Model for an elastic-plastic spherical contact with the DMT adhesion

This paper studied the elastic-plastic spherical contact with the DMT adhesion, and presented an improved smooth formula for the local separation outside the elastic-plastic contact area on the KE empirical formula. The elastic-plastic local separation was equal to the elastic local separation with the same contact area and a equivalent elastic contact displacement. When the contact entered the elastic deformation regime, due to zero residual plastic contact displacement, the present formula for the elastic-plastic local separation could reduce to that for the elastic local separation naturally. Utilizing the present formula for the local separation, a unified adhesion model suitable for between the elastic and elastic-plastic spherical contact with the DMT adhesion was presented. In comparison with the KE adhesion model, the present adhesion model had higher fitting accuracy and could approach the Bradley's value as the contact displacement approached zero well, which was a good approximation to the complete integration calculation. The present adhesion model could be used for the study of the elastic and elastic-plastic spherical contact with adhesion.