Keywords: granular media, discrete element method, fragmentation, grinding process.

The grinding process is commonly used in many industrial fields such as: pharmaceutical, mineral or food. However, such a process Is expensive due to the energy cost and to the low quality of finished products (heterogeneity of grain size and shape). Hence, the economic stakes are high and the optimization of such a process seems crucial. Due to this energy cost, understanding the grinding process for granular media under compressive forces could be a good way to reach a better fragmentation efficiency. In order to be able to obtain answers to many questions about the grinding process, numerical simulations appear to be a good way to predict the mechanical behaviour of granular media.

To carry out such simulations, we must define the fragmentation mode of one grain subjected to a random contact force distribution induced by the adjacent grains. The investigations carried out on the fracture of grains [1,2,3,4,5,6] have shown that the fragmentation mechanism depends on several parameters, which are: the size, the shape, the material properties and the loading configuration. It has been concluded that a crack into the grain follows a transversal propagation leading to the fragmentation. In addition, the crack propagation depends on the stress field inside the grain [1] and the stress intensity factor of the material [1,2,3,4].

Throughout this study, we have developed a discrete modelling for granular packing subjected to compressive loading by using the discrete element method. We have used a grain fragmentation model depending on randomly spread contact forces [4,6]. The criterion of fracture depends on the tensile stress inside the grain and on the stress intensity factor of the material. The proposed model of fragmentation has been implemented in the MULTICOR software [7] and carried out for numerical calculations of granular packing under oedometric compression. Through this mechanical test, the objective is to be able to reproduce similar effects arising during the grinding process.

1

J.A. Aström, H.J. Herrmann, "Fragmentation of grains in a two-dimensional packing", Eur. Phys. J., B(5), 551-554, 1998. doi:10.1007/s100510050476

2

H. Morikawa, "Analytical studies on local damage to reinforced concrete structures under impact loading by discrete element method", Nuclear Eng. and Design, 179, 157-177, 1998. doi:10.1016/S0029-5493(97)00268-9

3

O. Tsoungui, D. Vallet, J.C. Charmet, "Use of contact area trace to study the force distributions inside 2D granular systems", Granular Matter 1, 65-69, 1998. doi:10.1007/s100350050010

4

O. Tsoungui, D. Vallet, J.C. Charmet, "Numerical model of crushing of grains inside two-dimensional branular materials", Powder Technology, 105, 190-198, 1999. doi:10.1016/S0032-5910(99)00137-0

5

J.P. Morris, M.B. Rubin, G.I. Block, M.P. Bonner, "Simulations of fracture and fragmentation of geologic materials using combined FEM/DEM analysis", Int. J. of Impact Engineering, 33, 463-473, 2006. doi:10.1016/j.ijimpeng.2006.09.006

6

S. Lobo-Guerrero, L.E. Vallejo, "Influence of pile shape and pile interaction on the crushable behaviour of granular material around driven piles: DEM analyses", Granular Matter, 9, 241-250, 2007. doi:10.1007/s10035-007-0037-3

7

J. Fortin, O. Millet, G. de Saxce, "Numerical simulation of granular materials by an improved discrete element method", Int. J. for Num. Meth. in Eng., 62, 639-663, 2004. doi:10.1002/nme.1209

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