The contact mechanics models incorporate various integral expressions that involve the probability density functions of the asperity heights. These integrals can be calculated numerically with the desired accuracy, however, in the practical applications of the contact mechanics, the computations are already quite time consuming. Consequently, various authors have proposed approximate solutions, mostly for the isotropic contact mechanics models. The current paper presents an approximate solution for the non-isotropic elasto-plastic model proposed by Horng. The probability density of the asperity heights is approximated, so the integrals that describe the elastic contact, as well as the integrals that describe the plastic contact, can be obtained as closed form expressions. Finally, the plastic supported load and the elastic supported load for the non-isotropic roughness are expressed using the gap, the spectral moments of the roughness and the plasticity index.

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