Analytical and experimental study of a circular membrane in Hertzian contact with a rigid substrate

The problem that is addressed here is that of a pressurized circular membrane in contact with a rigid substrate. A closed-form membrane analysis with Hertz-type contact is developed to describe the relationship between pressure, contact radius and contact force. Both the variation in the slope of the deflection profile of the portion of the membrane outside the contact zone and the contact radius itself are measured by an apparatus based on moiré deflectometry. Contact experiments with a 3 μm PET film and a glass substrate show that this analysis predicts both the slope field and contact radius well.