Control of Friction Laws in Tangential Adhesive Contacts by Surface Geometry

Adhesive quasi-static tangential contact between a rigid indenter and a linearly viscoelastic half-space is investigated numerically using the Boundary Element Method. The indenter geometry is described by a power-law profile including parabolic (n = 2), conical (n = 1), and sharp-tip (n = 1/2) indenters. Adhesion is incorporated through a stress-based detachment criterion with effective works of adhesion derived from an energetic approach for quasi-static viscoelastic contacts. During sliding, elements at the leading edge of the contact attach, while those at the trailing edge detach. Due to the viscoelastic response of the material, adhesion at the leading edge is weak, whereas adhesion at the trailing edge is significantly stronger. This asymmetry generates a tangential force acting at the contact boundary. Numerical simulations performed for different ratios of the shear moduli G₀/G₁ show that the friction force strongly depends on the indenter geometry and follows different power-law relations to the normal force: a one-third power for parabolic indenters, a square-root dependence for conical indenters, and a two-thirds power for sharp-tip indenters.