Adhesive transition from noncontacting to contacting elastic spheres: extension of the Maugis-Dugdale model

In this paper, an adhesion model for spherical noncontact is proposed based on the Maugis-Dugdale (MD) adhesive contact model. The proposed noncontact model is combined with the MD contact model, thus providing a full range adhesion model with analytical transition from noncontacting to contacting asperity geometry. The proposed model is favorably compared with the full range improved DMT model for low surface energy values. The transition process from noncontact to contact and the adhesion instability that occurs during this transition are also investigated. It is found that jump-off points are different for displacement control and force control. Moreover, under displacement control, jump-on and jump-off points are different when the adhesion parameter λ is greater than 0.95, whereas they are identical for λ<0.95. By curve fitting a relationship between the critical approach under displacement and force control separately and the adhesion parameter λ, approach prediction equations for jump-on and jump-off under different adhesion levels were obtained.