. Dans-ce-mémoire, nous nous sommes attachésattachés`attachésà développer des méthodes aboutissantà aboutissant`aboutissantà la détermination de comportements macroscopiques en tenant compte de non linéarités linéarités`linéaritésà l'´ echelle microscopique et

]. S. Bibliographie1, Y. Andrieux, J. Bamberger, and . Marigo, Un modèle de matériau microfissuré pour les roches et les bétons, J. Méca. Théor. Appl, vol.5, issue.3, pp.471-513, 1986.

J. Auriault and E. Sanchez-palencia, ´ Etude du comportement macroscopique d'un milieu poreux saturé déformable, J. Méc, vol.16, issue.4, pp.575-603, 1977.

C. Barret and S. Baste, Induced damage by ellipsoidal cracks in an anisotropic medium, International Journal of Solids and Structures, vol.36, issue.24, pp.3709-3729, 1999.
DOI : 10.1016/S0020-7683(98)00162-0

J. Barthélémy and L. Dormieux, Micromechanical approach to the modelling of compaction at large strains, 2nd Biot Conference on Poromechanics, 2002.
DOI : 10.1016/S0266-352X(03)00006-5

J. Barthélémy and L. Dormieux, D??termination du comportement macroscopique d'un milieu ?? fissures frottantes, XVIème Congrès Français de Mécanique, 2003.
DOI : 10.1016/S1631-0721(02)00010-4

J. Barthélémy and L. Dormieux, D??termination du crit??re de rupture macroscopique d'un milieu poreux par homog??n??isation non lin??aire, Comptes Rendus M??canique, vol.331, issue.4, pp.271-276, 2003.
DOI : 10.1016/S1631-0721(03)00063-9

J. Barthélémy and L. Dormieux, A micromechanical approach to the strength criterion of Drucker-Prager materials reinforced by rigid inclusions, International Journal for Numerical and Analytical Methods in Geomechanics, vol.28, issue.78, pp.565-582, 2004.
DOI : 10.1002/nag.368

J. Barthélémy, L. Dormieux, and D. Kondo, D??termination du comportement macroscopique d'un milieu ?? fissures frottantes, Comptes Rendus M??canique, vol.331, issue.1, pp.77-84, 2003.
DOI : 10.1016/S1631-0721(02)00010-4

J. Barthélémy, L. Dormieux, and E. Lemarchand, A micromechanical approach to the strength criterion of composite materials, Computational Modelling of Concrete Structures, 2003.

J. Barthélémy, L. Dormieux, and S. Maghous, Micromechanical approach to the modelling of compaction at large strains, Computers and Geotechnics, vol.30, issue.4, pp.321-338, 2003.
DOI : 10.1016/S0266-352X(03)00006-5

O. Bernard, F. J. Ulm, and E. Lemarchand, A multiscale micromechanics-hydration model for the early-age elastic properties of cement-based materials, Cement and Concrete Research, vol.33, issue.9, pp.1293-1309, 2003.
DOI : 10.1016/S0008-8846(03)00039-5

URL : https://hal.archives-ouvertes.fr/hal-00139284

N. Bilger, M. Bornert, F. Auslender, A. Zaoui, and R. Masson, Surface d'´ ecoulement macroscopique des milieux poreux : modification du critère de Gurson par une approche micromécanique, XVème Congrès Français de Mécanique, 2001.

M. A. Biot, General Theory of Three???Dimensional Consolidation, Journal of Applied Physics, vol.12, issue.2, pp.155-164, 1941.
DOI : 10.1063/1.1712886

URL : https://hal.archives-ouvertes.fr/hal-01368635

M. A. Biot, Theory of Elasticity and Consolidation for a Porous Anisotropic Solid, Journal of Applied Physics, vol.26, issue.2, pp.182-185, 1955.
DOI : 10.1063/1.1721956

URL : https://hal.archives-ouvertes.fr/hal-01368659

M. A. Biot, Variational Lagrangian-thermodynamics of nonisothermal finite strain mechanics of porous solids and thermomolecular diffusion, International Journal of Solids and Structures, vol.13, issue.6, pp.579-597, 1977.
DOI : 10.1016/0020-7683(77)90031-2

URL : https://hal.archives-ouvertes.fr/hal-01368304

J. Bony and M. Bornert, Théorie des distributions et analyse de Fourier Cours de l' ´ Ecole Polytechnique Morphologie microstructurale et comportement mécanique ; caractérisations expérimentales, approches par bornes et estimations autocohérentes généralisées, 1996.

