H. Amor, J. Marigo, and C. Maurini, Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments, Journal of the Mechanics and Physics of Solids, vol.57, issue.8, pp.1209-1229, 2009.
DOI : 10.1016/j.jmps.2009.04.011

Z. Ba?ant, Instability, ductility and size effect in strain softening concrete, J. Eng. Mech, vol.102, issue.2, pp.331-344, 1976.

Z. Ba?ant and A. Zubelewicz, Strain-softening bar and beam: Exact non-local solution, International Journal of Solids and Structures, vol.24, issue.7, pp.659-673, 1988.
DOI : 10.1016/0020-7683(88)90015-7

Z. P. Ba?ant and G. Pijaudier-cabot, Measurement of Characteristic Length of Nonlocal Continuum, Journal of Engineering Mechanics, vol.115, issue.4, pp.755-767, 1989.
DOI : 10.1061/(ASCE)0733-9399(1989)115:4(755)

A. Benallal, R. Billardon, and G. Geymonat, Bifurcation and localization in rate independent materials, C.S.I.M Lecture Notes on Bifurcation and Stability of Dissipative Systems, vol.190, pp.1-44, 1993.

A. Benallal and J. Marigo, Bifurcation and stability issues in gradient theories with softening, Modelling and Simulation in Materials Science and Engineering, vol.15, issue.1, pp.283-295, 2007.
DOI : 10.1088/0965-0393/15/1/S22

URL : https://hal.archives-ouvertes.fr/hal-00551073

B. Bourdin, The variational formulation of brittle fracture: numerical implementation and extensions, Interfaces Free Bound, vol.9, pp.411-430, 2007.
DOI : 10.1007/978-1-4020-6530-9_22

B. Bourdin, G. Francfort, and J. Marigo, The variational approach to fracture, J. Elast, vol.91, pp.1-148, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00551079

H. Brezis, Analyse Fonctionnelle : Théorie et Applications, 1983.

C. Comi, Computational modelling of gradient???enhanced damage in quasi???brittle materials, Mechanics of Cohesive???frictional Materials, vol.4, issue.1, pp.17-36, 1999.
DOI : 10.1002/(SICI)1099-1484(199901)4:1<17::AID-CFM55>3.0.CO;2-6

C. Comi, A non-local model with tension and compression damage mechanisms, European Journal of Mechanics - A/Solids, vol.20, issue.1, pp.1-22, 2001.
DOI : 10.1016/S0997-7538(00)01111-6

C. Comi and U. Perego, Fracture energy based bi-dissipative damage model for concrete, International Journal of Solids and Structures, vol.38, issue.36-37, pp.36-37, 2001.
DOI : 10.1016/S0020-7683(01)00066-X

B. Dacorogna, Introduction au calcul des variations, Cahiers Mathématiques de l' ´ Ecole Polytechnique Fédérale de Lausanne. Editions Presses Polytechniques et Universitaires Ro- mandes, 1992.

M. Frémond and B. Nedjar, Damage, gradient of damage and principle of virtual power, International Journal of Solids and Structures, vol.33, issue.8, pp.1083-1103, 1996.
DOI : 10.1016/0020-7683(95)00074-7

M. Geers, R. Peerlings, W. Brekelmans, and R. De-borst, Phenomenological nonlocal approaches based on implicit gradient-enhanced damage, Acta Mechanica, vol.33, issue.1-2, pp.1-15, 2000.
DOI : 10.1007/BF01181824

R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, vol.6, issue.3, pp.236-249, 1958.
DOI : 10.1016/0022-5096(58)90029-2

R. Hill, Acceleration waves in solids, Journal of the Mechanics and Physics of Solids, vol.10, issue.1, pp.1-16, 1962.
DOI : 10.1016/0022-5096(62)90024-8

E. Lorentz and S. Andrieux, A variational formulation for nonlocal damage models, International Journal of Plasticity, vol.15, issue.2, pp.119-138, 1999.
DOI : 10.1016/S0749-6419(98)00057-6

E. Lorentz and S. Andrieux, Analysis of non-local models through energetic formulations, International Journal of Solids and Structures, vol.40, issue.12, pp.2905-2936, 2003.
DOI : 10.1016/S0020-7683(03)00110-0

E. Lorentz and A. Benallal, Gradient constitutive relations: numerical aspects and application to gradient damage, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.50-52, pp.5191-5220, 2005.
DOI : 10.1016/j.cma.2004.12.016

URL : https://hal.archives-ouvertes.fr/hal-00089126

J. Marigo, Formulation d'une loi d'endommagement d'un matériaú elastique, C. R. Acad. Sci. Paris Sér. II, vol.292, pp.1309-1312, 1981.

J. Marigo, Constitutive relations in plasticity, damage and fracture mechanics based on a work property, Nuclear Engineering and Design, vol.114, issue.3, pp.249-272, 1989.
DOI : 10.1016/0029-5493(89)90105-2

J. Marigo, L'endommagement et la rupture : hier, aujourd'hui et demain, Lecture notes of the IPSI course " Comportements non linéaires des matériaux, 2000.

J. Mazars, A model of a unilateral elastic damageable material and its application to concrete. In: Fracture Toughness and Fracture Energy of Concrete, 1986.

J. Mazars, S. Ramtani, and Y. Berthaud, An experimental procedure to delocalize tensile failure and to indentify the unilateral effect of tensile damage Workshop on strain localization and size effect due to damage and cracking, pp.581-587, 1988.

A. Mielke, Evolution of Rate-Independent Systems, II of Handb. Differ. Equ, pp.461-559, 2005.
DOI : 10.1016/S1874-5717(06)80009-5

Q. S. Nguyen, Bifurcation and post-bifurcation analysis in plasticity and brittle fracture, Journal of the Mechanics and Physics of Solids, vol.35, issue.3, pp.303-324, 1987.
DOI : 10.1016/0022-5096(87)90010-X

Q. S. Nguyen, Stability and Nonlinear Solid Mechanics, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00105248

R. Peerlings, M. Geers, R. Deborst, and W. Brekelmans, A critical comparison of nonlocal and gradient-enhanced softening continua, International Journal of Solids and Structures, vol.38, issue.44-45, pp.44-45, 2001.
DOI : 10.1016/S0020-7683(01)00087-7

K. Pham, H. Amor, J. Marigo, and C. Maurini, Gradient Damage Models and Their Use to Approximate Brittle Fracture, International Journal of Damage Mechanics, vol.30, issue.4, p.25, 2010.
DOI : 10.1016/0029-5493(92)90094-C

URL : https://hal.archives-ouvertes.fr/hal-00549530

K. Pham and J. Marigo, CONSTRUCTION AND ANALYSIS OF LOCALIZED RESPONSES FOR GRADIENT DAMAGE MODELS IN A 1D SETTING, Vietnam Journal of Mechanics, vol.31, issue.3-4, pp.31-34, 2009.
DOI : 10.15625/0866-7136/31/3-4/5651

URL : https://hal.archives-ouvertes.fr/hal-00490539

K. Pham and J. Marigo, STABILITY OF NON LOCALIZED RESPONSES FOR DAMAGING MATERIALS, Vietnam Journal of Mechanics, vol.30, issue.4, pp.1-11, 2009.
DOI : 10.15625/0866-7136/30/4/5636

URL : https://hal.archives-ouvertes.fr/hal-00490540