O. Allix, C. Ouzel, A. Gassen, P. J. Et-ladevèze, G. Chermant et al., Modélisation des composites céramique-céramique à différentes échelles, éds, Revue des composites et des matériaux avancés, pp.277-297, 1993.

S. Andrieux, Un modèle de matériau microfissuré avec frottement, C. R. Acad. Sei. Paris, vol.293, issue.î981, pp.329-332

Z. Bazant, P. Et-oh, and P. H. , Crack band theory for fracture of concrete, Materials and structures, RILEM, vol.16, issue.93, pp.155-177, 1983.

Z. P. Bazant and P. H. Et-oh, Microplane model for progressive of concrete and rock, J. Eng. Mech. ASCE, vol.Ill, pp.559-582, 1985.

Z. P. Bazant and P. C. Et-prat, Microplane model for brittle-plastic material, 1987.

Z. P. Bazant and J. Et-ozbolt, Nonlocal Microplane Model for Fracture, Damage, and Size Effect in Structures, Journal of Engineering Mechanics, vol.116, issue.11, pp.2485-2505, 1990.
DOI : 10.1061/(ASCE)0733-9399(1990)116:11(2485)

Z. P. Bazant and Y. Et-xi, Statistical Size Effect in Quasi???Brittle Structures: II. Nonlocal Theory, Journal of Engineering Mechanics, vol.117, issue.11, pp.2623-2640, 1991.
DOI : 10.1061/(ASCE)0733-9399(1991)117:11(2623)

A. Benallal, R. Billardon, and G. Et-geymonat, Some mathematical aspects of the damage softening rate problem, cracking and damage, éds Cracking and damage, strain localization and size effect, J. Mazars et Z. P. Bazant, pp.247-258, 1988.

A. Benallal and C. Et-comí, Closed form solutions to localization conditions for rateindependent materials, C. R. Acad. Sei. Paris, serie II, pp.318-325, 1994.

R. Billardon, Etude de la rupture par la mécanique de l'endommagement, Thèse de doctorat d'état es Science Mécanique, 1989.

R. Billardon and I. Et-doghri, Prévision de l'amorçage d'une macro-fissure par localisation de l'endommagement, pp.308-347, 1989.

L. Biolzi, P. G. Gambarova, G. P. Rosati, and C. Et-schuum, On fracture and size effect in concrete beams, Comp.modelling of concrete struc, Proc Int. conf. Austria, vol.1, pp.53-62, 1994.

D. Borst, R. Huerta, A. Et-pijaudier-cabot, and G. , Localization limiters: Properties, Implementation and Solution Control, internal report, LMT, vol.114, 1991.

C. M. Brauner, B. Nicolaenco, and M. Et-frémond, Homographie approximations of free boundary problems characterized by variational inequalities, Advances in Mathematics Supplementary studies, pp.119-151, 1989.

H. D. Bui, Mécanique de la rupture fragile, 1977.

A. Carpinteri and S. Et-valente, Size-scale transition from ductile to brittle failure: A dimensional analysis approach, cracking and damage, éds Cracking and damage, strain localization and size effect, J. Mazars eî Z. P. Bazant, pp.477-490, 1989.

J. L. Chaboche, Le concept de contrainte effective appliquée à l'élasticité et à la viscoplasticité en présence d'un endommagemenî anisotrope, Colloque Euromech, vol.115, 1979.

C. Mattos, H. Frémond, M. Et-namiya, and E. N. , A simple model of the mechanical behaviour of ceramic like materials, Int. J. Solids Structures, vol.29, pp.24-3185, 1992.

L. Davenne, C. Saouridis, and J. T. Et-piau, Un code de calcul pour la prévision du comportement de structures endommageables en béton, en béton armé ou en béton de fibres, Annales de l'I, pp.478-138, 1989.

A. Dragon and Z. Et-mroz, A model for plastic creep of rock-like materials accounting for the kinetics of fracture, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.16, issue.4, pp.253-259, 1979.
DOI : 10.1016/0148-9062(79)91200-2

A. Dragon, Dilatational creep in rock-like solids, 3rd IUTAM SymposiumCreep in Structures, A. R. S. Ponter et D. R. Hayhrust, 1980.

A. Dragon, F. Cormery, T. Désoyer, and D. Et-halm, Localised filure analysis using damage modelsLocalization and bifurcation theory for soils and rocks, éds, 1994.

