S. Pietruszczak and Z. Mróz, Finite element analysis of deformation of strain-softening materials, International Journal for Numerical Methods in Engineering, vol.105, issue.3, pp.327-334, 1981.
DOI : 10.1002/nme.1620170303

Z. Ba?ant and T. Belytschko, Wave Propagation in a Strain???Softening Bar:Exact Solution, Journal of Engineering Mechanics, vol.111, issue.3, pp.381-389, 1985.
DOI : 10.1061/(ASCE)0733-9399(1985)111:3(381)

N. Triantafyllidis and E. Aifantis, A gradient approach to localization of deformation. I. Hyperelastic materials, Journal of Elasticity, vol.5, issue.3, pp.225-237, 1986.
DOI : 10.1007/BF00040814

D. Lasry and T. 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

D. Borst, R. Sluys, L. Muhlaus, H. Pamin, and J. , FUNDAMENTAL ISSUES IN FINITE ELEMENT ANALYSES OF LOCALIZATION OF DEFORMATION, Engineering Computations, vol.10, issue.2, pp.99-121, 1993.
DOI : 10.1108/eb023897

A. Hillerborg, M. Modeer, and P. 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

Z. Ba?ant and B. Oh, Crack band theory for fracture of concrete, Mat??riaux et Constructions, vol.41, issue.No. 1, pp.155-177, 1983.
DOI : 10.1007/BF02486267

G. Pijaudier-cabot and Z. Ba?ant, 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)

Z. Ba?ant and G. Pijaudier-cabot, Nonlocal continuum damage, localization instability and convergence, J Appl Mech, vol.55, pp.521-539, 1988.

D. Borst, R. Mühlhaus, and H. , Gradient-dependent plasticity: Formulation and algorithmic aspects, International Journal for Numerical Methods in Engineering, vol.137, issue.3, pp.521-539, 1992.
DOI : 10.1002/nme.1620350307

M. Manzari and R. Regueiro, Gradient plasticity modeling of geomaterials in a meshfree environment. Part I: Theory and variational formulation, Mechanics Research Communications, vol.32, issue.5, pp.536-546, 2005.
DOI : 10.1016/j.mechrescom.2005.02.013

R. Peerlings, R. De-borst, W. Brekelmans, and M. Geers, Gradient-enhanced damage modelling of concrete fracture, Mechanics of Cohesive-frictional Materials, vol.48, issue.4, pp.323-342, 1998.
DOI : 10.1002/(SICI)1099-1484(1998100)3:4<323::AID-CFM51>3.0.CO;2-Z

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

R. Peerlings, R. De-borst, W. Brekelmans, and J. Vree, Computational modelling of gradient-enhanced damage for fracture and fatigue problems, Computational Plasticity, Fundamentals and Applications: Proceedings of the 4th International Conference, pp.975-986, 1995.

R. Peerlings, Enhanced damage modelling for fracture and fatigue (Phd thesis), 1999.

V. Godard, Modélisation de l'endommagement anisotrope du béton avec prise en compte de l'effet unilatéral : ApplicationàApplicationà la simulation des enceintes de confinement nucléaires (PhD thesis), 2005.

J. Carmeliet and R. De-borst, Stochastic approaches for damage evolution in standard and non-standard continua, International Journal of Solids and Structures, vol.32, issue.8-9, pp.1149-1160, 1995.
DOI : 10.1016/0020-7683(94)00182-V

J. Carmeliet and R. De-borst, Probabilistic Nonlocal Damage Model for Continua with Random Field Properties, Journal of Engineering Mechanics, vol.120, issue.10, pp.2013-2027, 1994.
DOI : 10.1061/(ASCE)0733-9399(1994)120:10(2013)

E. Vanmarcke, Random Fields: Analysis & Synthesis, Journal of Vibration Acoustics Stress and Reliability in Design, vol.107, issue.2, 1983.
DOI : 10.1115/1.3269255

