. Vassaux, exposé dans cette thèse n'inclut pas les dernières avancées en terme de contact-frottant Une fois ces développements intégrés, il semble important d'étudier la possibilité d'étendre l'analyse globale, 2013.

R. and L. Cnrs, Cet axe va faire l'objet d'une étude dans le cadre de l'institut SEISM, dont le LMT est partenaire avec l Description à deux échelles des mécanismes locaux appliquée aux matériaux fragiles renforcés C

A. , L. , C. , R. Et, R. et al., Numerical modelling of large reinforced concrete specimencs based on experimental tests from benchmark concrack, VIII International Conference on Fracture Mechanics of Concrete and Concrete Structures, 2013.

A. , L. Richard, B. Ragueneau, F. Et, C. et al., Thermodynamical admissibility of a set of constitutive equations coupling elasticity, isotropic damage and internal sliding, C. R. Mécanique, vol.338, pp.158-163, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00508777

A. , Y. S. Grondin, F. Et, L. , and A. , Rapport de synthèse sur les expérimentations de mesure d'ouverture de fissure en flexion, pp.3-5, 2010.

A. , Y. S. Loukili, A. Grondin, and F. , Monitoring size effect on crack opening in concrete by digital image correlation, European Journal of Environmental and CivilEngineering, vol.16, issue.7, pp.818-836, 2012.

A. , A. Ince, R. Et, K. , and B. , Improved lattice model for concrete fracture, Journal of Engineering Mechanics, vol.128, issue.1, pp.57-65, 2002.

B. , T. Et, M. , and J. , The partition of unity method, Int. J. Numer. Meth. Eng, vol.40, pp.727-758, 1997.

K. Bagi, Stress and strain in granular assemblies, Mechanics of Materials, vol.22, issue.3, pp.165-177, 1996.
DOI : 10.1016/0167-6636(95)00044-5

B. , Z. Et, O. , and B. , Crack band theory for fracture of concrete, Materials and structures, vol.16, issue.93, pp.155-177, 1983.

B. , Z. Tabbara, M. Kazemi, M. Et-pijaudier-cabot, and G. , Random particle model for fracture of aggregate and fibre composites, Journal of Engineering Mechanics ASCE, issue.8, pp.1161686-1705, 1990.

B. , Z. Et, Y. , and Q. , Universal size effect law and effect of crack depth on quasi-brittle structure strength, J. Eng. Mech, vol.135, issue.2, pp.78-84, 1999.

T. Belytschko and T. Black, Elastic crack growth in finite elements with minimal remeshing, International Journal for Numerical Methods in Engineering, vol.55, issue.5, pp.601-620, 1999.
DOI : 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S

T. Belytschko, L. Et, and W. , Nonlinear finite elements for continua and structures, 2000.

T. Belytschko, Y. Lu, G. Et, and L. , Element-free Galerkin methods, International Journal for Numerical Methods in Engineering, vol.95, issue.2, pp.229-256, 1994.
DOI : 10.1002/nme.1620370205

T. Belytschko, X. Et, and S. , Coupling methods for continuuma model with molecular dynamics, International Journal for Multiscale Computational Engineering, vol.1, pp.115-126, 2003.

B. , G. Hild, H. Et, R. , and S. , Finite-element displacement fields analysis from digital images : application to portevin-le châtelier bands, Experimental Mechanics, vol.46, pp.789-804, 2006.

B. , J. E. Saito, and S. , Fracture analysis using spring networks with random geometry, Engineering Fracture Mechanics, vol.61, pp.569-591, 1998.

C. , V. Geoffroy, D. Riolo, V. Et, B. et al., An adaptive algorithm for cohesive zone model and arbitrary crack propagation, European Journal of Computational Mechanics, vol.21, pp.208-218, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00752797

C. , S. Et, S. , and S. , Measurement of deformations on concrete subjected to compression using image correlation, Experimental Mechnanics, vol.37, issue.3, pp.307-313, 1997.

C. Peyrot and I. , Development and validation of a 3d computational tool to describe damage and fracture due to alkali silica reaction in concrete, 2006.
URL : https://hal.archives-ouvertes.fr/pastel-00002096

C. , C. Mariani, S. Et, P. , and U. , An extended fe strategy for transition from continuum damage to mode i cohesive crack propagation, Int. J. Numer. Anal. Meth. Geomech, vol.31, pp.213-238, 2007.

