Shape Bifurcation of a Spherical Dielectric Elastomer Balloon under the Actions of Internal Pressure and Electric Voltage

TL;DR

This study reveals that spherical dielectric elastomer balloons can bifurcate into non-spherical shapes under certain conditions, with stability depending on the control mode, impacting their failure mechanisms.

Contribution

It introduces a linear perturbation analysis demonstrating shape bifurcation and stability conditions of dielectric elastomer balloons under combined electromechanical loading.

Findings

Bifurcation to non-spherical shapes occurs under specific conditions.

Non-spherical shapes exhibit inhomogeneous electric and stress distributions.

Stability depends on the control mode: unstable under pressure/voltage control, stable under charge/mass control.

Abstract

Under the actions of internal pressure and electric voltage, a spherical dielectric elastomer balloon usually keeps a sphere during its deformation, which has also been assumed in many previous studies. In this article, using linear perturbation analysis, we demonstrate that a spherical dielectric elastomer balloon may bifurcate to a non-spherical shape under certain electromechanical loading conditions. We also show that with a non-spherical shape, the dielectric elastomer balloon may have highly inhomogeneous electric field and stress/stretch distributions, which can lead to the failure of the system. In addition, we conduct stability analysis of the dielectric elastomer balloon in different equilibrium configurations by evaluating its second variation of free energy under arbitrary perturbations. Our analyses indicate that under pressure-control and voltage-control mode, non-spherical deformation of the dielectric elastomer balloon is energetically unstable. However, under charge-control or ideal gas mass-control mode, non-spherical deformation of the balloon is energetically stable.