The multilevel multi-integration technique has been used here to numerically solve the normal and tangential loading of rough surfaces, employing the theory of Ciavarella [1] & Ja¨ger [2] to determinine the tangential shear tractions. Regular asperity surfaces, for which analytical solutions have previously been reported, have been analysed and results showed good agreement with the analytical solution. Random Gaussian surfaces have also been investigated to assess the effect of roughness on contact compliance and frictional energy dissipation.

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