C. , T. T. Leiserson, C. E. Et, L. , and R. R. , Introduction to algorithms, 1990.

C. , D. Accardi, M. Graham-brady, L. Et, S. et al., Digital image correlation analysis of interfacial debonding properties and fracture behavior in concrete, Engineering Fracture Mechanics, vol.74, pp.109-121, 2007.

C. , P. A. Et, S. , and O. D. , A discrete numerical model for granular assemblies, Geotechnique, vol.29, pp.47-60, 1979.

C. , G. Ba?ant, Z. Et, C. , and L. , Confinement-shear lattice model for concrete damage in tension and compression : I. theory, Journal of Engineering Mechanics, issue.12, pp.1291439-1448, 2003.

C. , G. Ba?ant, Z. Et, C. , and L. , Confinement-shear lattice csl model for fracture propagation in concrete, Comput. Methods Appl. Mech. Engrg, issue.52, pp.195-7154, 2006.

C. , G. Mencarelli, A. Pelessone, D. Et, B. et al., Lattice discrete particle model (ldpm) for failure behavior of concrete. i : Theory. Cement Concrete Comp, pp.881-890, 2011.

C. , G. Mencarelli, A. Pelessone, D. Et, B. et al., Lattice discrete particle model (ldpm) for failure behavior of concrete. ii : Calibration and validation, 2011.

D. , C. Et, B. Bi´canic, and N. , Failure criteria for quasi-brittle materials in lattice-type models, Commun. Numer. Meth. Engng, vol.19, pp.703-713, 2003.

B. De, R. Et, M. , and H. , Gradient-dependent plasticity : formulation and algorithmic aspects, Internation Journal For Numerical Methods In Engineering, vol.35, pp.521-539, 1992.

D. , A. Et, D. , and R. , Discrete 3d model as complimentary numerical testing for anisotropic damage, Int J Fract, vol.148, pp.115-128, 2007.

D. , F. , V. Richefeu, V. Et, M. et al., Advances in discrete element method applied to soil, rock and concrete mechanics. State of the art of geotechnical engineering, Electronic Journal of Geotechnical Engineering, p.44, 2009.

D. , F. Legrain, G. Pijaudier-cabot, G. Huerta, and A. , Estimation of crack opening from a two-dimensional continuum-based finite element computation, International Journal for Numerical and Analytical Methods in Geomechanics, issue.16, pp.36-1813, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00854615

D. , F. Pijaudier-cabot, G. Choinska, M. Huerta, and A. , Extraction of a crack opening form a continuous approach using regularized damage models, Computers and Concrete, vol.5, issue.4, pp.375-388, 2008.

D. , G. Ramm, E. Diebels, S. Et, E. et al., A particle center based homogeneization strategy for particle assemblies, Engng. Comp, vol.21, pp.360-383, 2004.

E. , D. Berryman, and J. , Contact force-displacement laws and the mechanical behavior of random packs of identical spheres, Mechanics of Materials, vol.24, pp.229-240, 1996.

F. , C. Lesoinne, M. Le-tallec, P. Pierson, K. Et et al., Fetidp : a dual-primal unified feti method. i. a faster alternative to the two-level feti method, Internat. J. Numer. Methods Engrg, pp.1523-1544, 2001.

F. , J. Van, D. , A. Feiner, S. Et et al., A parametric line-clipping algorithm, Computer Graphics, pp.3-12, 1996.

G. , L. Allix, O. Gosselet, P. Et, C. et al., Non-intrusive and exact global/local techniques for structural problems with local plasticity, Computational Mechanics, vol.44, issue.2, pp.233-245, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00437023

G. , D. Ransing, R. Lewis, R. Dutko, M. Et et al., Numerical comparison of a deformable discrete element model and an equivalent continuum analysis for the compaction of ductile porous material, Computers and Structures, vol.79, pp.1287-1294, 2001.

G. , C. Dufour, F. Et, M. , and J. , Stress based nonlocal damage model, International Journal of Solids and Structures, vol.48, pp.25-263431, 2011.

G. , C. Oliver-leblond, C. Dufour, F. Et, R. et al., Cracking analysis of reinforced concrete structures, European Journal of Environmental and Civil Engineering, 2013.

H. , K. Pijaudier-cabot, G. Dubé, J. F. Et, A. et al., Correlation between the internal length, the fracture process zone and size effect in model materials, Material and Structures, pp.201-210, 2005.

H. , S. Daudeville, L. Et, D. , and F. , Identification and validation of a discrete element model for concrete, J. Eng. Mech, vol.130, pp.709-719, 2004.

