Nonlinear response of circular hyperelastic dielectric membranes subject to inflation

In this paper, the inflation of initially stretched circular hyperelastic and dielectric membranes is analyzed. This problem commonly appears in many emerging engineering fields. However, due to its mathematical complexity, it has been addressed mostly numerically, requiring the solution of a system of nonlinear differential equations. Here, an alternative semi-analytical approach is developed based on the minimization of the potential energy of the system by a Ritz method, considering an incompressible Mooney–Rivlin material model with ideal dielectric elastomer behavior. In this manner, the whole shape of the inflated membrane is determined by simply solving few algebraic nonlinear equations. Further, a novel approximate analytical expression for the pressure–deflection relation is proposed, based on reasonable assumptions on the kinematics of the membrane. The formulation is then appropriately modified introducing a simple polynomial function to capture the behavior of the membrane for a wide range of parameters. Finally, the accuracy of the proposed formulation is assessed by comparisons with finite element simulations and the solution of the differential equations. • Proposed approximate analytical approach to determine the shape of the inflated membrane by minimizing the potential energy using a Ritz method. • The approach requires solving few algebraic equations instead of a system of nonlinear differential equations. • Analytical pressure–deflection relations for circular inflated membranes assuming the deformed shape. • Novel adjusted accurate solution with few given parameters. • Results valid for both hyperelastic and dielectric elastomer membranes.