P. A. Cundall and O. D. Strack, A discrete numerical model for granular assemblies, G??otechnique, vol.29, issue.1, pp.47-65, 1979.
DOI : 10.1680/geot.1979.29.1.47

T. Kawai, New discrete models and their application to seismic response analysis of structures, Nuclear Engineering and Design, vol.48, issue.1, pp.207-229, 1978.
DOI : 10.1016/0029-5493(78)90217-0

A. Kikuchi, T. Kawai, and N. Suzuki, The rigid bodies???spring models and their applications to three-dimensional crack problems, Computers & Structures, vol.44, issue.1-2, pp.469-480, 1992.
DOI : 10.1016/0045-7949(92)90269-6

E. Schlangen and E. J. Garboczi, New method for simulating fracture using an elastically uniform random geometry lattice, International Journal of Engineering Science, vol.34, issue.10, pp.1131-1144, 1996.
DOI : 10.1016/0020-7225(96)00019-5

J. E. Bolander and S. Saito, Fracture analyses using spring networks with random geometry, Engineering Fracture Mechanics, vol.61, issue.5-6, pp.569-591, 1998.
DOI : 10.1016/S0013-7944(98)00069-1

J. G. Van-mier, M. R. Van-vliet, and T. K. Wang, Fracture mechanisms in particle composites: statistical aspects in lattice type analysis, Mechanics of Materials, vol.34, issue.11, pp.705-724, 2002.
DOI : 10.1016/S0167-6636(02)00170-9

H. J. Herrmann and S. Roux, Statistical Models for the Fracture of Disordered Media, 1990.

G. Shi and R. E. Goodman, Generalization of two-dimensional discontinuous deformation analysis for forward modelling, International Journal for Numerical and Analytical Methods in Geomechanics, vol.94, issue.4, pp.359-380, 1989.
DOI : 10.1002/nag.1610130403

S. Hentz, L. Daudeville, and F. Donzé, Identification and Validation of a Discrete Element Model for Concrete, Journal of Engineering Mechanics, vol.130, issue.6, pp.709-719, 2004.
DOI : 10.1061/(ASCE)0733-9399(2004)130:6(709)

H. J. Tillemans and H. J. Herrmann, Simulating deformations of granular solids under shear. Physica A: Statistical Mechanics and its Applications, pp.261-288, 1995.
DOI : 10.1016/0378-4371(95)00111-j

D. 'addetta, G. A. Kun, F. Ramm, and E. , On the application of a discrete model to the fracture process of cohesive granular materials, Granular Matter, vol.4, issue.2, pp.77-90, 2002.
DOI : 10.1007/s10035-002-0103-9

F. Kun and H. J. Herrmann, A study of fragmentation processes using a discrete element method, Computer Methods in Applied Mechanics and Engineering, vol.138, issue.1-4, pp.3-18, 1996.
DOI : 10.1016/S0045-7825(96)01012-2

J. J. Moreau, Unilateral contact and dry friction in finite freedom dynamics . CISM Courses and Lectures (1988) Nonsmooth Mechanics and Applications, pp.1-82

G. H. Shi and R. E. Goodman, Two dimensional discontinuous deformation analysis, International Journal for Numerical and Analytical Methods in Geomechanics, vol.9, issue.6, pp.541-556, 1985.
DOI : 10.1002/nag.1610090604

L. Jing, Formulation of discontinuous deformation analysis (DDA) ??? an implicit discrete element model for block systems, Engineering Geology, vol.49, issue.3-4, pp.371-381, 1998.
DOI : 10.1016/S0013-7952(97)00069-0

A. Delaplace and R. Desmorat, Discrete 3D model as complimentary numerical testing for anisotropic damage, International Journal of Fracture, vol.140, issue.2/3, pp.115-128, 2008.
DOI : 10.1007/s10704-008-9183-9
URL : https://hal.archives-ouvertes.fr/hal-00270147

C. Moukarzel and H. J. Herrmann, A vectorizable random lattice, Journal of Statistical Physics, vol.235, issue.FS11, pp.911-923, 1992.
DOI : 10.1007/BF01048880

J. Oliver, A. E. Huespe, and J. Cante, An implicit/explicit integration scheme to increase computability of non-linear material and contact/friction problems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.21-24, pp.1865-1889, 2008.
DOI : 10.1016/j.cma.2007.11.027

J. G. Rots and S. Invernizzi, Regularized sequentially linear saw-tooth softening model, International Journal for Numerical and Analytical Methods in Geomechanics, vol.28, issue.78, pp.821-856, 2004.
DOI : 10.1002/nag.371

C. Oliver-leblond, A. Delaplace, F. Ragueneau, and B. Richard, Non-intrusive global/local analysis for the study of fine cracking, International Journal for Numerical and Analytical Methods in Geomechanics, vol.18, issue.106, pp.973-992, 2013.
DOI : 10.1002/nag.2155

E. Perkins and J. R. Williams, A fast contact detection algorithm insensitive to object sizes, Engineering Computations, vol.18, issue.1/2, pp.48-61, 2001.
DOI : 10.1108/02644400110365770

O. 'rourke, J. Chien, C. B. Olson, T. Naddor, and D. , A new linear algorithm for intersecting convex polygons, Computer Graphics and Image Processing, vol.19, issue.4, pp.384-391, 1982.
DOI : 10.1016/0146-664X(82)90023-5

Y. T. Feng and D. R. Owen, A 2D polygon/polygon contact model: algorithmic aspects, Engineering Computations, vol.21, issue.2/3/4, pp.265-277, 2003.
DOI : 10.1108/02644400410519785

G. Cusatis, A. Mencarelli, D. Pelessone, and J. Baylot, Lattice Discrete Particle Model (LDPM) for failure behavior of concrete. II: Calibration and validation. Cement and Concrete composites, pp.891-905, 2011.

J. G. Rots, B. Belletti, and S. Invernizzi, Robust modeling of RC structures with an ???event-by-event??? strategy, Engineering Fracture Mechanics, vol.75, issue.3-4, pp.590-614, 2008.
DOI : 10.1016/j.engfracmech.2007.03.027

J. C. Simo and T. A. Laursen, An augmented lagrangian treatment of contact problems involving friction, Computers & Structures, vol.42, issue.1, pp.97-116, 1992.
DOI : 10.1016/0045-7949(92)90540-G

E. F. Moore, The shortest path through a maze, Proceedings of the International Symposium on the Theory of Switching, pp.292-285, 1959.

P. Rossi, F. Ulm, and F. Hachi, Compressive Behavior of Concrete: Physical Mechanisms and Modeling, Journal of Engineering Mechanics, vol.122, issue.11, pp.1038-1043, 1996.
DOI : 10.1061/(ASCE)0733-9399(1996)122:11(1038)

H. A. Cornelissen, D. A. Hordijk, and H. W. Reinhardt, Experimental determination of crack-softening characteristics of normalweight and lightweight concrete, Heron, vol.31, pp.45-56, 1986.

R. A. Vonk, Softening of concrete loaded in compression, The Netherlands, 1992.

A. Rinaldi and Y. C. Lai, Statistical damage theory of 2D lattices: Energetics and physical foundations of damage parameter, International Journal of Plasticity, vol.23, issue.10-11, pp.1796-1825, 2007.
DOI : 10.1016/j.ijplas.2007.03.005

B. Richard and F. Ragueneau, Continuum damage mechanics based model for quasi brittle materials subjected to cyclic loadings: Formulation, numerical implementation and applications, Engineering Fracture Mechanics, vol.98, pp.383-406, 2013.
DOI : 10.1016/j.engfracmech.2012.11.013