H. , H. Hansen, A. Et, R. , and S. , Fracture of disordered, elastic lattices in two dimensions, Physical Review B, vol.39, issue.1, pp.637-648, 1989.

H. , H. J. Et, R. , and S. , Statistical models for the fracture of disordered media, 1990.

H. , F. Et, R. , and S. , Correliq4 : A software for "finite-element" displacement field measurements by digital image correlation, 2008.

H. , F. Roux, S. Bernard, D. Hauss, G. Et et al., On the use of 3d images and 3d displacement measurements for the analysis of damage mechanics in concrete-like materials, Conference Proceeding, Plenary Lecture, p.8, 2013.

H. , A. Modeer, M. Et, P. , and P. , Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research, vol.6, pp.773-782, 1976.

H. , X. Et, W. , and F. , Fracture energy and fracture process zone, Mat. Struct, vol.25, pp.319-326, 1992.

I. , R. Arslan, A. Et, K. , and B. , Lattice modelling of size effect in concrete strength, Engineering Fracture Mechanics, vol.70, pp.2307-2320, 2003.

J. , M. Et, Z. , and T. , Analyse or rotating crack model, ACSE Engineering Mechanics, vol.124, issue.8, pp.842-851, 1998.

K. Oliver-leblond and L. M. , Description à deux échelles des mécanismes locaux appliquée aux matériaux fragiles renforcés C On the creep rupture time, Otd. Tekn. Nauk, vol.8, pp.26-31, 1958.

K. , E. Oliver-leblond, C. Giry, C. Et, R. et al., Milieux nonlocaux continus et réanalyse locale discrète pour l'étude de l'effet d'échelle du béton, 2013.

K. , N. Et, R. , and L. , Micromechanical definition of the strain tensor for granular materials, Journal of Applied Mechanics, vol.63, pp.706-711, 1996.

K. , M. Bagi, and K. , Contact rolling and deformation in granular media, International Journal of Solids and Structures, vol.41, pp.5793-5820, 2004.

L. Borderie and C. , Phénomènes unilatéraux dans un matériau endommageable : Modélisation et Application à l'analyse des structures en béton, Thèse de doctorat, 1991.

L. , P. Et, L. , and J. , Damage effective stress in quasi-unilateral material conditions, 1984.

L. , E. Et, K. , and D. , X-ray microtomography, Materials characterization, vol.61, pp.1305-1316, 2010.

L. , E. Nagy, E. Et, K. , and D. , Microstructure and fracture in three dimensions, Engineering Fracture Mechanics, vol.70, pp.911-925, 2003.

L. , E. Et, S. , and S. , Recovery of microcrack parameters in mortar using quantitative acoustic emission, Journal of Nondestructive Evaluation, vol.12, issue.4, pp.219-232, 1993.

L. Bellégo, C. Dubé, J. Pijaudier-cabot, G. Et, G. et al., Calibration of nonlocal damage model from size effect tests, European Journal of Mechanics A/Solids, vol.22, p.3346, 2003.

L. , J. Et, C. , and J. L. , A non-linear model of creep-fatigue damage cumulation and interaction(for hot metallic structures) Mechanics of visco-elastic media and bodies, 1975.

L. , G. Van, M. , and J. , 3d lattice type fracture model for concrete, Engineering Fracture Mechanics, vol.70, pp.927-941, 2003.

L. , H. Et, T. , and E. , Fracture energy determination of concrete with cube-shaped specimens, pp.38-40, 1986.

M. , A. Et, S. , and S. , Process zone and acoustic-emission measurements in concrete, Experimental Mechanics, vol.28, issue.1, pp.27-33, 1988.

M. , M. , L. Borderie, C. Et, M. et al., A practical method to estimate crack openings in concrete structures, International Journal for Numerical and Analytical Methods in Geomechanics, vol.34, pp.1615-1633, 2010.

M. , F. Hild, F. Et, R. , and S. , Identification of a crack propagation law by digital image correlation, International Journal of Fatigue, vol.36, pp.146-154, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00694317

M. , J. Et-pijaudier-cabot, and G. , From damage to fracture mechanics and conversely : a combined approach, Int. J. Solids Structures, vol.33, pp.3327-3342, 1996.

M. , K. Et, H. , and M. , Fracture analyses of concrete structures by the modified distinct element method, Structural Engineering/Earthquake Engineering, vol.6, issue.2, pp.283-294, 1989.

