Analysis of Elastic-Plastic Loading and Unloading Contact between Ellipsoid and Rigid Flat

The loading contact behaviour of ellipsoids has been extensively studied, although there is limited research on their loading and unloading contact behaviour. This study uses the finite element method to analyse loading and unloading contact between an elastic-plastic ellipsoid and a rigid body. Unloading of an ellipsoid with different ellipticities was precisely conducted at the end of the elastic-plastic state. The ellipticity of the contact area is related to interference during loading and is independent of interference during unloading. When the interference is sufficiently large, the ellipticity of the contact area asymptotically approaches that of the ellipsoid. A new empirical formula is presented to describe the residual plastic interference of the ellipsoid after elastic-plastic unloading. The ellipsoid contact parameters (contact pressure, contact load, interference, and contact area) during the loading and unloading processes are numerically fitted based on the finite element analysis results, and dimensionless expressions are proposed for practical applications. The correctness and validity of the current study are evaluated through comparison with the prediction results of previous models and experiments.