Modelling the static contact between a fingertip and a rigid wavy surface

Surface topography is one of the major parameters affecting friction during touch and consequently tactility. In order to understand and control friction, fine controlled surfaces with a sinusoidal topography are studied to derive an analytical contact model. The Westergaard model on a unidirectional (2D) and bidirectional wavy surface (3D) is applied to unveil the contact area. The Hertz line and elliptic contact theory are applied to determine the relation between the contact pressure and area in the early contact on the 2D and 3D case respectively. The 2D case allows determining the effective elastic modulus of the fingertip from experimental data. The analytical solution obtained from the 3D case allows estimating the real contact area from a straightforward equation.