M. , H. Et, N. , and N. , Correlation between characteristics of fracture process zone and tension-softening properties of concrete, Nuclear Engrg. and Des, vol.165, pp.359-376, 1996.

M. , N. Stolz, C. Bernard, P. Et, C. et al., A level set based model for damage growth : The thick level set approach, Int. J. Numer. Meth. Engng, vol.86, pp.358-380, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00456098

M. Azevedo, N. Lemos, J. Et-rocha-de, A. , and J. , Influence of aggregate deformation and contact behaviour on discrete particle modelling of fracture of concrete, Engineering Fracture Mechanics, vol.75, issue.6, pp.1569-1586, 2008.
DOI : 10.1016/j.engfracmech.2007.06.008

M. , M. Et, R. , and B. , Meso-scale studies in fracture of concrete : A numerical simulation, Computers and Structures, vol.89, pp.912-920, 2011.

N. , K. Sato, Y. Et, U. , and T. , Mesoscopic simulation of failure of mortar and concrete by 3d rbsm, Journal of Advanced Concrete Technology, vol.3, issue.3, pp.385-402, 2005.

N. , D. Et, S. , and A. C. , Finite element analysis of reinforced concrete beams, J. Am. Concr. Inst, vol.64, pp.152-163, 1967.

O. , C. Delaplace, A. Et, R. , and F. , Application of a global/local analysis to study size effect in concrete, 2013.

O. , C. Richard, B. Delaplace, A. Et, R. et al., Cracking analysis of reinforced concrete beams using a finite-discrete element methods approach, 2013.

P. , R. De, B. , R. Brekelmans, W. De et al., Gradient enhanced damage for quasi-brittle materials, International Journal for Numérical Methods in Engineering, vol.39, pp.3391-3403, 1996.

P. , G. Et, B. , and Z. , Nonlocal damage theory, Journal of Engineering Mechanics, vol.1113, pp.1512-1533, 1987.

R. , T. Belytschko, and T. , Application of particle methods to static fracture of reinforced concrete structures, International Journal of Fracture, vol.137, pp.19-49, 2006.

R. , T. Et, E. , and J. , Simulation of high velocity concrete fragmentation using sph/mlsph, International Journal for Numerical Methods in Engineering, vol.56, issue.10, pp.1421-1444, 2003.

R. , T. Xiao, S. Sauer, and M. , Coupling of meshfree methods with finite elements : Basic concepts and test results, Commun. Numer. Meth. Engng, vol.0, pp.1-6, 2000.

R. , J. B. Mccleary, S. L. Aminpour, M. A. Et, K. et al., Computational methods for global/local analysis, 1992.

R. , B. Epaillard, S. Cremona, C. Elfgren, L. Et et al., Nonlinear finite element analysis of a 50 years old reinforced concrete trough bridge, Engineering Structures, issue.8, pp.323899-3910, 2010.

R. , B. Et, R. , and F. , 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.

R. , B. Ragueneau, F. Cremona, C. Et, A. et al., Isotropic continuum damage mechanics for concrete under cyclic loading : Stiffness recovery, inelastic strains and frictional sliding, Engineering Fracture Mechanics, issue.8, pp.771203-1223, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00509022

R. , B. Ragueneau, F. Cremona, C. Adelaide, L. Et et al., A three-dimensional steel/concrete interface model including corrosion effects, Engineering Fracture Mechanics, issue.6, pp.77951-973, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00508776

R. , A. Et, L. , and Y. C. , Statistical damage theory of 2d lattices : Energetics and physical foundations of damage parameter, Int. J. Plast, vol.23, pp.1796-1825, 2007.

R. , P. Et, R. , and S. , Numerical modelling of concrete cracking based on a stochastic approach, Materials and Structures, vol.20, pp.334-337, 1987.

R. , P. Et, U. , and F. , Size effects in the biaxial tensile-compressive behaviour of concrete : physical mechanisms and modelling, Materials and Structures, vol.30, pp.210-216, 1997.

R. , P. Ulm, F. Et, H. , and F. , Compressive behavior of concrete : physical mechanisms and modeling, Journal of Engineering Mechanics ASCE, vol.11, pp.1038-1043, 1996.

R. , P. Wu, X. Le-maou, F. Belloc, and A. , Scale effect of concrete in tension, Materials and Structures, vol.20, pp.437-444, 1997.

