.. Idée-de-la-démonstration, 73 3.5.3 Addition d'un chargement à l'infini, p.76

V. Taille-de and .. De-kanit, 109 4.5.1 Description des deux erreurs commises sur l'estimation des propriétés élastiques, p.109

.. Écriture-abstraite-de-l-'énergie-avec-les-tenseurs-de-localisation, 158 6.2.4 Calcul des termes de la fonction énergie élastique, p.161

C. F. Dunant and K. L. Scrivener, Micro-mechanical modelling of alkali???silica-reaction-induced degradation using the AMIE framework, Cement and Concrete Research, vol.40, issue.4, pp.517-525, 2010.
DOI : 10.1016/j.cemconres.2009.07.024

J. D. Eshelby, The Elastic Field Outside an Ellipsoidal Inclusion, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.252, issue.1271, pp.561-569, 1959.
DOI : 10.1098/rspa.1959.0173

B. Fedelich and A. Ehrlacher, Sur un principe de minimum concernant des matériaux à comportement indépendant du temps physique, Comptes Rendus de l'Académie des Sciences II, pp.1311-1394, 1993.

G. A. Francfort and J. Marigo, Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, vol.46, issue.8, pp.1319-1342, 1998.
DOI : 10.1016/S0022-5096(98)00034-9

A. A. Griffith, The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.221, issue.582-593, pp.163-198, 1921.
DOI : 10.1098/rsta.1921.0006

M. Hori and S. Nemat-nasser, Double-inclusion model and overall moduli of multi-phase composites, Mechanics of Materials, vol.14, issue.3, pp.189-206, 1992.
DOI : 10.1016/0167-6636(93)90066-Z

T. Kanit, S. Forest, I. Galliet, V. Mounoury, and D. Jeulin, Determination of the size of the representative volume element for random composites: statistical and numerical approach, International Journal of Solids and Structures, vol.40, issue.13-14, pp.3647-3679, 2003.
DOI : 10.1016/S0020-7683(03)00143-4

D. Leguillon, D. Quesada, C. Putot, and E. Martin, Prediction of crack initiation at blunt notches and cavities ??? size effects, Engineering Fracture Mechanics, vol.74, issue.15, pp.2420-2436, 2007.
DOI : 10.1016/j.engfracmech.2006.11.008

D. Leguillon, Strength or toughness? A criterion for crack onset at a notch, European Journal of Mechanics - A/Solids, vol.21, issue.1, pp.61-72, 2002.
DOI : 10.1016/S0997-7538(01)01184-6

V. M. Levin, Thermal expansion coefficients of heterogeneous materials, Mechanics of Solids, vol.2, issue.1, pp.58-61, 1967.

J. Marigo, Initiation of Cracks in Griffith???s Theory: An Argument of Continuity in Favor of Global Minimization, Journal of Nonlinear Science, vol.35, issue.2, pp.831-868, 2010.
DOI : 10.1007/s00332-010-9074-x

T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, vol.21, issue.5, pp.571-574, 1973.
DOI : 10.1016/0001-6160(73)90064-3

S. Multon, A. Sellier, and M. Cyr, Chemo-mechanical modeling for prediction of alkali silica reaction (ASR) expansion. Cement and Concrete Research, pp.490-500, 2009.

T. Mura, Micromechanics of defects in solids, p.74, 1991.

S. Nemat-nasser and M. Hori, Micromechanics: Overall Properties of Heterogeneous Materials, Journal of Applied Mechanics, vol.63, issue.2, pp.67-112, 1993.
DOI : 10.1115/1.2788912

P. , P. Castañeda, and J. R. Willis, The effect of spatial distribution on the effective behavior of composite materials and cracked media, J. Mech. Phys. Solids, vol.118, pp.43-121919, 1995.

H. W. Reinhardt and O. Mielich, A fracture mechanics approach to the crack formation in alkali-sensitive grains, Cement and Concrete Research, vol.41, issue.3, pp.255-262, 2011.
DOI : 10.1016/j.cemconres.2010.11.008

J. Gregory, Y. Rodin, and . Hwang, On the problem of linear elasticity for an infinite region containing a finite number of non-intersecting spherical inhomogeneities, International Journal of Solids and Structures, pp.27-2145, 1991.

