Simulation of granular media using parallel processing
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.