Bradley Model Interaction between Rigid Bodies

2 Bradley Model (Interaction between Rigid Bodies) 

While adhesion between spheres was not considered in the Hertzian contact model, understanding of interactive forces between solids, and particularly colloids, showed a big progress in the early twentieth century. By integrating attractive interactions that follow the power law, Bradley found the total force between two rigid spheres separated at an equilibrium distance Zq is given by Ppuii-off = - JirwR, where w is the work of adhesion [11]. While Bradley only took Zq to be the atomic equilibrium separation, that is, a constant value, one can obtain 

By the 1960s, several experimental results that are contradictory to the Hertz theory had been reported, especially at low loads [12]. These observations strongly suggested the intervention of attractive surface forces in the elastic contact of two bodies. 

Incorporating the effect of adhesion in Hertzian contaet, Johnson et aL formulated a theory of adhesive contact using a balance between the stored elastic energy and the loss in surface energy, which is now renowned as the JKR theory [12], In this model, adhesion works only inside the contact area and the net traction p(r) acting on the eontact area is given by the sum of Hertzian repulsion pi and adhesive traction p, that is, 

These equations give the pull-off force by the form 

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