Bifurcation of a dielectric elastomer balloon under pressurized inflation and electric actuation

It is previously known that under inflation alone a spherical rubber membrane balloon may bifurcate into a pear shape when the tension in the membrane reaches a maximum, but the existence of such a maximum depends on the material model used: the maximum exists for the Ogden model, but does not exist for the neo-Hookean, Mooney–Rivlin or Gent model. This paper discusses how such a situation is changed when a pressurized dielectric elastomer balloon is subjected to additional electric actuation. A similar bifurcation condition is first deduced and then verified numerically by computing the bifurcated solutions explicitly. It is shown that when the material is an ideal dielectric elastomer, bifurcation into a pear shape is possible for all material models, and similar results are obtained when a typical non-ideal dielectric elastomer is considered. It is further shown that whenever a pear-shaped configuration is possible it has lower total energy than the co-existing spherical configuration.