W. Weibull, A Statistical theory of the strength of materials, Royal Swedish Institute for Engineering Research, 1939.

Z. Ba?ant, Y. Xi, and S. Reid, Statistical Size Effect in Quasi???Brittle Structures: I. Is Weibull Theory Applicable?, Journal of Engineering Mechanics, vol.117, issue.11, pp.2609-2622, 1991.
DOI : 10.1061/(ASCE)0733-9399(1991)117:11(2609)

Z. Ba?ant and Y. 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)

Z. Ba?ant and D. Novák, Probabilistic Nonlocal Theory for Quasibrittle Fracture Initiation and Size Effect.???I: Theory, Journal of Engineering Mechanics, vol.126, issue.2, pp.166-174, 2000.
DOI : 10.1061/(ASCE)0733-9399(2000)126:2(166)

Z. Ba?ant, Probability distribution of energetic-statistical size effect in quasibrittle fracture, Probabilistic Engineering Mechanics, vol.19, issue.4, pp.307-319, 2004.
DOI : 10.1016/j.probengmech.2003.09.003

M. Kanninen, F. Brust, J. Ahmad, and I. Abou-sayed, The numerical simulation of crack growth in weldinduced residual stress fields, Residual stress and stress relaxation, pp.975-986, 1982.

B. Liaw, A. Kobayashi, and A. Emery, Double noding technique for mixed mode crack propagation studies, International Journal for Numerical Methods in Engineering, vol.7, issue.5, pp.967-977, 1984.
DOI : 10.1002/nme.1620200512

M. Rashid, The arbitrary local mesh replacement method: An alternative to remeshing for crack propagation analysis, Computer Methods in Applied Mechanics and Engineering, vol.154, issue.1-2, pp.133-150, 1998.
DOI : 10.1016/S0045-7825(97)00068-6

M. Seyedi, S. Taheri, and F. Hild, Numerical modeling of crack propagation and shielding effects in a striping network, Nuclear Engineering and Design, vol.236, issue.9, pp.954-964, 2006.
DOI : 10.1016/j.nucengdes.2005.10.002

URL : https://hal.archives-ouvertes.fr/hal-00086961

M. Aliabadi, A new generation of boundary element methods in fracture mechanics, International Journal of Fracture, vol.86, issue.1/2, pp.91-125, 1997.
DOI : 10.1023/A:1007381025099

M. Charlotte, L. J. Marigo, and J. , Initiation of cracks with cohesive force models: a variational approach, European Journal of Mechanics - A/Solids, vol.25, issue.4, pp.649-669, 2006.
DOI : 10.1016/j.euromechsol.2006.05.002

URL : https://hal.archives-ouvertes.fr/hal-00551071

N. Moes, J. Dolbow, and T. Belytschko, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, vol.46, issue.1, pp.131-150, 1999.
DOI : 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.3.CO;2-A

URL : https://hal.archives-ouvertes.fr/hal-01004829

R. Peerlings, M. Geers, R. De-borst, 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.7723-7746, 2001.
DOI : 10.1016/S0020-7683(01)00087-7

A. Freudenthal, Statistical approach to brittle fracture, pp.591-619, 1968.

M. Kanninen and C. Popelar, Advanced Fracture Mechanics, 1985.

A. Polyanin, Handbook of linear partial differential equations for engineers and scientists, 2002.
DOI : 10.1201/9781420035322

M. Abramowitz and I. Stegun, Handbook of mathematical functions with formulas, graphs and mathematical tables, 1972.

J. Lemaitre and J. Chaboche, Mechanics of Solid Materials, 1990.

M. Abbas, 03.01 : Algorithme non-linéaire quasi-statique, Documentation Code Aster. EDF R&D, 2009.

E. Galenne, 02 : Modélisation non localè a gradient de déformation, Documentation Code Aster. EDF R&D, 2009.

X. Desroches, 03.01 : Fonctions de forme et points d'intégration desélémentsdeséléments finis, Documentation Code Aster. EDF R&D, 2009.

Y. Murakami, Stress Intensity Factor Handbook, 1987.