Adhesive Friction Law
Description
This frictional contact law implements a velocity-dependent Coulomb friction law with adhesion. When the surfaces are in contact, the frictional sliding force is
[math]\displaystyle{ S_{slide} = \left({\mu_s v_{1/2} + \mu_d \Delta v\over v_{1/2}+\Delta v} + k \Delta v\right) N + S_a \quad{\rm if}\quad S_{stick}\gt \mu_s N+S_a }[/math]
and µs and µd are the static and dynamic coefficients of friction, v1/2 allows a smooth transition from µs to µd, k allows friction coefficient to depend linearly on sliding velocity (Δv), and Sa is a shear adhesion strength. In other words, the sliding will begin when it overcomes the static friction plus adhesion force, but thereafter will slide with a velocity-dependent dynamic coefficient of friction plus an adhesion term.
Simulations show the dynamic fluctuations can result in simulations that are barely affected by static coefficient of friction. The problem is resolving the instantaneous drop in coefficient of friction at the onset of sliding. One way to simulate real static/dynamic effects is to implement a smooth transition from µs to µd. The leading term in the above law achieves this goal by monotonically transitioning from µs when Δv = 0 to µd for high Δv. The law parameter v1/2 is the velocity at which that term is half way from µs to µd. The default value of v1/2 = 0 models an instantaneous change in friction coefficient. Choosing the appropriate value for v1/2 for a given problem may require experimentation.
If the surfaces are not in contact, the surface continue to stick as long as:
[math]\displaystyle{ \left({S_{stick}\over S_a}\right)^2 + \left({N\over N_a}\right)^2 \lt 1 }[/math]
where Na is the normal adhesion strength. If this criterion is not met, the surfaces move apart freely with zero tractions. If either Sa or Na are zero, the surfaces will have no separation adhesion and therefore always move freely when not in contact.
Note that the adhesion in this law is reversible. In other words, if the stresses break the adhesion as moving apart, they will stick with the same adhesive strengths when the surfaces come back into contact. Also note that the simple Coulomb friction contact law is a special case of this law for Sa = 0, k = 0, and v1/2 = 0. If all these properties are zero, the simpler law is slightly more efficient (although the simpler law cannot model a smooth transition µs to µd).
Properties
The properties for this law are:
| Property | Description | Units | Default |
|---|---|---|---|
| coeff | The dynamic coefficient of friction | none | 0 |
| coeffStatic | The static coefficient of friction. If this optional static coefficient of friction is changed to a positive number, it must be greater than the dynamic coefficient or friction. | none | -1 |
| Sa | The shear adhesive strength of the interface | pressure units | 0 |
| Na | The normal adhesive strength of the interface | pressure units | 0 |
| kmu | Slope for dynamic coefficient of friction vs. velocity | 1/(velocity units) | 0 |
| vhalf | Velocity where transition from µs to µd is half done | (velocity units) | 0 |