Closure Equations for CEB Elastic-Plastic Contact

The CEB elastic-plastic contact of nominally flat rough surfaces based on conservation of volume during plastic flow was forwarded by Chang, Etsion and Bogy [1]. The CEB model presents contact force as integral functions of the mean plane separation. A closed-form approximate function providing an explicit relation between contact force and surface parameters and mean plane separation would be desirable for several reasons. First, it facilitates implementation of the contact relation in the dynamics of mechanical system and, second, it provides expediency and efficiency for calculation of contact force when repetitive computation of the contact force is required. This paper presents closed-form approximate equations expressing contact force explicitly as a function of critical interference and mean plane separation. Two alternative approximate equations are provided. The first equation, in simpler form, is shown to yield error within six percent (6%) of the exact integral equations. The second form of approximate equations provides contact force accuracy within 0.1 percent of the original integral equations.