I. Doghri, Etude de la localisation de l'endommagement, Thèse de doctorat d'université, 1989.

M. Elices and J. Et-planas, Material models, Chap, 1988.

D. François, A. Pineau, and A. Et-zaoui, Comportement mécanique des matériaux, viscoplasticité, endommagement, mécanique de la rupture, 1993.

M. Frémond, Adhérence des solides, Journal de Mécanique Théorique Appliquée, vol.6, issue.3, pp.383-407, 1987.

M. Frémond, Sur l'inégalité de Clausius-Duhem, C. R. Acad. Sei. Paris t.311, serie II, pp.757-762, 1990.

M. Frémond and B. Et-nedjar, Endommagement et principe des puissances virtuelles, C. R. Acad. Sei. Paris, serie II, issue.7, pp.317-857, 1993.

M. Frémond and B. Et-nedjar, Damage and gradient of damage. The unilateral phenomenon, SMÍRT12 (12 lh Structural Mechanics in Reactor Technology), éd. F. Kussmaul, North-holüand, pp.375-380, 1993.

M. Frémond and B. Et-nedjar, Damage, Gradient of Damage and Principle of Virtual Power. Accepté pour publication à, Int. J. Solids Structures, 1994.

M. Frémond and B. Et-nedjar, L'endommagement et son gradient, Le phénomène unilatéral. Actes du 7ème Colloque annuel MECMAT, pp.14-17, 1994.

M. Frémond and B. Et-nedjar, Damage of concrete, the unilateral phenomenon. Accepté pour publication à int, 1994.

M. Frémond and B. Et-nedjar, Damage modelling of concrete. XXIII Convegno

A. Gasser and . Nedjar, Une première méso-modélisation d'un composite à matrice céramique Sic-Sic, 1991.

A. Gérard and S. Et-baste, Comportement non linéaire des composites à matrice céramique en cycle charge-décharge, pp.1361-1366, 1991.

P. Germain, Mécanique des milieux continus, Editions Ellipses, 1982.

P. Germain, Q. S. Nguyen, and P. Suquet, Continuum Thermodynamics, Journal of Applied Mechanics, vol.50, issue.4b, pp.1010-1021, 1983.
DOI : 10.1115/1.3167184

URL : https://hal.archives-ouvertes.fr/hal-00105630

B. Halphen and Q. S. Nguyen, Sur les matériaux Standartds Généralisés, Journal de Mécanique, vol.14, pp.39-63, 1975.

G. Hermann and J. Kestin, On the thermodynamic Fundation of damage theory in elastic solids Cracking and damage, strain localization and size effect, Eds. J. Mazars et Z. P. Bazant, pp.228-232, 1988.

L. 'hermite and R. , Influence de la dimension absolue sur la résistance à la flexion, annales ITBTP, pp.309-310, 1973.

A. Hillerborg, M. Modéer, and P. Et-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

A. Hillerborg, Analysis of a single crack, Fracture Mechanics of concrete, pp.223-249, 1983.

A. Hillerborg, Results of three comparative test series for determining the fracture energyG F of concrete, Materials and Structures, vol.18, issue.5, pp.407-413, 1985.
DOI : 10.1007/BF02472416

D. A. Hordijk, J. G. Van-mier, and H. W. Et-reinhardt, Material properties, 1988.

D. A. Hordijk, Tensile and tensile fatigue behaviour of concrete: Experiments, modelling and analyses The netherland, 1992.

L. M. Kachanov, Time of the rupture process under creep conditions, Izv Akad Nauk SSR Otd Tech Nauk, pp.26-31, 1958.

D. Krajcinovic and G. U. Et-fonseka, The Continuous Damage Theory of Brittle Materials, Part 1: General Theory, Journal of Applied Mechanics, vol.48, issue.4, pp.809-824, 1981.
DOI : 10.1115/1.3157739

J. F. Knott, Fundamentals of Fracture Mechanics, 1973.

R. Labbens, Introduction à la mécanique de la rupture, Editions. Piuralis, 1980.

L. Borderie and C. , Phénomènes unilatéraux dans un matériau endommageable : modélisation et application a l'analyse des structures en béton, 1991.

