  Limiting chain extensibility is a characteristic that plays a vital role in
the stretching of highly elastic materials. The Gent model has been widely used
to capture this behaviour, as it performs very well in fitting stress-stretch
data in simple tension, and involves two material parameters only. Recently,
Anssari-Benam and Bucchi [Int. J. Non. Linear. Mech. 2021, 128, 103626]
introduced a different form of generalised neo-Hookean model, focusing on the
molecular structure of elastomers, and showed that their model encompasses all
ranges of deformations, performing better than the Gent model in many respects,
also with only two parameters. Here we investigate the nonlinear vibration and
stability of a dielectric elastomer balloon modelled by that strain energy
function. We derive the deformation field in spherical coordinates and the
governing equations by the Euler-Lagrange method, assuming that the balloon
retains its spherical symmetry as it inflates. We consider in turn that the
balloon is under two types of voltages, a pure DC voltage and a DC voltage
superimposed on an AC voltage. We analyse the dynamic response of the balloon
and identify the influential parameters in the model. We find that the
molecular structure of the material, as tracked by the number of segments in a
single chain, can control the instability and the pull-in/snap-through critical
voltage, as well as chaos and quasi-periodicity. The main result is that
balloons made of materials exhibiting early strain-stiffening effects are more
stable and less prone to generate chaotic nonlinear vibrations than softer
materials, such as those modelled by the neo-Hookean strain-energy density
function.
