Page 191 - The Combined Finite-Discrete Element Method

174 DEFORMABILITY OF DISCRETE ELEMENTS

an equivalent nodal force
1
f = s (4.222)
3
is assigned.

4.9 NUMERICAL DEMONSTRATION OF FINITE ROTATION
ELASTICITY IN THE COMBINED FINITE-DISCRETE ELEMENT
METHOD

In Figure 4.23 a combined finite-discrete element problem comprised of two discrete
elements is shown. Each discrete element is discretised into constant strain triangular
finite elements. The discrete elements move towards each other with initial velocity. The
initial motion sequence involves the simplest form of deformation, namely translation. It
is evident from Figure 4.23 that in this translation no stress is produced.
As discrete elements move closer towards each other (Figure 4.24), the discrete ele-
ments start impacting each other. Discretised distributed potential contact force is used
to resolve contacts. In this process, discretisation coinciding with the finite element mesh
is used on both discrete elements, thus the same grid is used to process interaction
and deformability. No energy dissipation either at contact or due to material damping
(dissipation due to stretching of discrete elements) is present.
Due to impact, contact forces are generated on the edges of both discrete elements,
resulting in material of discrete elements both stretching and rotating (Figure 4.25).
In Figures 4.26–4.28, the discrete elements continue to deform and move away from
each other, performing a sort of ‘dancing motion’, which is the reason why the discrete
elements were called ‘dancing triangles’. It is worth mentioning that although straining

Figure 4.23 Dancing triangles:translation towards each other.