Contact Force: Coulomb’s Criterion
Coulomb’s criterion is used to prevent the unphysical sliding between grains or between grain and wall. The gross-sliding occurs when Coulomb’s criterion is violated or achieved; the criterion is (Ref. 1)
(3-19)
where μs is the coefficient of sliding friction. Hence, to not violate Coulomb’s criterion, the following form of the tangential force is used:
(3-20)
When Coulomb’s criterion is satisfied, the tangential displacement is limited as
(3-21)
Equation 3-19 to Equation 3-21 are true when the contact force model is either linear elastic or Hertz–MD. However, for the Contact Force: Hertz–MD with Adhesion Model these equations need to be slightly modified to account for the cohesive effects. A separation force, Fc is needed to separate two grains in equilibrium with no external force present and is given by
(3-22)
So, now Coulomb’s criterion becomes
Accordingly, the tangential force needs to be updated by the relation
And the tangential displacement is limited as