Elastic beam over an adhesive wavy foundation

The adhesive behavior of a thin infinitely long elastic beam resting over a wavy rigid foundation with wavelength lambda is studied. Three governing parameters have been identified describing the physical and geometrical properties of the system: the dimensionless surface energy gamma=gamma/Es, the dimensionless amplitude h=h/lambda of the substrate, and thickness of the beam s=s/lambda. Analyzing the variation of the total energy of the system as a function of the governing parameters three different adhesive regimes have been individuated: full adhesion, partial adhesion, and no adhesion (point contact). An effective surface energy has been considered showing that the effect of surface waviness could be beneficial in increasing the adhesive strength of the system. In particular for gamma=1.0 and s=0.1, it has been evaluated a maximum effective interface energy of about 1.4gamma under full contact conditions. Larger amplifications are expected for higher gamma and smaller s.