Numerical and experimental analysis of inflating a circular hyperelastic membrane over a rigid and elastic foundation

This work investigates the numerical and experimental behaviour of a flat, circular membrane inflated by an incompressible fluid over rigid and elastic foundations. The membrane is assumed to be homogeneous, elastic, and isotropic. The friction between the silicone bag used to fill the membrane with liquid, the membrane, and the foundation are not considered, although there is contact over the entire area of the membrane. The membrane was modelled as neo-Hookean to describe the membrane used in the experimental analysis. The Runge-Kutta and the Shooting methods are used to solve the well-known equilibrium differential equations for hyperelastic membranes under finite deformations. The numerical and experimental results of the expanded membrane were in good agreement. The results showed that for the same amount of liquid inserted, there is considerably less pressure inside the membrane over the elastic foundation and a smaller superficial area for the expanded membrane. This work focused on applying structural knowledge to Biomechanical Engineering and was motivated by the puzzling results obtained during the surgical procedure of skin expansion realized on some patients.