P. Ladevèze and E. N. Lmt, Sur une théorie de l'endommagement anisotrope, 1983.

P. Ladevèze, Modélisation et calcul des structures : de nouveaux défis, Rapport interne, 1989.

P. Ladevèze, On an anisotropic damage theory. Failure criteria of structured media, éd, pp.355-363, 1993.

P. Ladevèze, A. Gasser, and O. Et-allix, Damage mechanics modelling for ceramic composites, 1993.

D. Lasry and T. Et-belytschko, Localization limiters in transient problems, International Journal of Solids and Structures, vol.24, issue.6, pp.581-597, 1988.
DOI : 10.1016/0020-7683(88)90059-5

J. B. Leblond, Mécanique de la rupture. Cours de l'école polytechnique, 1991.

J. Lemaitre, A Course on Damage Mechanics, 1992.

J. Lemaitre and J. L. Et-chaboche, Mécanique des matériaux solides, 1990.

Y. N. Li and Z. P. Et-bazant, Eigenvalue analysis of size effect for cohesive crack model, International Journal of Fracture, vol.84, issue.2, pp.213-226, 1994.
DOI : 10.1007/BF00042585

M. P. Luong, Fracture testing of concrete and rock materials, Nuclear Engineering and Design, vol.133, issue.1, pp.83-95, 1992.
DOI : 10.1016/0029-5493(92)90093-B

J. J. Marigo, Modelling of brittle and fatigue damage for elastic material by growth of microvoids, Engineering Fracture Mechanics, vol.21, issue.4, pp.4-861, 1985.
DOI : 10.1016/0013-7944(85)90093-1

J. J. Marigo and P. Et-miallon, Justification of some brittle damage laws by Illiushin's postulate and study of their singular character, éds Cracking and damage, strain localization and size effect, J. Mazars et Z. P. Bazant, pp.391-403, 1988.

G. A. Maugin, Internal variables and dissipative structures, J. of Non-equilibrium Thermodynamic, vol.15, pp.2-173, 1990.

J. Mazars and D. Et-waiter, Endommagement mécanique du béton, 1980.

J. Mazars, Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure, Thèse de doctorat es Science, 1984.

J. Mazars and Z. P. Et-bazant, Cracking and damage, Strain localization and Size effect, 1988.

J. Mazars and G. Et-pijaudier-cabot, Continuum Damage Theory???Application to Concrete, Journal of Engineering Mechanics, vol.115, issue.2, pp.345-365, 1989.
DOI : 10.1061/(ASCE)0733-9399(1989)115:2(345)

J. Mazars, G. Pijaudier-cabot, and C. Et-saouridis, Size effect and continuous damage in cemeniitious materials, Int. Jour, of Fracture, vol.51, pp.159-173, 1991.

J. J. Moreau, Fonctionnelles convexes, Séminaire sur les équations aux dérivées partielles, 1966.

J. J. Moreau, Sur les lois de Frottement, de Viscosité et de Plasticité, C. R. Acad, 1970.

H. Murakami, D. M. Kendall, and K. C. Et-valanis, A nonlocal elastic damage theory: Mesh-insensitivity under strain softening, Computers & Structures, vol.48, issue.3, pp.415-422, 1993.
DOI : 10.1016/0045-7949(93)90317-7

B. Nedjar, A first gradient theory for damage. Actes du "first forum of young european researchers, pp.199-204, 1993.

B. Nedjar, Modélisation de l'endommagement des matériaux. L'effet unilatéral, actes du 1 lème Congrès Français de Mécanique, pp.281-284, 1993.

A. Needieman, Material rate dépendance and mesh sensitivity in localization problems, Comput. Meth. Apll. Mech. Engng, vol.67, pp.64-85, 1988.

S. Nemat-nasser, N. Yu, and M. Et-hori, Solids with periodically distributed cracks, International Journal of Solids and Structures, vol.30, issue.15, pp.2071-2095, 1993.
DOI : 10.1016/0020-7683(93)90052-9

G. Pijaudier-cabot and Z. P. Et-bazant, 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)

G. Pijaudier-cabot and L. Et-bodé, Localization of damage in a nonlocal continuum, Mechanics Research Communications, vol.19, issue.2, pp.145-153, 1992.
DOI : 10.1016/0093-6413(92)90039-D

G. Pijaudier-cabot, A. Huerta, and L. Et-bodé, Nonlocal continuum damage and adapted solution strategies in computational failure mechanics, Proc. of the European Conf. on new advances in computational structural mechanics, éds. P. Ladevèze et O, 1992.

