A strain energy function for the inflation of hyperelastic membranes

We propose a deviatoric strain energy function (SEF) for inflated elastic membranes. The proposed function is specifically designed to capture the essential features of the pressure-deflection response of circular membranes. The model parameters are calibrated on pressure-deflection data obtained from bulge tests performed on two different elastomers. Besides the pressure curve, we measure the transversal stretch and radial stretch at the membrane's pole, as well as the deformed profiles. These data are used to further validate the proposed SEF, demonstrating that it overcomes the limitations of current models in accurately simulating both the mechanics and kinematics of inflated membranes. In addition, the proposed SEF offers several advantages: (1) a simple polynomial expression, (2) a clear interpretation of each term's role on the pressure response, and (3) a well defined strategy for parameter fitting. Combined with a volumetric SEF previously developed by the authors, the proposed function forms a complete SEF for modeling the inflation of compressible membranes. This study helps bridge a gap in the literature by providing original experimental insights and theoretical advancements in the modeling of inflated membranes.