R. , J. G. Invernizzi, S. Et, B. , and B. , Saw-tooth softening/stiffening -a stable computational procedure for rc structures, Computers & Concrete, vol.3, pp.213-233, 2006.

R. , T. Peng, C. Burlion, N. Et, B. et al., Why is it necessary to use a damage model to simulate the mechanical behavior of concrete under drying and leaching, Europ. J. Envir. Civil Eng, vol.14, pp.6-7923, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00526394

S. , E. Et, G. , and E. J. , New method for simulating fracture using an elastically uniform randon geometry lattice, Int. J. Eng. Sci, vol.34, issue.10, pp.1131-1144, 1996.

S. , E. Et, G. , and E. J. , Fracture simulations of concrete using lattice models : computational aspects, Eng. Fracture Mech, vol.57, pp.319-332, 1997.

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

S. , S. , C. Kishen, and J. , Fracture properties of concrete?concrete interfaces using digital image correlation, Experimental Mechanics, vol.51, pp.303-313, 2011.

S. , S. Et, C. , and S. , Nondestructive techniques for studying fracture processes in concrete, International Journal of Fracture, vol.98, pp.351-359, 1998.

S. , W. Donzé, F. Et, D. , and L. , Discrete element modelling of missile impacts on a reinforced concrete target, International Journal of Computer Applications in Technology, vol.34, pp.33-41, 2009.

S. , L. Caballero, A. Et, M. , and J. , Influence of the meso-structure in dynamic fracture simulation of concrete under tensile loading, Cement and Concrete Research, issue.11, pp.411130-1142, 2011.

S. , M. Wolters, W. Peters, W. Ranson, W. Et et al., Determination of displacements using an improved digital correlation method, Im. Vis. Comp, vol.1, pp.133-139, 1983.

J. Van-mier, Internal crack detection in single edge notched concrete plates subjected to uniform boundary displacement, Micromechanics of Failure of Quasi- Brittle Materials, pp.33-42, 1990.

J. Van-mier, B. M. , C. Vervuurt, and A. , Numerical simulation of chaotic and self-organizing damage in brittle disordered materials, Computer Methods in Applied Mechanics and Engineering, vol.142, issue.1-2, pp.189-201, 1997.
DOI : 10.1016/S0045-7825(96)01128-0

J. G. Van-mier and M. R. Van-vliet, Influence of microstructure of concrete on size/scale effects in tensile fracture, Engineering Fracture Mechanics, vol.70, issue.16, pp.2281-2306, 2003.
DOI : 10.1016/S0013-7944(02)00222-9

J. G. Van-mier, M. R. Van-vliet, W. Et, and T. K. , 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

V. Vliet, M. R. Van-mier, and J. G. , Experimental investigation of size effect in concrete and sandstone under uniaxial tension, Engineering Fracture Mechanics, vol.65, issue.2-3, pp.165-188, 2000.
DOI : 10.1016/S0013-7944(99)00114-9

V. , M. Richard, B. Ragueneau, F. Et, A. et al., Modèle discret adapté à l'étude des phénomènes liés à la fissuration et à sa refermeture, 2013.

V. , M. Richard, B. Ragueneau, F. , A. et al., An implicit solving algorithm adapted to numericl identification for simple lattice discrete element models of quasi-brittle materials, 2013.

V. , C. V. Scott, M. A. Hughes, T. J. Et-de, B. et al., An isogeometric analysis approach to gradient damage models, Int. J. Numer. Meth. Engng, vol.86, pp.115-134, 2011.

V. , A. Van, M. , J. Et, S. et al., Analyses of anchor pull-out in concrete, Materials and Structures, vol.27, pp.251-259, 1994.

V. , S. R. Chandra, N. Et, M. , and J. R. , Global-local analysis of largescale composite structures using finite element methods, Comp Struct, vol.58, issue.3, pp.453-464, 1995.

W. , Z. Rong, H. Zheng, J. Xu, F. Et et al., An experimental investigation on the fpz properties in concrete using digital image correlation technique, Engineering Fracture Mechanics, vol.78, pp.2978-2990, 2011.

X. , S. P. Belytschko, and T. , A bridging domain decomposition for coupling continua with molecular dynamics, Comput. Methods Appl. Mech. Engrg, vol.193, pp.1645-1669, 2004.

Z. , A. Et, B. , and Z. , Interface element modeling of fracture in aggregate composites, Journal of Engineering Mechanics, vol.113, issue.11, pp.1619-1630, 1987.