G. Pijaudier-cabot and A. Benallal, Strain localization and bifurcation in a nonlocal continuum, International Journal of Solids and Structures, vol.30, issue.13, pp.1761-1775, 1993.
DOI : 10.1016/0020-7683(93)90232-V

G. Pijaudier-cabot, L. Borderie, C. Et-fichant, S. H. Mang, N. Bicanic et al., Damage mechanics for concrete modelling: application and comparison with plasticity and fracture mechanicsComputer modelling of concrete structures, pp.17-36, 1994.

J. Piañas and M. Et-elices, Size-effect in concrete structures: Mathematical approximations and expérimental validation, éds Cracking and damage, strain localization and size effect, J. Mazars et Z. P. Bazant, pp.462-476, 1989.

N. Point, Unilateral contact with adherence, Mathematical Methods in the Applied Sciences, vol.26, issue.4, pp.367-381, 1988.
DOI : 10.1002/mma.1670100403

N. Point, Approches mathématiques de problèmes à frontières libres. Application à des exemples physiques, 1989.

S. Ramtani, Contribution a la modélisation du comportement multiaxial du béton avec description du caractère unilatéral, 1990.

J. R. Rice and J. W. Et-rudnicki, A note on some features of the theory of localization of deformation, International Journal of Solids and Structures, vol.16, issue.7, pp.597-605, 1980.
DOI : 10.1016/0020-7683(80)90019-0

P. Rossi, E. Bruhwiler, S. Chhuy, Y. S. Jeng, and S. P. Shah, Fracture properties of concrete as determined by means of wedge splitting tets and tapered double \ cantiievar beam tests, Fractures Mechanics, Tests Methods for concrete, 1991.

P. Rossi and J. M. Et-piau, The usefulness of statistical models to describe damage and fracture in concrete, éds Cracking and damage, strain localization and size effect, J. Mazars et Z. P. Bazant, pp.91-103, 1988.

J. W. Rudnicki and J. R. Et-rice, Conditions for the localization of deformation in pressure-sensitive dilatant materials, Journal of the Mechanics and Physics of Solids, vol.23, issue.6, pp.371-394, 1980.
DOI : 10.1016/0022-5096(75)90001-0

K. Saanouni, J. L. Chaboche, and P. M. Et-lesne, Creep crack-growth prediction by a non-local damage formulation, éds Cracking and damage, strain localization and size effect, J. Mazars et Z. P. Bazant, pp.404-414, 1988.

C. Saouridis and J. Mazars, A multiscale approach to distributed damage and its usefullness for capturing structural size effect, éds Cracking and damage, strain localization and size effect, J. Mazars et Z. P. Bazant, pp.391-403, 1988.

C. Saouridis, Identification et numérisation objective des comportements adoucissants : une approche multiéchelle de l'endommagement du béton, 1988.

H. L. Shreyer, Analytical Solutions for Nonlinear Strain-Gradient Softening and Localization, Journal of Applied Mechanics, vol.57, issue.3, pp.522-528, 1990.
DOI : 10.1115/1.2897054

J. C. Simo, Strain softening and dissipation: A unification of approaches, éds Cracking and damage, strain localization and size effect, J. Mazars et Z. P. Bazant, pp.440-461, 1988.

L. J. Sluys and R. Et-de-borst, Wave propagation and localization in a rate-dependent cracked medium???model formulation and one-dimensional examples, International Journal of Solids and Structures, vol.29, issue.23, pp.2945-2958, 1992.
DOI : 10.1016/0020-7683(92)90151-I

L. J. Sluys, R. De-borst, and H. Et-mühlhaus, Wave propagation, localization and dispersion in a gradient-dependent medium, International Journal of Solids and Structures, vol.30, issue.9, pp.1153-1171, 1993.
DOI : 10.1016/0020-7683(93)90010-5

P. Suquet, Approche par homogénéisation d'une forme d'endommagement, C. R, 1981.

P. Suquet, Plasticité et homogénéisation, 1982.

M. Terrien, Emission acoustique et comportement mécanique post-critique d'un béton sollicité en traction, Bull, de liaison Lab, des Ponts et Chaussées, vol.105, p.2398, 1980.

J. M. Truong-dinh-tien, Contact avec adhérence, 1990.

R. A. Vonk, A micromechanical investigation of softening of concrete loaded in compression, Heron Publication The netherland, p.3, 1993.