Adhesive contact of an inflated circular membrane with curved surfaces

Inflated elastomeric membranes have been utilized as compliant probes to achieve sensitive adhesion measurement or pneumatic control of adhesive forces. This paper presents an analytical model for the adhesive contact between a circular elastic membrane under inflation and a rigid curved substrate. By adopting an incompressible neo-Hookean model for the membrane and introducing an approximation under large stretch, we obtain analytical solutions describing the three stages of adhesive contact: making contact, contact pinning and delamination. Among these three stages, the making contact stage is assumed to be adhesionless and frictionless, while the other two stages are subjected to a given work of adhesion between the membrane and the substrate. Two limiting cases of tangential interface behaviors (i.e., no slip and frictionless) are considered for the stages of contact pinning and delamination. Our analytical model provides solutions to the deformed membrane profile as well as relationships between key parameters such as applied pressure, contact force, contact radius and displacement, and is verified against computational results from finite element analysis. This analytical model can enable faster solutions for the adhesive contact mechanics of inflated membranes and is applicable as a design, optimization, and system refinement tool for applications such as adhesion measurement, transfer printing and soft robotic gripping.