Effect of pressure on pull-off of punch adhered to circular or 1-D rectangular plate

Pressure can sometimes be utilized to increase or decrease the strength of adhesion. This phenomenon is analyzed for upward pull-off of (i) a flat, circular cylindrical punch from a circular plate and (ii) a long, flat, rectangular punch from a long rectangular plate. The pressure is applied, and then the punch is pulled upward. The pressure may act upward (positive) or downward (negative) on the plate. Both force control and displacement control are considered. The plate is assumed to be linearly elastic, and nonlinear von Kármán theory is used to allow moderate displacements. A transversality (debonding) condition is obtained, and the effects of the work of adhesion, the relative size of the punch, and residual stress are investigated. With an increase in pressure, the pull-off force decreases, the pull-off deflection of the punch relative to the initial flat plate level increases, and the pull-off deflection with respect to the pressurized plate may increase or decrease. Some of the results are quite different from those for a membrane (where bending stiffness is neglected).