E. Bourgeois, Mécanique des milieux poreux : formulation desprobì emes et méthodes de résolution, Thèse de doctorat, ´ Ecole Nationale des Ponts et Chaussées, 1997.

H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, Mathematic studies, 1973.

B. Budiansky and R. J. , Elastic moduli of a cracked solid, International Journal of Solids and Structures, vol.12, issue.2, pp.81-97, 1976.
DOI : 10.1016/0020-7683(76)90044-5

H. D. Bui, ´ Etude de l'´ evolution de lafrontì ere du domainé elastique avec l'´ ecrouissage et relations de comportementélastocomportementélasto-plastique des métaux cubiques, Thèse de doctoratèsratès-sciences, 1969.

H. D. Bui, La mécanique de la rupture fragile, 1978.

N. Burlion, F. Bourgeois, and J. F. Shao, Coupling damage-drying shrinkage : Experimental study and modeling, International RILEM workshop on shrinkage of concrete, 2000.

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

G. Constantinides and F. J. Ulm, The effect of two types of C-S-H on the elasticity of cement-based materials: Results from nanoindentation and micromechanical modeling, 27] P. de Buhan. Approche fondamentale du calcuì a la rupture des ouvrages en sols renforcés Thèse de doctoratèsdoctoratès-sciences, pp.67-80, 1986.
DOI : 10.1016/S0008-8846(03)00230-8

P. De-buhan and L. Dormieux, On the validity of the effective stress concept for assessing the strength of saturated porous materials: A homogenization approach, Journal of the Mechanics and Physics of Solids, vol.44, issue.10
DOI : 10.1016/0022-5096(96)00046-4

URL : https://hal.archives-ouvertes.fr/hal-00111515

P. De-buhan, L. Dormieux, and S. Maghous, Analyse mécanique de l'effet de la compaction d'une couche géologique sur la réduction de porosité du matériau sédimentaire, Congrès Français de Mécanique, 1997.

J. Desrues, Limitations du choix de l'angle de frottement pour le crit??re de plasticit?? de Drucker-Prager, Revue Fran??aise de G??nie Civil, vol.29, issue.3, pp.853-862, 2002.
DOI : 10.1080/12795119.2002.9692406

V. Deudé, L. Dormieux, D. Kondo, and V. Pensée, Propri??t??s ??lastiques non lin??aires d'un milieu m??sofissur??, Comptes Rendus M??canique, vol.330, issue.8, pp.587-592, 2002.
DOI : 10.1016/S1631-0721(02)01489-4

V. Deudé, Non linéarités géométriques et physiques dans les milieux poreux : Apport des méthodes de changement d'´ echelle, Thèse de doctorat, ´ Ecole Nationale des Ponts et Chaussées, 2002.

V. Deudé, L. Dormieux, D. Kondo, and S. Maghous, Micromechanical Approach to Nonlinear Poroelasticity: Application to Cracked Rocks, Journal of Engineering Mechanics, vol.128, issue.8, pp.848-855, 2002.
DOI : 10.1061/(ASCE)0733-9399(2002)128:8(848)

L. Dormieux, Poroelasticity and strength of fully or partially saturated porous materials, Applied micromechanics of porous materials
DOI : 10.1007/3-211-38046-9_4

L. Dormieux and E. Bourgeois, IntroductionàIntroduction`Introductionà la micromécanique des milieux poreux, 2002.

L. Dormieux and D. Kondo, Approche microm??canique du couplage perm??abilit?????endommagement, Comptes Rendus M??canique, vol.332, issue.2, pp.135-140, 2004.
DOI : 10.1016/j.crme.2003.11.003

L. Dormieux and D. Kondo, Poroelasticity and damage theory for saturated cracked media, Applied micromechanics of porous materials
DOI : 10.1007/3-211-38046-9_5

