Finite inflation of an initially stretched hyperelastic circular membrane

In this paper, finite axisymmetric inflation of an initially stretched flat circular hyperelastic membrane has been analyzed. The membrane material has been assumed to be a homogeneous and isotropic Mooney–Rivlin solid. The inflation problem has been reduced to a set of three first order ordinary differential equations using a set of appropriately defined variables. An interesting method based on the invariance of these equations to scaling has been used to solve the two point boundary value problem without much effort. This method does not require any special technique for negotiating the limit points in the pressure–stretch relations of the membrane. Several inflation results of an initially unstretched and pre-stretched circular membrane for various material parameters are obtained. The roles of pre-stretch and internal pressure on the inflation mechanics are clearly delineated. The initial stretch is observed to have some interesting counter-intuitive effects on the inflation of the membrane.