Granular Matter, 2013, Volume 15, Issue 5, pp 595-606,
Paul Langston, Jun Ai, Hai-Sui Yu.
Nottingham Centre for Geomechanics, The University of Nottingham, University Park, Nottingham, NG7 2RD, UK
We develop a discrete element model (DEM) simulation of mixed regular rounded polyhedra and spheres in simple shear with walls and periodic boundaries in 3-dimensions. The results show reasonably realistic behaviour developing shear and dilation or compaction depending on whether the initial state is dense or loose. Similarly non-coaxiality of principal stress direction and strain rate direction are shown. Polyhedra show more general realistic behaviour than spheres but take significantly longer to run. Particle forces include normal elastic, damping, and tangential friction and rolling friction. No cohesion or interstitial fluid is modelled. A separate simplified dynamic implicit finite difference Eulerian continuum model is developed and its parameters are used to fit the DEM results. This uses mass and momentum balances, a non-linear constitutive model and Mohr–Coulomb failure criterion. It runs in 2D with periodic boundaries effectively making it pseudo-1D. The model can reproduce the general trend of the DEM results and is a good basis for further development and understanding the physics.
Following publication of this paper we undertook further studies on Discrete element modelling of material non-coaxiality in simple shear flows, Int. J. Numer. Anal.Meth.Geomech. (2013) DOI: 10.1002/nag.223. This uses a discretised-wall granular cell where the boundary dilates or contracts with the sample. A near uniform shear field is achieved across the sample, which can help in generalising constitutive laws.
We have also been developing our3D DEM code to model flexible fibres. It can be challenging to attain numerical stability in the simulations for particles with high aspect ratio (>30), but the model offers a range of potential applications. The results show realistic packing fractions for rigid particles. Further validation is required for flexible fibres.The figure below shows an example of 1200 fibres dropped into a cylinder (walls not shown). Each fibre has an aspect ratio of 30 and is modelled by 3 connected sphero-cylinders.