problems involving complex electromechanical instabilities, including creasing and wrinkling [11,22,28,29], bursting drops in dielectric solids [10,30], and 3D problems. In all cases, the staggered methodology provides effectively identical results as a previous dynamic, fully coupled monolithic formulation [11], though for a significantly reduced computational cost.…”

“…However, no reference or discussion on the stability and accuracy aspects of partitioned explicit-implicit procedures [25,26,27] was provided; hence, they offered no rationale for its stability restrictions and accuracy analysis. Moreover, they did not report any comparison of their work to a series of reported benchmark monolithic solutions obtained by fully implicit-implicit procedures [10,11,22]. As a result, it is unclear as to the applicability ranges, effectiveness, and overall potential for staggered methods in addressing electromechanically coupled phenomena in electroactive polymers like DEs.…”

“…Various computational formulations for DEs based on the finite element method (FEM) have emerged in the past decade [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. While these differ depending on various factors, including the field theory they are formulated on, whether they account for material effects such as viscoelasticity, or whether they are quasi-static or dynamic, nearly all of them have been solved using a fully coupled, monolithic formulation.…”

Finite-element modeling of soft solids with liquid inclusions

“…Surface tension can drive deformation in soft solids (Mora et al, 2013;Paretkar et al, 2014;Mora and Pomeau, 2015) and modify contact, adhesion, and wetting behavior (Style et al, 2013;Xu et al, 2014;Jensen et al, 2015;Hui et al, 2015). Surface tension can also drive the Rayleigh-Plateau instability (Mora et al, 2010); introduce an energy barrier for cavitation (Zimberlin et al, 2007;Kundu and Crosby, 2009;Hutchens and Crosby, 2014) and surface instabilities, such as creasing and wrinkling (Chen et al, 2012;Mora et al, 2011), in soft solids; and play an important role in the electro-creasing and electro-cavitation instabilities in dielectric elastomers (Seifi and Park, 2016). One recent observation of elasto-capillary coupling is in composite materials made up of a soft solid matrix with fluid-filled inclusions (Style et al, 2015a;Ducloué et al, 2014).…”