A simple numerical approach for solving the frictionless contact problem of elastic wavy surfaces

The contact between rough surfaces plays an important role in numerous situations of theoretical and practical interest. The present work deals with the problem of frictionless contact between the periodically wavy surfaces of two elastic half-spaces. To solve this problem, a numerical approach, which is reminiscent of the boundary element method, is proposed on the basis of the matrix inversion method and by exploiting the periodicity of the problem. Compared with the finite element method, the proposed numerical approach turns out to be very simple and efficient for computing the actual contact areas and the contact pressure distribution. It is first tested and validated in the cases where periodical roughness is sinusoidal for the one- and two-dimensional situations. It is then applied to other cases where periodical roughness is paraboloidal, conical or pyramidal.