L. Dormieux, E. Lemarchand, D. Kondo, and E. Fairbairn, Elements of poro-micromechanics applied to concrete, Materials and Structures, vol.128, issue.8, pp.31-42, 2004.
DOI : 10.1007/BF02481625

URL : https://hal.archives-ouvertes.fr/hal-00137262

L. Dormieux and S. Maghous, Poroelasticity and Poroplasticity at Large Strains. Oil and Gas Science and Technology, Rev. IFP, vol.54, pp.773-784, 1999.
DOI : 10.2516/ogst:1999065

URL : http://doi.org/10.2516/ogst:1999065

L. Dormieux, A. Molinari, and D. Kondo, Micromechanical approach to the behavior of poroelastic materials, Journal of the Mechanics and Physics of Solids, vol.50, issue.10, pp.502203-2231, 2002.
DOI : 10.1016/S0022-5096(02)00008-X

URL : https://hal.archives-ouvertes.fr/hal-00140491

H. I. Ene and E. Sanchez-palencia, ´ Equations et phénomènes de surface pour l'´ ecoulement dans un modèle de milieu poreux, Journal de Mécanique, vol.14, issue.1, pp.73-108, 1975.

J. D. Eshelby, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. Roy. Soc. London, pp.376-396, 1957.

G. Faivre, H??t??rog??n??it??s ellipso??dales dans un milieu ??lastique anisotrope, Journal de Physique, vol.32, issue.4, pp.325-331, 1971.
DOI : 10.1051/jphys:01971003204032500

M. Frémond and A. Frià, Analyse limite Comparaison des méthodes statique et cinématique, Cr. R. Acad. Sci. Paris, Série A, issue.286, pp.107-110, 1978.

M. Gologanu, J. Leblond, G. Perrin, and J. Devaux, Recent Extensions of Gurson???s Model for Porous Ductile Metals, Continuum micromechanics, pp.61-130, 1997.
DOI : 10.1007/978-3-7091-2662-2_2

M. L. Guiton, Contribution de la fracturation diffusè a la déformation d'ensemble durant le plissement de roches sédimentaires, Thèse de doctorat, ´ Ecole Polytechnique, 2001.

M. L. Guiton, Y. M. Leroy, and W. Sassi, Activation of diffuse discontinuities and folding of sedimentary layers, Journal of Geophysical Research: Solid Earth, vol.66, issue.8/9, 2003.
DOI : 10.1029/2002JB001770

URL : https://hal.archives-ouvertes.fr/hal-00111388

A. Gurson, Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I???Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, vol.99, issue.1, pp.2-15, 1977.
DOI : 10.1115/1.3443401

Z. Hashin, The Elastic Moduli of Heterogeneous Materials, Journal of Applied Mechanics, vol.29, issue.1, pp.143-150, 1962.
DOI : 10.1115/1.3636446

Z. Hashin, The Spherical Inclusion With Imperfect Interface, Journal of Applied Mechanics, vol.58, issue.2, pp.444-449, 1991.
DOI : 10.1115/1.2897205

Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials, Journal of the Mechanics and Physics of Solids, vol.11, issue.2, pp.127-140, 1963.
DOI : 10.1016/0022-5096(63)90060-7

E. Hervé and A. Zaoui, inclusion-based micromechanical modelling, International Journal of Engineering Science, vol.31, issue.1, pp.1-10, 1993.
DOI : 10.1016/0020-7225(93)90059-4

F. H. Heukamp, E. Lemarchand, and F. J. Ulm, The effect of interfacial properties on the cohesion of highly filled composite materials, International Journal of Solids and Structures, vol.42, issue.1, pp.287-30579, 1967.
DOI : 10.1016/j.ijsolstr.2004.07.007

URL : https://hal.archives-ouvertes.fr/hal-00137124

M. L. Kachanov, A microcrack model of rock inelasticity part I: Frictional sliding on microcracks, Mechanics of Materials, vol.1, issue.1, pp.19-27, 1982.
DOI : 10.1016/0167-6636(82)90021-7

M. L. Kachanov, A microcrack model of rock inelasticity part II: Propagation of microcracks, Mechanics of Materials, vol.1, issue.1, pp.29-41, 1982.
DOI : 10.1016/0167-6636(82)90022-9

