JKR Contact Mechanics Theory
It is a common experience that one needs to apply force to pull apart two bodies placed in intimate contact with each other signifying that adhesive forces act between the two bodies. While the origin of the adhesive forces is not a subject of this course, here we will worry about how to estimate the effect of these forces in contact deformation.
Let's consider the deformation of two smooth elastic spheres of radius  and  pressed together under load  . If  and  are the elastic modulii of the two spheres, then according to the Hertzian mechanics, the expressions for contact radius  , displacement  and contact pressure  are obtained as,
Where,  and  .
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