An improved elastic–plastic contact model with asperity interactions based on Greenwood–Williamson theory

Real contact area plays a critical role in tribology. However, few contact models can give accurate load-area relation at very large contact fraction due to the lack of asperity interactions. In this work, an improved Greenwood–Williamson model is advanced for elastic–plastic rough surfaces. To include the asperity interactions in a simple way, the random distribution of contacting spots is treated as hexagonal distribution, which possesses the same overall isotropic property on surface. A representative asperity is then simulated by finite element method, and the load-area relation is calculated up to almost full contact. It is found that surface morphology and material properties govern the initial linear relationship at small contact fraction, and the interactions among asperities are closely related to contact fraction and lead to a larger load than that neglecting asperity interactions. The load-area relation is further formulated for general rough surfaces by comparing with an incremental equivalent contact model at initial contact. Direct simulations on typical rough surfaces verify the accuracy of the advanced load-area relation within a large range of contact fraction. This result provides a foundation for further analysis of friction, wear and sealing in tribology.