A Numerical Approach Based on Finite Element Method for the Wrinkling Analysis of Dielectric Elastomer Membranes

Abstract

Dielectric elastomer (DE) actuators are deformable capacitors capable of a muscle-like actuation when charged. When subjected to voltage, DE membranes coated with compliant electrodes may form wrinkles due to the Maxwell stress. Here, we develop a numerical approach based on the finite element method (FEM) to predict the morphology of wrinkled DE membranes mounted on a rigid frame. The approach includes two steps, I) pre-buckling and II) post-buckling. In step I, the first buckling mode of the DE membrane is investigated by substituting the Maxwell stress with thermal stress in the built-in function of the FEM platform SIMULIA Abaqus. In step II, we use this first buckling mode as an artificial geometric imperfection to conduct the post-buckling analysis. For this purpose, we develop an equivalent model to simulate the mechanical behavior of DEs. Based on our approach, the thickness distribution and the thinnest site of the wrinkled DE membranes subjected to voltage are investigated. The simulations reveal that the crests/troughs of the wrinkles are the thinnest sites around the center of the membrane and corroborate these findings experimentally. Finally, we successfully predict the wrinkles of DE membranes mounted on an isosceles right triangle frame with various sizes of wrinkles generated simultaneously. These results shed light on the fundamental understanding of wrinkled dielectric elastomers but may also trigger new applications such as programmable wrinkles for optical devices or their prevention in DE actuators.

Mechanics of tension-induced film wrinkling and restabilization: a review

“…In 2009, Zheng [45] uncovered the restabilization phenomenon in a highly stretched sheet, showing that wrinkles appear first, then decrease, and eventually disappear with the continuous increase of applied stretching. To consider large deformations of soft films, some plate/shell theories accounting for finite in-plane strain [62][63][64][65] and advanced numerical methods [32,[66][67][68][69][70] for capturing multiple bifurcations in nonlinear post-buckling paths were developed. General mechanics models to characterize large deformations of thin films can be placed into three categories: extended Föppl-von Kármán plate model (EFvK) [32][33][34], finite-strain plate model derived from three-dimensional nonlinear elasticity [71][72][73][74], and consistent finite-strain plate model [64,65,70,75].…”

Control Strategies for Soft Robot Systems

“…[166][167][168] Increasingly accurate models for DEAs are being developed by including the effects of material viscoelasticity and the rate of heat generation due to viscoelastic dissipation. [169] Including the effect of electrode resistance could improve simulations of the dynamics of DEAs. [170] IEAPAs are simulated by using the Nernst-Planck equation to determine the ionic concentration caused by the applied potential difference and then deriving the strain through the relationship between force and ionic concentration.…”

Improved electrical actuation and dielectric strength of rubber composites with polydopamine noncovalent and silane covalent modification of carbon nanotube

“…[5][6][7] Such a DEA exhibits numerous advantages, including a simple structure, low weight, high energy density, large conversion efficiency and fast response. [8][9][10] DEAs have the potential to be utilized in numerous emerging technologies, including soft robots, loudspeakers, haptic devices, micropumps, tunable lenses and medical devices. [11][12][13] However, a DEA typically operates close to the dielectric breakdown to obtain a large deformation, 14,15 which easily results in a ''pinhole'' defect in DE films and causes them to lose function.…”

“…1), producing actuation 5–7 . Such a DEA exhibits numerous advantages, including a simple structure, low weight, high energy density, large conversion efficiency and fast response 8–10 . DEAs have the potential to be utilized in numerous emerging technologies, including soft robots, loudspeakers, haptic devices, micropumps, tunable lenses and medical devices 11–13 .…”