An Investigation into the Mechanics of Regular Arrays of Discs and Spheres

Abstract

Before the behaviour of granular material can be fully understood, it is necessary to study the simpler case of idealised regular packings. Two approaches towards this end are reported here; one analytical and one using computer simulation. In the first part of the thesis regular packings of rigid spheres (arranged in a body-centred orthorhombic manner) are analysed in order to define the conditions necessary to cause slip at the contacts. The macroscopic stress and strain-increment tensors are derived to define both the initial yield conditions and subsequent plastic (softening) deformation. The geometry of the corresponding yield surface is described by an oblique cone which rotates during plastic deformation. Plastic strain-increment vectors are at right angles to the cone axis. The computer simulation uses the Distinct Element Method to study regular packings of discs as they deform under a loading imposed by end plattens. The method employs an explicit finite difference scheme to model the propagation of boundary originated forces and displacements through the assembly. The results of the simulation tests show that end plattens produce discrete shear bands which propagate through the assembly and that softening is associated with gap widening along the existing shear bands.