On the mechanics of inflated hyperelastic membrane–membrane contact problem

Abstract

The membrane–membrane contact mechanics plays an important role in several biological processes, such as drug delivery, cell infection, cell destruction, etc. at microscales. The problem at macroscales is relevant to air inflated and air supported structures. In this work, we have chosen a simple system in which contact mechanics of two inflated membranes (initially flat circular membranes parallelly placed, fixed circumferentially and pressurized in opposite direction to make contact) has been studied. Friction and effects of adhesion are neglected for simplicity. We have considered the Mooney–Rivlin hyperelastic membrane material. The governing equations are derived using the principle of minimum potential energy. The problem has been solved separately for contacting and non-contacting region and joined by appropriate junction and boundary conditions. Indentation on the low-pressure membrane by the high-pressure membrane for different loading and rigidity constants has been studied. We observe a critical radius of contact of the low-pressure membrane, which depends upon the characteristics of high-pressure membrane, beyond which the stretch and stress values start to rise with indentation. At this critical radius, maximum meridional curvature discontinuity jump exists. Variation of contact force, along with principal stretches and stresses, are also discussed.