Z. Shige and W. Tzuchiang, Effective elastic moduli of inhomogeneous solids by embedded cell model Jun-Ho Shin. Modeling alkali-silica reaction using image analysis and finite-element method, The Chinese society of theoretical and applied mechanics, pp.40-152, 2009.

L. Struble and S. Diamond, Unstable swelling behaviour of alkali silica gels, Cement and Concrete Research, vol.11, issue.4, pp.611-617, 1981.
DOI : 10.1016/0008-8846(81)90091-0

K. Tanaka and T. Mori, Note on volume integrals of the elastic field around an ellipsoidal inclusion, Journal of Elasticity, vol.23, issue.3, pp.199-200, 1972.
DOI : 10.1007/BF00125528

L. J. Walpole, Elastic Behavior of Composite Materials: Theoretical Foundations, Advances in Applied Mechanics, pp.169-242, 1981.
DOI : 10.1016/S0065-2156(08)70332-6

G. J. Weng, The theoretical connection between Mori-Tanaka's theory and the Hashin-Shtrikman-Walpole bounds, International Journal of Engineering Science, vol.28, issue.11, pp.1111-1120, 1990.
DOI : 10.1016/0020-7225(90)90111-U

F. H. Wittmann, Crack formation and fracture energy of normal and high strength concrete. S¯ adhan¯ a, pp.27-4413, 2002.

Q. Zheng and D. Du, An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution, Journal of the Mechanics and Physics of Solids, vol.49, issue.11, pp.2765-2788, 2001.
DOI : 10.1016/S0022-5096(01)00078-3

R. Application-À-notre-problème-de, 210 9.2.1 Présentation du problème de départ, p.211

.. Écriture-des-propriétés-homogénéisées, 212 9.2.4 Réécriture des propriétés homogénéisées en utilisant les fractions volumiques, p.215

.. Rappel-des-expressions-de-l-'énergie-potentielle, 230 10.2.1 Rappel sur la morphologie considérée, p.230

.. Étude-de-l-'essai-de-multon, Répartition des tailles de grains, p.272

M. G. Alexander, The effects of ageing on the interfacial transition zone in concrete

. Maso, Interfacial transition zone in concrete, E & FN SPON, pp.150-174, 1996.

S. Caré and E. Hervé, Application of a n-Phase Model to the Diffusion Coefficient of Chloride in Mortar, Transport in Porous Media, pp.119-135, 2004.
DOI : 10.1023/B:TIPM.0000021730.34756.40

L. Charpin and A. Ehrlacher, A computational linear elastic fracture mechanics-based model for alkali???silica reaction, Cement and Concrete Research, vol.42, issue.4, pp.613-625, 0193.
DOI : 10.1016/j.cemconres.2012.01.004

URL : https://hal.archives-ouvertes.fr/hal-00843899

R. M. Christensen and K. H. Lo, Solutions for effective shear properties in three phase sphere and cylinder models, Journal of the Mechanics and Physics of Solids, vol.27, issue.4, pp.315-330, 1979.
DOI : 10.1016/0022-5096(79)90032-2

C. Comi, R. Fedele, and U. Perego, A chemo-thermo-damage model for the analysis of concrete dams affected by alkali-silica reaction, Mechanics of Materials, vol.41, issue.3, pp.210-230, 2009.
DOI : 10.1016/j.mechmat.2008.10.010

D. Du and Q. Zheng, A further exploration of the interaction direct derivative (IDD) estimate for the effective properties of multiphase composites taking into account inclusion distribution, Acta Mechanica, vol.452, issue.149, pp.61-80, 2002.
DOI : 10.1007/BF01182155

J. Farran, Contribution minéralogique à l'étude de l'adhérence entre les consituants hydratés des ciments et les matériaux enronés, Revue des Matériaux de Construction, pp.490-491, 1956.

Y. Furusawa, H. Ohga, and T. Uomoto, An analytical study concerning prediction of concrete expansion due to alkali-silica reaction. Durability of concrete, Proceedings of the third international conference, pp.757-780, 1994.

A. B. Giorla, K. L. Scrivener, and C. F. Dunant, Finite elements in space and time for the analysis of generalized visco-elastic materials, International Journal for Numerical Methods in Engineering

É. Grimal, A. Sellier, Y. L. Pape, and É. Bourdarot, Creep, shrinkage, and anisotropic damage in alkali-aggregate reaction swelling mechanism -Part I : Constitutive model, ACI Materials Journal, pp.105-3227, 2008.

