A numerical simulation method in which quasi static
mechanical equilibrium is achieved in distinct elements
has been developed for two dimensional applications with
elasto- frictional interactions. The method works on a
step- by-step basis, using small strain steps, achieving
equilibrium by means of a least squares routine
in which particle displacements and spins are updated
to minimise the sum of forces and the sum of moments
on all elements. An error analysis is carried out
which shows that for small strain steps a stable, robust
routine is obtained.
Some elements of the routine can be run in parallel and
an implementation on a parallel processing system
of 17 Transputers (including the Master Processor)
is discussed. Various aspects of parallel
implimentation are discussed. The language OCCAM is used.
The routine uses a novel nonlinear elasto-frictional
interaction, which can be integrated analytically.
A number of simulations with discs at high packing
density is shown. Dominant mechanisms are detected, both
for isotropic compression and for a deviatoric stress
path. These mechanisms include the making and breaking of
contacts and the formation of force bridges. Observed
macroscopic effects are dilatancy and reduced stiffness
at higher stress ratio, followed by failure. The failure
phenomena are identified indirectly by identification
with a theoretical model.
Simulations of metal-matrix composites are presented
as mixtures of circular discs and rectangular fibres.
Loose assemblies are considered. Similar mechanisms as in
the case of circular discs are found and in addition the
bending moment on the fibres is calculated. Great
heterogeneity characterises all simulations
