Johnson-Kendall-Roberts (JKR) model of elastic contact between two spheres ( contact radius)


Contact mechanics is the study of the deformation of solids that touch each other at one or more points.When two solid surfaces are brought into close proximity, they experience attractive van der Waals forces. Johnson, Kendall, and Roberts formulated the JKR theory of adhesive contact using a balance between the stored elastic energy and the loss in surface energy. The JKR model considers the effect of contact pressure and adhesion only inside the area of contact. The Hertz equation for the area of contact between two spheres, modified to take into account the surface energy.

Related formulas


aContact radius (m)
RRadius R = (R1*R2)/(R1+R2) (m)
EYoung's modulus of the two spheres (Pa)
FForce applied on the body (N)
γHalf of the total surface energy of both surfaces per unit area (J/m2)