Page 45 - The Combined Finite-Discrete Element Method

28 INTRODUCTION

Figure 1.43 The combined finite-discrete element problem comprising two discrete elements–in
the combined finite-discrete element method, each discrete element is discretised into finite elements.

captures the deformability of a single discrete element (particle, body). This is shown in
Figure 1.43, where a combined finite-discrete element problem comprising two discrete
elements is shown. Each discrete element is discretised into finite elements.

1.5 TRANSITION FROM CONTINUA TO DISCONTINUA

In flexible container type problems, it is often the case that individual particles can also
fracture or fragment in addition to being deformable and interacting with each other.
Fracture and fragmentation processes are in essence processes of transition from continua
to discontinua. It is also in principle possible to imagine an inverse process of particles
merging together.
There exists a whole class of engineering problems where transition from continua to
discontinua plays a major role. Transition from continua to discontinua is in general a
result of failure, fracture or fragmentation. Very often, the purpose of industrial operation
itself is to induce failure, fracture or fragmentation of a solid. This is best demonstrated
by a rock blasting operation, where an explosive charge is introduced into a borehole to
break and fragment the rock.
Similar rock fracture and fragmentation processes can be observed in the case of rock
crushers, where rock is broken by machinery to achieve a desired size distribution.
Failure, fracture and fragmentation is also observed in structural demolition. Very often,
tall buildings are demolished by introducing carefully placed explosive charges to initiate
the collapse using the potential energy of the building itself, together with inertia effects
of individual parts of the building.
Structural collapse also occurs due to hazardous loading conditions such as impacts,
earthquakes, blasts, explosions, etc. Structural collapse due to these loads can be pro-
gressive (e.g. Twin Towers, New York, September 2001). In progressive collapse, the