
		FORCES

Since the particles forming granular materials (grains, pills, spheres etc)
are of the order of millimeter (mm) the van der Waals forces are neglectable
and we consider only forces acting on particles in contact with other particles
or with the walls.

For simplicity consider the contact (collision) of two particles for now. Walls
will be represented by particles with infinite radius and mass in this picture.

During contact two kind of forces act on each particle. One in the direction
of the line joining the two centers of mass which we will call the normal
force and another one in the direction perpendicular to it which we will call
the shear force.


The normal force consists of two parts:

a) an energy conserving repulsive part
modeled by a linear (Hooke's law) or a non linear (Hertz' law) spring 

b) a dissipative part modeled by a viscous (Stokes' law) friction term
proportional to the relative normal velocity of the two centers of mass.
The strength of this term can be varied interactively with the parameter
labeled DISSIPATION. E.g. a value of 500 makes the particles loose ca.
30 percent of their velocities during collisions.


The shear force also consists of two parts:

a) a dynamic part modeled by a viscous (Stokes' law) friction term 
proportional to the relative shear velocity of the two centers of mass.
The strength of this term can be varied interactively with the parameter
labeled DYNAMIC FRICTION.

b) a static part modeled by a linear (Hooke's law) spring at the first
contact point of a collision. It makes the particles want to stick to an
inclined surface until a threshold angle is reached. This angle is given
through Theta = arctan(MU) where the parameter MU can be varied with the
slider labeled COULOMB THRESHOLD. This behavior can be turned ON and OFF 
with the button labeled STATIC FRICTION.
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