Keywords: non smooth contact dynamics, contact dynamics, fragmentation, fracture, cohesion.

In several engineering fields such as geomechanics, masonry, mechanics or minerals, the materials which are used during the processes can be considered as a cohesive discrete medium. But as we know, it is the heterogeneity of contact interactions (and the mechanical properties), the particles size (and shape), the cohesive effects and other physical parameters that are responsible for the complexity of such materials. Several studies have been carried out to investigate the strength and fracture mode under uniaxial compressive loading. These studies showed that the mechanical behavior depends on the chain forces (contact network) and the adhesion between particles or between the particles and the matrix in the case of cemented granular materials [1,2,3].

The contact conditions include the normal and tangential adhesion effects depending on the cohesion parameter of material. Hence, we distinguish two cases, the first one with adhesion forces ensuring a cohesive state between the particles and the second one where the particles are non-cohesive and are submitted only to friction contact conditions. The cohesive status is checked by a failure criterion, depending on the tensile, shearing and momentum loadings at the contact interface [4].

The proposed modeling is implemented in a numerical software, MULTICOR, based on the non smooth contact dynamics formulation [5] and the bipotential method for the unilateral dry contact condition [6]. The contact reaction between two particles is computed by a predictor-corrector scheme of the augmented contact force [7].

Through this numerical study, we attempted to reproduce some mechanisms of fracture into a rigid and cohesive multi-contact systems subjected to given loading. The numerical simulations allowed us to track the local fracture arising between two particles and its propagation. Also, the macroscopic behavior seems very realistic in comparison with the experimental tests shown in [3].

1

M. Jean, V. Acary, Y. Monerie, "Non-smooth contact dynamics approach of cohesive matrials", Phil. Trans. R. Soc. Lond. A, 359, 2497-2518, 2001. doi:10.1098/rsta.2001.0906

2

A. Benhamida, F. Bouchelaghem, H. Dumontet, "Effective properties of a cemented or an injected granular material", Int. J. Numer. Anal. Method Geomech, 29, 187-208, 2005. doi:10.1002/nag.411

3

J.-Y. Delenne, Y. Haddad, J.C. Bénet, J. Abecassis, "Use of mechanics of cohesive granular media for analysis of hardness and vitreousness of wheat endosperm", Journal of Cereal Science, 47, 438-444, 2008. doi:10.1016/j.jcs.2007.05.009

4

J.-Y. Delenne, M.S. el Youssoufi, J.-C. Bénet, "Comportement mécanique et rupture de milieux granulaires cohèsifs", C. R. Mécanique, 330, 475-482, 2002.

5

M. Jean, "The Non Smooth Contact Dynamics Method", Compt. Methods Appl. Math. Engrg., 177, 235-257, 1999. doi:10.1016/S0045-7825(98)00383-1

6

G. De Saxcé, Z.Q. Feng, "The bipotential method: a constructive approach to design the complete contact law with friction animproved numerical algorithms", Int. J. Math. Comput. Model., 28, 225-245, 1998. doi:10.1016/S0895-7177(98)00119-8

7

J. Fortin, G. de Saxce, "Modélisation numerique des milieux granulaires par l'approchedu bi-potentiel", C. R. Acad. Sci., 327, 721-724, 1999.

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