  We introduce a strain-energy based nonlinear hyper-elastic formulation to
model the material properties of ultrasoft dielectric elastomers over a wide
range of elastic properties, prestretch, and thicknesses. We build on the
uniaxial Gent formulation, and under the conditions of equi-biaxial strain,
derive an expression for the bulge deformation versus pressure. A circular
bulge test methodology is developed to experimentally measure the mechanical
response of the silicone membranes. The Gent model captures both neo-Hookean
and strain-stiffening behaviors, and gives predictions which are in agreement
with experimental measurements. Membranes with different thinner fractions are
characterized over nearly one order of magnitude variation in shear modulus.
Stiffer membranes are observed to harden at lower stretch ratios due to the
increased fraction of polymer chains in them. The present approach offers a
simple and cost-effective procedure for characterizing soft membranes under
commonly encountered biaxial deformation conditions.