É. Grimal, A. Sellier, Y. L. Pape, and É. Bourdarot, Creep, shrinkage, and anisotropic damage in alkali-aggregate reaction swelling mechanism -Part II : Indentification of model parameters and application, ACI Materials Journal, pp.105-3236, 2008.

Z. Hashin and P. J. Monteiro, An inverse method to determine the elastic properties of the interphase between the aggregate and the cement paste, Cement and Concrete Research, vol.32, issue.8, pp.1291-1300, 2002.
DOI : 10.1016/S0008-8846(02)00792-5

E. Hervé, S. Caré, and J. P. Seguin, Influence of the porosity gradient in cement paste matrix on the mechanical behavior of mortar, Cement and Concrete Research, vol.40, issue.7, pp.1060-1071, 2010.
DOI : 10.1016/j.cemconres.2010.02.010

A. Edward and H. Love, A Treatise on the Mathematical Theory of Elasticity, Fourth Edition, p.216, 1927.

S. Multon, M. Cyr, A. Sellier, P. Diederich, and L. Petit, Effects of aggregate size and alkali content on ASR expansion, Cement and Concrete Research, vol.40, issue.4, pp.508-516, 2010.
DOI : 10.1016/j.cemconres.2009.08.002

URL : https://hal.archives-ouvertes.fr/hal-01006003

S. Multon, A. Sellier, and M. Cyr, Chemo-mechanical modeling for prediction of alkali silica reaction (ASR) expansion. Cement and Concrete Research, pp.490-500, 2009.

S. Multon, Évaluation expérimentale et théorique des effets mécaniques de l'alcaliréaction sur des structures modèles. Laboratoire Central des Ponts et Chaussés, pp.273-274, 2004.

S. Multon and F. Toutlemonde, Effect of applied stresses on alkali???silica reaction-induced expansions, Cement and Concrete Research, vol.36, issue.5, pp.912-920, 2006.
DOI : 10.1016/j.cemconres.2005.11.012

J. C. Nadeau, Water???cement ratio gradients in mortars and corresponding effective elastic properties, Cement and Concrete Research, vol.32, issue.3, pp.481-490, 2002.
DOI : 10.1016/S0008-8846(01)00710-4

A. Nielsen, F. Gottfredsen, and F. Thøgersen, Development of stresses in concrete structures with alkali-silica reactions, Materials and Structures, vol.65, issue.32, pp.152-158, 1993.
DOI : 10.1007/BF02472932

P. , P. Castañeda, and J. R. Willis, The effect of spatial distribution on the effective behavior of composite materials and cracked media, J. Mech. Phys. Solids, vol.118, pp.43-121919, 1995.

E. D. Ramesh, G. Sotelino, and W. F. Chen, Effect of transition zone on elastic moduli of concrete materials, Cement and Concrete Research, vol.26, issue.4, pp.611-622, 1996.
DOI : 10.1016/0008-8846(96)00016-6

A. Sellier, Modélisations probabilistes du comportement de matériaux et de structures en génie civil, pp.36-43, 1995.

J. Shin, Modeling alkali-silica reaction using image analysis and finite-element method, pp.40-152, 2009.

L. Struble and S. Diamond, Unstable swelling behaviour of alkali silica gels, Cement and Concrete Research, vol.11, issue.4, pp.611-617, 1981.
DOI : 10.1016/0008-8846(81)90091-0

F. H. Wittmann, Crack formation and fracture energy of normal and high strength concrete. S¯ adhan¯ a, pp.27-4413, 2002.

Q. Zheng and D. Du, An explicit and universally applicable estimate for the effective properties of multiphase composites which accounts for inclusion distribution, Journal of the Mechanics and Physics of Solids, vol.49, issue.11, pp.2765-2788, 2001.
DOI : 10.1016/S0022-5096(01)00078-3

C. Générale and . Perspectives, énergie totale, ce qui devrait atténuer la tendance de notre modèle à trop orienter la fissuration en fonction du chargement. Les connaissances accumulées peuvent enfin être appliquées au problème de l'alcali-réaction dans les bétons contenant des granulats à réactivité lente. Certains des défauts de notre modèle ne se manifesteraient probablement pas, puisque dans ces bétons l'essentiel de l'endommagement est localisé dans les granulats qui contiennent des poches de gel gonflant