A theoretical model for line contact of rough surfaces from partial to complete contact

The contact behaviors of rough surfaces are critical in tribology, yet predicting their load-area relationship across the entire contact regime remains challenging. This paper presents a novel semi-analytical model for line contact between unidirectional rough surfaces and rigid planes under the plane-strain condition. Finite element simulations are performed for both elastic and elastic-perfectly plastic rough solids to capture the load-area relationship up to complete contact. The results reveal a gradual deviation from linearity at higher loads due to asperity interactions. To account for this nonlinear behavior, a general unified load-area formulation covering the full contact regime is established by integrating the simulation results with the theoretical line contact model at light loads. The accuracy of this advanced model is validated through direct finite element simulations on typical rough surfaces.