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 µ_s and µ_d are the static and dynamic coefficients of friction, v_1/2 allows a smooth transition from µ_s to µ_d, k allows friction coefficient to depend linearly on sliding velocity (Δv), and S_a 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 µ_s to µ_d. The leading term in the above law achieves this goal by monotonically transitioning from µ_s when Δv = 0 to µ_d for high Δv. The law parameter v_1/2 is the velocity at which that term is half way from µ_s to µ_d. The default value of v_1/2 = 0 models an instantaneous change in friction coefficient. Choosing the appropriate value for v_1/2 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 N_a 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 v_1/2 = 0. If all these properties are zero, the simpler law is slightly more efficient (although the simpler law cannot model a smooth transition µ_s to µ_d).

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
displacementOnly	Set to: 0 to detect contact when COD<0 and stress<0; 1 to detect contact whenever COD<0 regardless of stress; <0 to detect contact when COD<0 and stress<-displacementOnly (in pressure units)	none	0
Dc	<0 to find separation assuming perfect interfaciall contact, ≥0 to use imperfect interface methods to find separation.	pressure/length units	none

See some comments about the displacementOnly and Dc parameters.