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2.2.7.5 Comparison of DMT, JKR and Maugis models

To compare the foregoing models we introduce the normalized radius of the contact area , force and penetration depth :

,     ,    

(1)

In Table 1 are collected major assumptions and restrictions of every theory while in Table 2 – corresponding normalized equations [1].

Model Assumptions Restrictions
Hertz No surface forces Not applied to small loads in the presence of surface forces
DMT Long-range surface forces act only outside the contact area. Model geometry is as in the Hertz model Contact area can be decreased due to the limited geometry. Applied only to small
JKR Short-range surface forces act only within the contact area Force magnitude can be decreased due to surface forces.Applied only to large
Maugis Tip-sample interface is modeled as a ring. The solution is analytical but equations are parametric. Applied to all values.

Table 1.  Comparison of quantitative adhesion models.

Model Normalized equations
Hertz
DMT
JKR
Maugis

Table 2. Normalized equations of quantitative adhesion models.

Fig. 1 shows plots of normalized force vs. normalized penetration depth for DMT, JKR and Maugis models at different . As can be seen, at small the Maugis model approaches the DMT model while at large – the JKR model.

Fig. 1. Plot of the force vs. the penetration depth for the DMT, JKR and Maugis models
for the different values.


Summary.

  • Several theoretical models of adhesion having different ranges of application are proposed. The most accurate one is the Maugis model.

References.

  1. Handbook of Micro/Nanotribology / Ed. by Bhushan Bharat. - 2d ed. - Boca Raton etc.: CRC press, 1999. – 859 p.