Errata corrige

In the present work we derive an analytical expression for the pressure-deflection curve of circular membranes
subjected to inflation. This problem has been studied mostly from a numerical point of view and there is still
a lack of accurate closed-form solutions in nonlinear elasticity. The analytical formulation is developed with
a semi-inverse method by setting a priori the kinematics of deformation of the membrane. A compressible
Mooney-Rivlin material model is considered and a pressure-deflection relation is derived from the equilibrium. The kinematics is approximated and therefore the obtained solution is not exact. Consequently, the
formulation is adjusted by introducing an additional polynomial function in the pressure-deflection equation.
The polynomial is calibrated by fitting numerical solutions of the exact system of differential equilibrium
equations. The calibration is done over a wide range of constitutive parameters that covers the response
of all rubber materials for technological applications. As a result, a definitive and accurate expression of
the applied pressure as a function of the deflection of the membrane is obtained. The formula is validated
with finite element (FE) simulations and compared with other solutions available in the literature. The
comparison shows that the present model is more accurate. In addition, unlike the other models, it can be
applied to compressible materials. Experimental uniaxial and bulge tests are carried out on rubber materials and the model proposed is used to characterize the Mooney-Rivlin constitutive parameters. Since the
pressure-deflection formula is accurate and easy-to-use, it is an innovative tool in engineering applications
of inflated membranes.