The Simplified Johnson-Kendall-Roberts Model

From the original JKR model, the contact radius can be determined as a function of the contact overlap \delta_n . The contact area between two particles is not a simple calculation to perform, therefore the simplied JKR model approximates the radius a of the contact zone
with:

a^2 \approx {R^*}\delta_n

Simplifying the original total normal force equation of contact with cohesion:

f_n = \frac{4a^3E^*}{3R^*} - \sqrt{8 \pi E^* \gamma_{sur} a^3}

the normal force is written as:

f_n = {E^*}{R^{\frac{1}{2}}}\delta_n^{\frac {3}{2}}-U_aE^{*\frac{1}{2}}R^\frac{3}{4}\delta_n^\frac{3}{4}

where

U_a = \sqrt{6 \pi \gamma_{sur}}

This eliminates the computation of radius a of the contact zone while still providing an explicit expression of the force as a function of the overlap.

 

 

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