K. Gylltoft, A fracture mechanics model for fatigue in concrete, Mat??riaux et Constructions, vol.64, issue.No. 3, pp.55-58, 1984.
DOI : 10.1007/BF02474057

H. W. Reinhardt, H. A. Cornelissen, and D. A. Hordijk, Tensile Tests and Failure Analysis of Concrete, Journal of Structural Engineering, vol.112, issue.11, pp.2462-2477, 1986.
DOI : 10.1061/(ASCE)0733-9445(1986)112:11(2462)

D. Z. Yankelevsky and H. W. Reinhardt, Uniaxial Behavior of Concrete in Cyclic Tension, Journal of Structural Engineering, vol.115, issue.1, pp.166-182, 1989.
DOI : 10.1061/(ASCE)0733-9445(1989)115:1(166)

D. A. Hordijk, Local approach to fatigue of concrete, 1991.

H. W. Reinhardt and H. A. Cornelissen, Post-peak cyclic behaviour of concrete in uniaxial tensile and alternating tensile and compressive loading, Cement and Concrete Research, vol.14, issue.2, pp.263-270, 1984.
DOI : 10.1016/0008-8846(84)90113-3

R. A. Guyer, K. R. Mccall, and G. N. Boitnott, Hysteresis, Discrete Memory, and Nonlinear Wave Propagation in Rock: A New Paradigm, Physical Review Letters, vol.74, issue.17, p.3491, 1995.
DOI : 10.1103/PhysRevLett.74.3491
URL : https://hal.archives-ouvertes.fr/hal-00301808

V. Pensée, D. Kondo, and L. Dormieux, Micromechanical Analysis of Anisotropic Damage in Brittle Materials, Journal of Engineering Mechanics, vol.128, issue.8, pp.889-897, 2002.
DOI : 10.1061/(ASCE)0733-9399(2002)128:8(889)

S. Mertens, J. Vantomme, and J. Carmeliet, Modelling of the influence of the damage on the behavior of concrete during tensile-compressive loading, Fracture mechanics of concrete structures

S. Mertens and K. U. , Hysteresis, damage and moisture effects in quasi-brittle porous materials, 2009.

P. Ladevèze, On an anisotropic damage theory 351 Villars-de-Lans, Failure criteria of structured media, Proc. CNRS Int. Coll, pp.355-363, 1983.

J. C. Simo and J. Ju, Strain- and stress-based continuum damage models???I. Formulation, International Journal of Solids and Structures, vol.23, issue.7, pp.821-840, 1987.
DOI : 10.1016/0020-7683(87)90083-7

G. Meschke, R. Lackner, and H. A. Mang, An anisotropic elastoplastic-damage model for plain concrete, International Journal for Numerical Methods in Engineering, vol.92, issue.4, pp.703-727, 1998.
DOI : 10.1002/(SICI)1097-0207(19980630)42:4<703::AID-NME384>3.0.CO;2-B

F. Ragueneau, C. La-borderie, and J. Mazars, Damage model for concrete-like materials coupling cracking and friction, contribution towards structural damping: first uniaxial applications, Mechanics of Cohesive-frictional Materials, vol.3, issue.8, pp.607-625, 2000.
DOI : 10.1002/1099-1484(200011)5:8<607::AID-CFM108>3.0.CO;2-K

M. Matallah and C. L. Borderie, Inelasticity???damage-based model for numerical modeling of concrete cracking, Engineering Fracture Mechanics, vol.76, issue.8, pp.1087-1108, 2009.
DOI : 10.1016/j.engfracmech.2009.01.020

A. Sellier, G. Casaux-ginestet, L. Buffolacarrì-ere, and X. Bourbon, Orthotropic damage coupled with localized crack reclosure processing. Part I: Constitutive laws, Engineering Fracture Mechanics, vol.97, pp.148-167, 2013.
DOI : 10.1016/j.engfracmech.2012.10.012

L. Buffo-lacarriere, C. Rospars, A. Delaplace, A. Duong, and L. Jason, International benchmark concrack: Synthesis of the results, Proceeding of ConCrack 2 Workshop, ACI, 2011.

O. Nouailletas, C. L. Borderie, C. Perlot, P. Rivard, and G. Ballivy, Experimental Study of Crack Closure on Heterogeneous Quasi-Brittle Material, Journal of Engineering Mechanics, vol.141, issue.11, p.4015041, 2015.
DOI : 10.1061/(ASCE)EM.1943-7889.0000928

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

I. Mihai and A. Jefferson, Smoothed contact in a micromechanical model for cement bound materials, Computers & Structures, vol.118, pp.115-125, 2013.
DOI : 10.1016/j.compstruc.2012.11.002

A. Jefferson and I. Mihai, The simulation of crack opening-closing and aggregate interlock behaviour in finite element concrete models, International Journal for Numerical Methods in Engineering, vol.28, issue.7
DOI : 10.1002/nme.4934

M. Vassaux, B. Richard, F. Ragueneau, A. Millard, and A. Delaplace, Lattice models applied to cyclic behavior description of quasi-brittle materials: advantages of implicit integration, International Journal for Numerical and Analytical Methods in Geomechanics, vol.98, issue.7, pp.775-798, 2015.
DOI : 10.1002/nag.2343
URL : https://hal.archives-ouvertes.fr/hal-01177051

A. Hillerborg, M. Modeer, 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.773-782, 1976.
DOI : 10.1016/0008-8846(76)90007-7

G. Pijaudier-cabot and Z. P. Ba?ant, Nonlocal Damage Theory, Journal of Engineering Mechanics, vol.113, issue.10, pp.1512-1533, 1987.
DOI : 10.1061/(ASCE)0733-9399(1987)113:10(1512)

