A rough surface contact model for anisotropically elastic materials

Abstract

A solution method for three-dimensional isothermal rough surface contact problems of anisotropically elastic materials is outlined. The half-space Fourier response function is calculated numerically by solving a quadratic eigenvalue problem. The surface displacements of an anisotropically elastic half-space due to uniform pressure applied to a rectangular region are obtained by fast Fourier transformation. The surface displacements and sub-surface stresses of the anisotropic half-space due to the normal and tractive contact stress are evaluated by superposition making use of the convolution theorem. The real contact area and the contact pressure are identified by applying multi-grid methods. The material symmetry may be arbitrary. Numerical results for smooth Hertzian contact of cubic and transversely isotropic material agree with the output of analytical models and different methods of numerical solution.