Viscoelastic adhesive contact between a sphere and a two-dimensional nano-wavy surface

For contact involving viscoelastic materials with nanoscale roughness surfaces, both the viscoelasticity and the adhesive interaction play significant roles, and an in-depth understanding of this viscoelastic adhesive contact behavior is essential. This paper establishes a numerical viscoelastic adhesive contact model between a smooth sphere and a two-dimensional nano-wavy surface based on the Derjaguin approximation and elastic–viscoelastic correspondence principle, and the wavy surface is considered by introducing the height distribution into the surface gap equation. Influences of approach speed, contact position and wavy surface parameters on the viscoelastic adhesive contact behavior are quantitatively analyzed. It is shown that the viscoelasticity can be ignored at large approach speed, while when the speed is small, viscoelasticity significantly increases the maximum contact area and pull-off force. Variations of maximum contact area and pull-off force with contact position or wavy surface parameters are not completely consistent, where the contact positions with relatively large maximum contact area may exhibit small pull-off force. The pull-off force changes monotonically with increasing wavy parameter, while the maximum contact area changes nonmonotonically. This study can offer guidance for the application of wavy surface in viscoelastic adhesion regulation, and provide basis for the surface design and parameter determination of viscoelastic materials.