M. L. Kachanov, Effective Elastic Properties of Cracked Solids: Critical Review of Some Basic Concepts, Applied Mechanics Reviews, vol.45, issue.8, pp.304-335, 1992.
DOI : 10.1115/1.3119761

W. Kreher, Residual stresses and stored elastic energy of composites and polycrystals, Journal of the Mechanics and Physics of Solids, vol.38, issue.1, pp.115-128, 1990.
DOI : 10.1016/0022-5096(90)90023-W

W. Kreher and A. Molinari, Residual stresses in polycrystals as influenced by grain shape and texture, Journal of the Mechanics and Physics of Solids, vol.41, issue.12, pp.1955-1977, 1993.
DOI : 10.1016/0022-5096(93)90075-Q

N. Laws, A short note on penny-shaped cracks in transversely isotropic materials

J. Leblond, Basic results for elastic fracture mechanics with frictionless contact between the crack lips, European Journal of Mechanics - A/Solids, vol.19, issue.4, pp.633-647, 2000.
DOI : 10.1016/S0997-7538(00)00178-9

J. Leblond, Mécanique de la rupture fragile et ductile, 2003.
DOI : 10.1016/s1251-8069(98)80033-x

J. Leblond, G. Perrin, and P. Suquet, Exact results and approximate models for porous viscoplastic solids, International Journal of Plasticity, vol.10, issue.3, pp.213-235, 1994.
DOI : 10.1016/0749-6419(94)90001-9

D. Leguillon and E. Sanchez-palencia, On the behavior of a cracked elastic body with (or without) friction, J. Méca. Théor. Appl, vol.1, issue.2, pp.195-209, 1982.

E. Lemarchand, Contribution de la micromécaniquè a l'´ etude des phénomènes de transport et de couplage poromécanique dans les milieux poreux : Application aux phénomènes de gonflement des géomatériaux, 2001.

E. Lemarchand, F. J. Ulm, and L. Dormieux, Effect of Inclusions on Friction Coefficient of Highly Filled Composite Materials, Journal of Engineering Mechanics, vol.128, issue.8, pp.876-884, 2002.
DOI : 10.1061/(ASCE)0733-9399(2002)128:8(876)

V. Levin, On the termal expansion coefficients of heterogeneous materials, Mekh. Tverd. Tela, vol.2, pp.83-94, 1967.

D. Lydzba and J. Shao, Stress equivalence principle for saturated porous media, Comptes Rendus M??canique, vol.330, issue.4
DOI : 10.1016/S1631-0721(02)01463-8

URL : https://hal.archives-ouvertes.fr/hal-00139975

S. Maghous, Détermination du critère de résistance macroscopique d'un matériau hétérogènè a structure périodique : approche numérique, Thèse de doctorat, ´ Ecole Nationale des Ponts et Chaussées, 1991.

R. Masson, M. Bornert, P. Suquet, and A. Zaoui, An affine formulation for the prediction of the effective properties of nonlinear composites and polycristals, J. Mech. Phys. Solids, vol.39, issue.1, pp.1203-1227, 2000.

G. Meschke and S. Grasberger, Numerical Modeling of Coupled Hygromechanical Degradation of Cementitious Materials, Journal of Engineering Mechanics, vol.129, issue.4, 2003.
DOI : 10.1061/(ASCE)0733-9399(2003)129:4(383)

J. Michel and P. Suquet, The constitutive law of nonlinear viscous and porous materials, Journal of the Mechanics and Physics of Solids, vol.40, issue.4, pp.783-812, 1992.
DOI : 10.1016/0022-5096(92)90004-L

A. Molinari, Extensions of the self-consistent tangent model, Modelling and Simulation in Materials Science and Engineering, vol.7, issue.5, pp.683-697, 1999.
DOI : 10.1088/0965-0393/7/5/303

A. Molinari, G. R. Canova, and S. Ahzi, A self consistent approach of the large deformation polycrystal viscoplasticity, Acta Metallurgica, vol.35, issue.12, pp.2983-2994, 1987.
DOI : 10.1016/0001-6160(87)90297-5

A. Molinari, F. Houdaigui, and L. S. Tóth, Validation of the tangent formulation for the solution of the non-linear Eshelby inclusion problem, International Journal of Plasticity, vol.20, issue.2, pp.291-307, 2004.
DOI : 10.1016/S0749-6419(03)00038-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. Nemat-nasser and M. Hori, Micromechanics : overall properties of heterogeneous materials (2 nd revised edition). North-Holland, 1999.

