DC dynamic pull-in instability of a dielectric elastomer balloon: an energy-based approach

Abstract

This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler-Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.

Instabilities of soft dielectrics

“…In the latter, bifurcation is possible for the Ogden model [69], but not for the neo-Hookean, Mooney-Rivlin or Gent models. Sharma et al [70] presented an energy-based method for investigating the dynamic performance of inflated, spherically shaped dielectric balloons. In particular, their analysis found that dynamic pull-in instability occurs at larger values of the circumferential stretch than for its static counterpart, the difference depending on the amount of pre-inflation pressure.…”

Flexible membrane structures for wave energy harvesting: A review of the developments, materials and computational modelling approaches

“…While increasing the sti↵ness, has allowed for higher operational pressures as demonstrated in a study on the Anaconda WEC [156]. For a DEG membrane, the electrical properties can result in additional electromechanical instabilities [157][158][159][160]. To avoid this, DEGs must operate within a certain range before reaching electromechanical instability and dielectric breakdown field as shown in Figure 3(a).…”

Gradient-based topology optimization of soft dielectrics as tunable phononic crystals

“…Moreover, the constitutive relations of DEs are nonlinear, such that their instantaneous moduli vary as functions of the electromechanical loads. These features have led to the design of various applications, such as haptic devices (Kim et al, 2016), soft robots (Gu et al, 2018), actuators (Hajiesmaili & Clarke, 2021;Sharma et al, 2018Sharma et al, , 2019Su et al, 2018Su et al, , 2019Kashyap et al, 2020;Sharma et al, 2017;Khurana et al, 2021) and artificial muscles (Lu et al, 2016), that are based on DEs.…”