N. S. Ottosen, Constitutive model for short-time loading of concrete, Journal of the Engineering Mechanics Division-ASCE, vol.105, issue.1, pp.127-141, 1979.

L. J. Sluys, Wave propagation, localisation and dispersion in softening solids, 1992.

J. Dubé, G. Pijaudier-cabot, and L. Borderie, Rate Dependent Damage Model for Concrete in Dynamics, Journal of Engineering Mechanics, vol.122, issue.10, pp.939-947, 1996.
DOI : 10.1061/(ASCE)0733-9399(1996)122:10(939)

J. Sercombe, F. Ulm, and . Toutlemonde, Viscous Hardening Plasticity for Concrete in High-Rate Dynamics, Journal of Engineering Mechanics, vol.124, issue.9, pp.1050-1057, 1998.
DOI : 10.1061/(ASCE)0733-9399(1998)124:9(1050)

Z. Bazant, . Fc-caner, S. Adley, and . Akers, Fracturing Rate Effect and Creep in Microplane Model for Dynamics, Journal of Engineering Mechanics, vol.126, issue.9, pp.962-970, 2000.
DOI : 10.1061/(ASCE)0733-9399(2000)126:9(962)

F. Gatuingt and G. Pijaudier-cabot, Coupled damage and plasticity modelling in transient dynamic analysis of concrete, International Journal for Numerical and Analytical Methods in Geomechanics, vol.37, issue.1, pp.1-24, 2002.
DOI : 10.1016/0029-5493(76)90015-7
URL : https://hal.archives-ouvertes.fr/hal-00994422

G. Hervé, A. Gatuingt, and . Ibrahimbegovic, On numerical implementation of a coupled rate dependent damage???plasticity constitutive model for concrete in application to high???rate dynamics, Engineering Computations, vol.22, issue.5/6, pp.5-6583, 2005.
DOI : 10.1016/S0045-7825(99)00223-6

R. R. Pedersen, A. Simone, and L. J. Sluys, An analysis of dynamic fracture in concrete with a continuum visco-elastic visco-plastic damage model, Engineering Fracture Mechanics, vol.75, issue.13, pp.3782-805, 2008.
DOI : 10.1016/j.engfracmech.2008.02.004

F. Gatuingt, R. Desmorat, M. Chambart, D. Combescure, and D. Guilbaud, Anisotropic 3d delay-damage model to stimulate concrete structures, pp.740-60, 2008.

C. Pontiroli, A. Rouquand, and J. Mazars, Predicting concrete behaviour from quasi-static loading to hypervelocity impact An overview of the PRM model, European Journal of Environmental and Civil Engineering, vol.14, pp.6-7703, 2010.

J. Weerheijm, I. Vegt, and K. Van-breugel, The rate dependency of concrete in tension ??? New data for wet, normal and dry conditions, DYMAT 2009, 9th International Conferences on the Mechanical and Physical Behaviour of Materials under Dynamic Loading, pp.95-101, 2009.
DOI : 10.1051/dymat/2009013

B. Erzar and P. Forquin, An Experimental Method to Determine the Tensile Strength of Concrete at High Rates of Strain, Experimental Mechanics, vol.24, issue.4, pp.941-955, 2010.
DOI : 10.1007/s11340-009-9284-z

S. Levy, J. F. Molinari, I. Vicari, and A. C. Davison, Dynamic fragmentation of a ring: Predictable fragment mass distributions, Physical Review E, vol.25, issue.6, p.2010
DOI : 10.1103/PhysRevLett.76.2492

L. Snozzi, A. Caballero, and J. Molinari, Influence of the meso-structure in dynamic fracture simulation of concrete under tensile loading, Cement and Concrete Research, vol.41, issue.11, pp.1130-1142, 2011.
DOI : 10.1016/j.cemconres.2011.06.016

P. Roelfstra, H. Sadouki, and F. Wittmann, Le b??ton num??rique, Materials and Structures, vol.17, issue.5, pp.309-317, 1985.
DOI : 10.1007/BF02479083

T. Stankowski, Numerical simulation of progressive failure in particle composites, 1990.

C. Lopez, Microstructural analysis of concrete fracture using interface elements. Application to various concretes, 1999.

A. Caballero, 3D meso-mechanical numerical analysis of concrete using interface elements, 2005.

T. D. N-'guyen, C. Lawrence, C. L. Borderie, and G. Nahas, A mesoscopic approach for a better understanding of the transition from diffuse damage to localized damage, European Journal of Environmental and Civil Engineering, vol.14, pp.751-776, 2010.

L. A. Langer, W. C. Carter, and E. R. Fuller, The ppm2oof manual, 2009.

A. Hillerborg, E. Modéer, and P. E. Petersson, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research, vol.6, issue.6, pp.773-781, 1976.
DOI : 10.1016/0008-8846(76)90007-7

G. T. Camacho and M. Ortiz, Computational modelling of impact damage in brittle materials, International Journal of Solids and Structures, vol.33, issue.20-22, pp.20-222899, 1996.
DOI : 10.1016/0020-7683(95)00255-3

I. Carol, C. M. Lopez, and O. Roa, Micromechanical analysis of quasi???brittle materials using fracture???based interface elements, International Journal for Numerical Methods in Engineering, vol.1, issue.12, pp.193-215, 2001.
DOI : 10.1108/eb023559

D. Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, issue.2, pp.100-108, 1960.
DOI : 10.1016/0022-5096(60)90013-2

G. I. Barenblatt, The mathematical theory of equilibrium of cracks in brittle fracture Advances in Applied Mechanics, pp.55-129, 1962.

O. Miller, L. B. Freund, and A. Needleman, Modeling and simulation of dynamic fragmentation in brittle materials, International Journal of Fracture, vol.96, issue.2, pp.101-125, 1999.
DOI : 10.1023/A:1018666317448

I. Vegt, R. R. Pedersen, L. J. Sluys, and J. Weerheijm, Modelling of impact behaviour of concrete -an experimental approach, Computational Modelling of Concrete Structures -EURO-C 2006, pp.451-458, 2006.

R. Pedersen, . Simone, L. J. Stroeven, and . Sluys, Mesoscopic modelling of concrete under impact, 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures -FRAMCOS VI, pp.571-578, 2007.

F. Gatuingt, L. Snozzi, and J. F. Molinari, Numerical determination of the tensile response and the dissipated fracture energy of concrete: role of the meso-structure and influence of the loading rate, International Journal for Numerical and Analytical Methods in Geomechanics
URL : https://hal.archives-ouvertes.fr/hal-00994253

P. Rossi, J. G. Van-mier, C. Boulay, and F. L. Maou, The dynamic behaviour of concrete: influence of free water, Materials and Structures, vol.19, issue.9, pp.509-514, 1992.
DOI : 10.1007/BF02472446