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 bulge deformation vs 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 that 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.
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