R. De-borst and H. Mühlhaus, Gradient-dependent plasticity: Formulation and algorithmic aspects, International Journal for Numerical Methods in Engineering, vol.137, issue.3, pp.521-539, 1992.
DOI : 10.1002/nme.1620350307

C. Giry, F. Dufour, and J. Mazars, Stress-based nonlocal damage model, International Journal of Solids and Structures, vol.48, issue.25-26, pp.25-26, 2011.
DOI : 10.1016/j.ijsolstr.2011.08.012
URL : http://doi.org/10.1016/j.ijsolstr.2011.08.012

C. Rospars and D. , CEOS.fr experimental programme and reference specimen tests results, European Journal of Environmental and Civil Engineering, vol.18, issue.7, pp.738-753, 2014.
DOI : 10.1080/19648189.2014.912163
URL : https://hal.archives-ouvertes.fr/hal-01314247

A. Hrennikoff, Solution of problems of elasticity by the framework method, Journal of applied mechanics, vol.8, issue.4, pp.169-175, 1941.

H. J. Herrmann, A. Hansen, and S. Roux, Fracture of disordered, elastic lattices in two dimensions, Physical Review B, vol.39, issue.1, pp.637-648, 1989.
DOI : 10.1103/PhysRevB.39.637

Z. P. Ba?ant, M. Tabbara, M. Kazemi, and G. Pijaudier-cabot, Random Particle Model for Fracture of Aggregate or Fiber Composites, Journal of Engineering Mechanics, vol.116, issue.8, pp.1686-1705, 1990.
DOI : 10.1061/(ASCE)0733-9399(1990)116:8(1686)

E. Schlangen and J. G. Van-mier, Experimental and numerical analysis of micromechanisms of fracture of cement-based composites, Cement and Concrete Composites, pp.105-118, 1992.

J. G. Van-mier, Fracture processes of concrete, 1996.

P. A. Cundall and O. D. Strack, A discrete numerical model for granular assemblies, G??otechnique, vol.29, issue.1, pp.47-60, 1979.
DOI : 10.1680/geot.1979.29.1.47

K. Meguro and M. Hakuno, Fracture analyses of concrete structures by the modified distinct element method., Doboku Gakkai Ronbunshu, vol.6, issue.410, pp.283-294, 1989.
DOI : 10.2208/jscej.1989.410_113

M. Vassaux, F. Ragueneau, B. Richard, and A. Millard, Compressive behavior of a lattice discrete element model for quasi-brittle materials, Computational Modelling of Concrete Structures, vol.1, pp.335-344, 2014.
DOI : 10.1201/b16645-38

M. Vassaux, C. Oliver-leblond, B. Richard, and F. Ragueneau, Beam-particle approach to model cracking and energy dissipation in concrete: Identification strategy and validation, Cement and Concrete Compositions

B. Karihaloo, P. Shao, and Q. Xiao, Lattice modelling of the failure of particle composites, Engineering Fracture Mechanics, vol.70, issue.17, pp.2385-2406, 2003.
DOI : 10.1016/S0013-7944(03)00004-3

D. Grégoire, L. B. Rojas-solano, and G. , Failure and size effect for notched and unnotched concrete beams, International Journal for Numerical and Analytical Methods in Geomechanics, vol.49, issue.52, pp.1434-1452, 2013.
DOI : 10.1002/nag.2180

M. Briffaut, F. Benboudjema, C. La-borderie, and J. Torrenti, Creep Consideration Effect on Meso-Scale Modeling of Concrete Hydration Process and Consequences on the Mechanical Behavior, Journal of Engineering Mechanics, vol.139, issue.12, pp.1808-1817, 2013.
DOI : 10.1061/(ASCE)EM.1943-7889.0000607
URL : https://hal.archives-ouvertes.fr/hal-00944344

J. Mazars, Application de la mécanique de l'endommagement au comportement non linéaire etàetà la rupture du béton de structure, 1984.

P. H. Feenstra and R. D. Borst, A composite plasticity model for concrete, International Journal of Solids and Structures, vol.33, issue.5, pp.707-730, 1996.
DOI : 10.1016/0020-7683(95)00060-N

M. Matallah, C. L. Borderie, and O. , A practical method to estimate crack openings in concrete structures, International Journal for Numerical and Analytical Methods in Geomechanics, vol.38, issue.276, pp.1615-1633, 2010.
DOI : 10.1002/nag.876

A. Signorini, Questioni di elasticità non linearizzata e semilinearizzata, Rend. Mat. Appl., V. Ser, vol.18, pp.95-139, 1959.

P. Rivillon and A. Gabs, Projet national de recherche ceos.fr, axe 2 ? expérimentations, rapport n°eem 09 26023877-c, Tech. rep, CSTB, 2011.

F. C. Filippou and A. Issa, Nonlinear analysis of reinforced concrete frames under cyclic load reversals, 1988.

B. Richard, F. Ragueneau, C. Cremona, L. Adelaide, and J. Tailhan, A three-dimensional steel/concrete interface model including corrosion effects, Engineering Fracture Mechanics, vol.77, issue.6, pp.951-973, 2010.
DOI : 10.1016/j.engfracmech.2010.01.017
URL : https://hal.archives-ouvertes.fr/hal-00508776

A. Casanova, L. Jason, and L. Davenne, Bond slip model for the simulation of reinforced concrete structures, Engineering Structures, vol.39, pp.66-78, 2012.
DOI : 10.1016/j.engstruct.2012.02.007
URL : https://hal.archives-ouvertes.fr/hal-01411079