On the contact problem of an inflated spherical hyperelastic membrane

In this paper, the mechanics of contact of an inflated spherical non-linear hyperelastic membrane pressed between two rigid plates has been studied. We have considered the membrane material to be a homogeneous and isotropic Mooney-Rivlin hyperelastic solid. All three cases, namely frictionless, no-slip and stick-slip conditions have been considered separately in the plate-membrane contact region. The stretch of the membrane, and the surface traction (for no-slip contact) has been determined. For the stick-slip case, the sliding front is observed to be initiated at the contact periphery which moves towards the pole. The state at which the impending wrinkling condition occurs has been determined analytically. It is observed that the impending wrinkling state occurs at the periphery of the contact. Based on this, the minimum initial stretch (inflation) required to prevent wrinkling at any point in the membrane has been determined.