Contact mechanics of a circular membrane inflated against a deformable substrate

Abstract

Finite inflation of a hyperelastic flat circular membrane against a deformable adhesive substrate and peeling upon deflation are analyzed. The membrane material is considered to be a homogeneous, isotropic and incompressible Mooney–Rivlin solid. The deformable substrate is assumed to be a distributed linear stiffness in the direction normal to the undeformed surface. The adhesive contact is considered to be perfectly sticking with no tangential slip between the dry surfaces of the membrane and the substrate. The inflation mechanics problem in the variational form yields the governing equations and boundary conditions, which are transformed to a nonlinear two-point boundary value problem by a careful choice of field variables for efficient computation. It is found that during inflation (deflation) with adhesive contact, the meridional stretch exhibits continuity up to C0 (C-1) at the contact junction, while the circumferential stretch remains continuous up to C1 (C0). Interestingly, stretch locking in an adhesive contact is found to give a higher indentation on the substrate than in a frictionless contact. Peeling at the contact junction has been studied, and numerical formulations for the energy release rate are proposed.