The contact behavior of a hemisphere pressed by a rigid plane is of great significance to the study of friction, wear, and conduction between two rough surfaces. A flattening contact behavior of an elastic–perfectly plastic hemisphere pressed by a rigid flat is researched by using the finite element method in this paper. This behavior, influenced by different elastic moduli, Poisson’s ratios, and yield strengths, is compared and analyzed in a large range of interference values, which have not been considered by previous models. The boundaries of purely elastic, elastic–plastic, and fully plastic deformation regions are given according to the interference, maximum mean contact pressure, Poisson’s ratio, and elastic modulus to yield strength ratio. Then, a new elastic–plastic constitutive model is proposed to predict the contact area and load in the elastic–plastic range. Compared with previous models and experiments, the rationality of the present model is verified. The study can be applied directly to the contact between a single sphere and a plane. In addition, the sphere contact can also be used to simulate the contact of single asperity on rough surfaces, so the present proposed model can be used to further study the contact characteristics of rough surfaces.

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.

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