The Johnson-Kendall-Roberts, JKR, model is improved over the Hertzian contact model. The JKR model takes into account the surface energy at the contact. This theory correlates the contact area of two contacting particles to the elastic material properties and the interfacial interaction strength. The cohesive force can be formed during the unloading cycle of contact as a force resisting separation. The JKR contact model between two particles leads to the radius  of the contact zone to be described by:

where is the surface energy in . The separation of the two particles is obtained from a maximum tensile force given by:

and does not depend on the elastic moduli of the material. The total normal force of contact with cohesion can be written as:

This represents a fully elastic model considering the cohesion between particles in the contact zone. The figure below provides an example of the JKR model and illustrates the tensile force between the particles in cohesive contact.

The Johnson-Kendall-Roberts Contact Mechanical Model

The JKR approximation is accurate for large cohesive energies and larger particles with low Young’s modulus. The model does not provide resistance in the tangential shearing direction. This limits the effect cohesion has on material flow as material is allowed to slide past each other with little resistance.

Johnson K. L., Kendall K., Roberts A., “Surface energy and the contact of elastic solids”, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 324 (1558), P301 – 313 1971.

Farhang R., Dubois F., Discrete-Element Modeling of Granular Materials, John Wiley & Sons Inc. 2011.

Johnson K., Contact Mechanics, Cambridge University Press, Cambridge, 1999.