An Extended Asymptotic Analysis for Elastic Contact of Three-Dimensional Wavy Surfaces

An analytical approach for an extended asymptotic analysis of 3D wavy surfaces contact was developed on the basis of expansion of a double-sinusoidal surface in Fourier series, using cylindrical coordinates. The two different problems were considered: indentation of a double-sinusoidal non-periodic punch into an elastic half-space and a penny-shaped crack under action of non-axisymmetric pressure. The closed-form expressions for determining the load–area and the load–separation curves for the light and the high loads, considering virtual circular contact and non-contact areas, were obtained. The results were compared with existing analytical and numerical studies. They show that the mean contact characteristics at the light and the high loads mainly depend on the axisymmetric component of Fourier series, representing the wavy surface. These parameters can be calculated analytically with sufficient accuracy for a large range of applied pressures except transitional region. The relation between 2D and 3D solutions is also shown.