Multi-Scale Modelling and Simulation

The spherical particles considered here are cohesionless, but elastic and frictional. The inter-particle
interactions are based on the well-known theories of contact mechanics (normal and tangential force  theories respectively).
The simulation assembly consists of 8000 poly-dispersed spheres following approximately normal distribution
displacement relations are governed by Hertzian and Mindlin-Deresiewicz with mean size 100mm (ten different sizes of the spheres were used in the diameter range 100±5mm). Elastic
modulus (E) of particles is 70 GPa. All the particles were assigned with Poisson’s ratio equal to 0.5. Interparticle
friction between particles  =0.10 for Case A and o.5 for Case B respectively.
The particles were initially randomly generated within a cuboidal periodic cell with zero contacts. The particles
were then subjected to isotropic compression under strain rate of 1e-5s-1
in large number of small-time steps.
During isotropic compression, a servo-control mechanism was periodically introduced to attain a mean stress
level p=100kPa and the samples were equilibrated to attain constant values of coordination number and
packing density. The initial assemblies thus created were in dense packing (initial packing density of the
samples was 0.635). All the initial assemblies were isotropic and homogeneous and held under a mean stress
of 100kPa. The assemblies were then slowly sheared by applying axi-symmetric tri-axial compression loading
under constant mean stress condition (Fig.1) inside a periodic cell.


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