Adhesive contact between solids with periodically grooved surfaces

• Adhesive contact between a periodically grooved surface and a flat surface is studied.
• Surface interaction is described by the Maugis–Dugdale adhesion model.
• Three stable equilibrium states are found.
• Adhesion hysteresis is demonstrated with loading and unloading.
• The analytical expressions are given to calculate pull-off stresses.

This paper presents a study on adhesive contact between a periodically grooved surface and a flat surface. The effect of interfacial adhesion is included through the use of the Maugis–Dugdale adhesive contact model. The contact problem is reduced to a singular integral equation with Hilbert kernel for a height of the interface gaps and a system of two transcendental equations for widths of the gaps and the adhesion zones. Solutions are obtained for three different equilibrium states of the contact pair involving loading and unloading. The effects of the dimensions of the initial grooves and the adhesive stress on dimensions of the interface gaps, pull-off stress and adhesion hysteresis are investigated.