  We investigate the contact of a rigid cylindrical punch with an adhesive beam
mounted on flexible end supports. Adhesion is modeled through an adhesive zone
model. The resulting Fredholm integral equation of the first kind is solved by
a Galerkin projection method in terms of Chebyshev polynomials. Results are
reported for several combinations of adhesive strengths, beam thickness, and
support flexibilities characterized through torsional and vertical
translational spring stiffnesses. Special attention is paid to the important
extreme cases of clamped and simply supported beams. The popular
Johnson-Kendall-Roberts (JKR) model for adhesion is obtained as a limit of the
adhesive zone model. Finally, we compare our predictions with preliminary
experiments and also demonstrate the utility of our approach in modeling
complex structural adhesives.
