Adhesive Friction Law

Description

This frictional contact law implements a velocity-dependent Coulomb friction law with adhesion. It is only available in OSParticulas. When the surfaces are in contact, the frictional sliding force is

      [math]\displaystyle{ S_{slide} = (\mu_d + k \Delta v) N + S_a \quad{\rm if}\quad S_{stick}\gt \mu_s N+S_a }[/math]

and µ_d and µ_s are the dynamic and static coefficients of friction, k allows effective friction coefficient to depend linearly on sliding velocity, and S_a is the shear adhesion strength. In other words, the sliding will begin when it overcomes the static frictional force, but thereafter will slide with a velocity-dependent dynamic coefficient of friction plus adhesion term. 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 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 part, 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 and k = 0. If both those properties are zero, the simpler law is slightnly more efficient.

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	velocity units	0