Professor David A. Dillard and his collaborators invented the constrained blister and the related punch test for characterizing thin film adhesion-delamination and the disjoining pressure at the interface of a clamped membrane and a rigid substrate. A new dimensionless parameter, s=[6(1-)a4/3Eh]1/4p, relating the membrane dimensions (radius, a, and thickness, h), materials properties (elastic modulus, E, and Poisson's ratio, ), and adhesion (interface energy, , and disjoining pressure, p), is shown to account for the transition from the long range surface force limit with small (Derjaguin-Muller-Toporov, DMT) to the short range limit with large (Johnson-Kendall-Roberts, JKR). This parameter serves as a flexible membrane counterpart to the classical Tabor's parameter for adhesion in bulk solids. An alternative form is defined for thick circular plate under bending, b=[6(1-)a4/Eh3]1/2p. Three case studies, namely, the standard pressurized blister, the constrained blister, and the punch tests are investigated for membranes under either pure bending or pure stretching deformations.