
		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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