Loading-unloading model of contact between elastic-plastic ellipsoid and rigid plane

The mechanical behaviour of the ellipsoidal asperity and rigid planes during loading and unloading are fundamental problems in contact mechanics. This study investigates the contact between elastic-perfectly plastic ellipsoidal asperity for different ellipticities and rigid planes under normal conditions during the loading and unloading process using the finite element method. The results show that the changing trend of the contact load, residual displacement, contact area, and plastic work with displacement under different ellipticities is similar, but the magnitude is different. The contact area during unloading is not always smaller than that during loading with the same displacement. Moreover, the initial unloading stage contact area is larger than that of the loading stage. Based on the numerical model calculation results, analytical dimensionless expressions are proposed for the residual displacement, plastic work, contact area, and contact load after fully unloading the ellipsoids with different ellipticities for a wide range of displacements. The prediction results from previous models are used to verify the effectiveness and correctness of the proposed equations. These empirical relations can be combined with statistical or fractal methods to study the contact behaviour of macroscopic rough surfaces.