Page 78 - The Combined Finite-Discrete Element Method

POTENTIAL CONTACT FORCE IN 3D 61

S 3
k

B 5
B1

i B 4

B 2
S 2
B 3
S 1 j

Figure 2.26 Intersection of the target sub-tetrahedron with the base of contactor sub-tetrahedron.

B 6

B 1

B 5

B 2

B 3 B 4

Figure 2.27 Intersection of contact force over the intersection polygon.

(e) Calculate the equivalent nodal forces on target sub-tetrahedra due to contact force
F:
F T = (F I ,F J ,F K ,F L ) (2.53)
(f) Calculate the equivalent nodal forces on the contactor sub-tetrahedra due to contact
force F:
F C = (F i ,F j ,F k ,F l ) (2.54)
(g) Multiply the nodal forces by the unit vector normal to the base of the contactor
sub-tetrahedron:
f T = (F I n c ,F J n c ,F K n c ,F L n c )
(2.55)
f C = (F i n c ,F j n c ,F k n c ,F l n c )

6. Each time contact forces are assigned to the nodes of a sub-tetrahedron, one of the
nodes of the sub-tetrahedra is the centre of the target or contactor tetrahedron. Thus,