This paper presents a compact and easily accepted continuous model for the elastic-plastic contact of a sphere and a flat, including the relationships of load and contact area versus displacement and the relationship between the residual plastic displacement and the total displacement. The relationships of load and contact area versus displacement hold in the elastic and elastic-plastic regime. The relationship between the total displacement and the residual plastic displacement, that is the total displacement to the power of 1/2 is linear with the residual plastic displacement to the power of 1/2, has a compact and easily accepted form.

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