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2.2.7.3 The JKR model of solids adhesion

The JKR model [1] (Johnson, Kendall, Roberts – 1964-1971) applies to tips with large curvature radius (most likely to macroscopic bodies) and small stiffness. Such systems are called strongly adhesive. The model accounts for the influence of Van der Waals forces within the contact zone.

Fig. 1a.  Applicability of the JKR model.

Fig. 1b.  Plot of the force vs. the penetration depth.

Due to these, the attraction arises which not only weakens the force of elastic repulsion (the right part of Fig. 1b) but results in the neck creation ( , the left part of Fig. 1b) and in the negative force. The plot is described by formulas:

,

(1)

where – tip curvature radius, – contact area radius, – effective Young's modulus , – work of adhesion (see chapter 2.2.7.1). An example of the system to which the model applies is an eraser and paper.


References.

  1. Johnson K.L. Mechanics of contact interaction – Moscow: Mir, 1987 (in Russian)