V. Pensée, Approche multiéchelle de l'endommagement des milieux poreux fissurés

V. Pensée, L. Dormieux, D. Kondo, and V. Deudé, Poro??lasticit?? d'un milieu m??sofissur?? : analyse microm??canique, Comptes Rendus M??canique, vol.330, issue.2, pp.147-152, 2002.
DOI : 10.1016/S1631-0721(02)01443-2

V. Pensée and D. Kondo, Une analyse microm??canique 3-D de l'endommagement par m??sofissuration, Comptes Rendus de l'Acad??mie des Sciences - Series IIB - Mechanics, vol.329, issue.4, pp.271-276, 2001.
DOI : 10.1016/S1620-7742(01)01340-X

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)

G. Perrin, ContributionàContribution`Contributionà l'´ etude théorique et numérique de la rupture ductile des métaux, Thèse de doctorat, ´ Ecole Polytechnique, 1992.

P. and P. Castañeda, The effective mechanical properties of nonlinear isotropic composites, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.45-71, 1991.
DOI : 10.1016/0022-5096(91)90030-R

P. , P. Castañeda, P. Ponte-castañeda, and J. Willis, New variational principles in plasticity and their application to composite materials The effect of spatial distribution on the effective behavior of composite materials and cracked media, J. Mech. Phys. Solids J. Mech. Phys. Solids, issue.812, pp.401757-1788, 1992.

Y. Qiu and G. Weng, A Theory of Plasticity for Porous Materials and Particle-Reinforced Composites, Journal of Applied Mechanics, vol.59, issue.2, pp.261-268, 1992.
DOI : 10.1115/1.2899515

]. J. Salençon, Calcuì a la rupture et analyse limite, p.366, 1983.

J. Salençon, IntroductionàIntroduction`Introductionà l'´ elastoplasticité et au calcuì a la rupture, 1997.

J. Salençon, Handbook of Continuum Mechanics, 2001.
DOI : 10.1007/978-3-642-56542-7

P. Suquet, Plasticité et homogénéisation Thèse de doctoratèsdoctoratès-sciences, 1982.

P. Suquet, Elastic perfectly plastic constituents, Homogenization Techniques for Composite Media, pp.245-278, 1985.
DOI : 10.1007/3-540-17616-0_19

P. Suquet, Overall Properties of Nonlinear Composites, Cr. R
DOI : 10.1007/978-94-009-1756-9_19

P. Suquet, Effective behavior of nonlinear composites, Continuum micromechanics, pp.197-264, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00214215

A. P. Suvorov and G. J. Dvorak, Rate form of the Eshelby and Hill tensors, International Journal of Solids and Structures, vol.39, issue.21-22, pp.5659-5678, 2002.
DOI : 10.1016/S0020-7683(02)00369-4

D. R. Talbot and J. R. Willis, Some simple explicit bounds for the overall behaviour of nonlinear composites, International Journal of Solids and Structures, vol.29, issue.14-15, pp.1981-1987, 1992.
DOI : 10.1016/0020-7683(92)90188-Y

J. R. Willis, ANISOTROPIC ELASTIC INCLUSION PROBLEMS, The Quarterly Journal of Mechanics and Applied Mathematics, vol.17, issue.2, pp.157-174, 1964.
DOI : 10.1093/qjmam/17.2.157

J. R. Willis, Mechanics of composites, 2001.

A. Zaoui, Matériaux hétérogènes et composites, 1997.

A. Zaoui, Structural Morphology and Constitutive Behaviour of Microheterogeneous Materials, Continuum micromechanics, pp.291-347, 1997.
DOI : 10.1007/978-3-7091-2662-2_6

URL : https://hal.archives-ouvertes.fr/hal-00112489

A. Zaoui, Continuum micromechanics, Survey. JEM, vol.128, issue.8, pp.808-816, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00111366