Page 21 - The Combined Finite-Discrete Element Method

4 INTRODUCTION

and most often used numerical methods are Discontinuous Deformation Analysis (DDA)
and Discrete Element Methods (DEM). These methods are designed to handle contact
situations for a large number of irregular particles. DDA is more suitable for static prob-
lems, while DEM is more suitable for problems involving transient dynamics until the
state of rest or steady state is achieved.
A division of computational mechanics dealing with computational solutions to the
problems of discontinua is called Computational Mechanics of Discontinua. Computa-
tional Mechanics of Discontinua is a relatively new discipline. Pioneering work in the
late 1960s and early 1970s was done by researchers (Williams, Cundal, Gen-She, Musto,
Preece, Thornton) from various disciplines. They handled complex problems of discon-
tinua with very modest computing hardware resources available at the time. A second
generation of researchers, such as Munjiza, Owen and O’Connor, benefited not only from
more sophisticated computer hardware, available with RAM space measured in megabytes,
but also from the UNIX operating system and graphics libraries combined with a new
generation of computer languages, such as C and C++. This has enabled the key algorith-
mic solutions to be developed and/or improved. The third generation of researchers (late
1990s and the early years of this century) has benefited further from increased RAM space,
now measured in gigabytes, relatively inexpensive CPU power, sophisticated visualisation
tools, the internet and public domain software. As a result of this progress, discontinua
methods have been applied to a wide range of engineering problems, which include both
industrial and scientific applications.

1.3 A TYPICAL PROBLEM OF COMPUTATIONAL MECHANICS
OF DISCONTINUA

The difference between problems of Computational Mechanics of Continua and problems
of Computational Mechanics of Discontinua are best illustrated by the container problem.
The container problem is about how many particles can be placed in a given volume,
how they interact and the mechanics of the pack in general. To demonstrate the key
elements of discontinua analysis, a numerical simulation of gravitational deposition of
different packs inside a rigid box of size 250 × 250 × 540 mm is shown in this section.
The total solid volume deposited is constant for all simulations shown, and is equal to
3
V = 9.150e−03 m .
The particles are deposited in three stages:
• In the first stage, a regular pattern is used to initially place all the particles inside the
box, (Figure 1.2 (left)).
• In the second stage, random velocity field is applied to all the particles, making particles
move inside the box until a near random distribution of particles inside the box is
achieved. There is no gravity at this stage (Figure 1.2 (right)).

• In the third stage, the velocity of all particles is set to zero, and acceleration of
2
gravity g = 9.81m/s is applied in the z-direction. Under gravity the particles move
towards the bottom of the box. Due to the interaction with the box and with each
other, the particles closer to the bottom of the box slowly settle into the final