E. Aifantis, The physics of plastic deformation, International Journal of Plasticity, vol.3, issue.3, pp.211-258, 1987.
DOI : 10.1016/0749-6419(87)90021-0

O. Allix and J. F. Deü, Delay-damage modelling for fracture prediction of laminated composites under dynamic loading, Engineering Transactions, vol.45, pp.29-46, 1997.

Z. P. Ba?ant and M. Jirásek, Nonlocal Integral Formulations of Plasticity and Damage: Survey of Progress, Journal of Engineering Mechanics, vol.128, issue.11, pp.1119-1149, 2002.
DOI : 10.1061/(ASCE)0733-9399(2002)128:11(1119)

Z. Ba?ant, J. Le, and C. Hoover, Nonlocal boundary layer (nbl) model: overcoming boundary condition problems in strength statistics and fracture analysis of quasibrittle materials, Proc., FraMCoS-7, Korea, pp.135-143, 2010.

T. Belytschko, Y. Y. Lu, and L. Gu, Crack propagation by element-free Galerkin methods, Engineering Fracture Mechanics, vol.51, issue.2, pp.295-315, 1995.
DOI : 10.1016/0013-7944(94)00153-9

G. Borino, B. Failla, and F. Parinello, A symmetric nonlocal damage theory, International Journal of Solids and Structures, vol.40, issue.13-14, pp.3621-3645, 2003.
DOI : 10.1016/S0020-7683(03)00144-6

L. Brillouin, La mécanique ondulatoire de Schrödinger: une méthode générale de résolution par approximations successives, Comptes Rendus de l, Academie des Sciences, vol.183, pp.24-26, 1926.

C. Comi and U. Pérego, Numerical aspects of nonlocal damage analyses, European Journal of Finite Elements, vol.10, pp.227-242, 2001.

C. Denoual and F. Hild, A damage model for the dynamic fragmentation of brittle solids, Computer Methods in Applied Mechanics and Engineering, vol.183, issue.3-4, pp.3-4, 2000.
DOI : 10.1016/S0045-7825(99)00221-2
URL : https://hal.archives-ouvertes.fr/hal-00013966

R. Desmorat, Modèle d'endommagement anisotrope avec forte dissymétrie traction/compression, 5e journées du Regroupement Francophone pour la Recherche et la Formation sur le Béton (RF2B),Lì ege, pp.5-6, 2004.

R. Desmorat, F. Gatuingt, and F. Ragueneau, Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials, Engineering Fracture mechanics, pp.1539-1560, 2007.

R. Desmorat, F. Gatuingt, and F. Ragueneau, Non standard thermodynamics framework for robust computations with induced anisotropic damage, International Journal of Damage Mechanics, pp.10-1177, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00994281

R. Desmorat and F. Gatuingt, Introduction of an internal time in nonlocal integral theories, Internal report LMT LMT, vol.268
DOI : 10.1201/b10546-15
URL : https://hal.archives-ouvertes.fr/hal-01017193

R. Desmorat and F. Gatuingt, Introduction of an internal time in nonlocal integral theories Computational modelling of concrete structures ? EURO-C 2010, pp.121-128, 2010.

E. W. Dijkstra, A note on two problems in connexion with graphs, Numerische Mathematik, vol.4, issue.1, pp.269-271, 1959.
DOI : 10.1007/BF01386390

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

J. F. Ganghoffer and R. De-borst, A new framework in nonlocal mechanics, International Journal of Engineering Science, vol.38, issue.4, pp.453-486, 2000.
DOI : 10.1016/S0020-7225(99)00030-0

J. F. Ganghoffer, New concepts in nonlocal continuum mechanics and new materials obeying a generalised continuum behaviour, International Journal of Engineering Science, vol.41, issue.3-5, pp.41-291, 2003.
DOI : 10.1016/S0020-7225(02)00206-9

M. Geers, R. De-borst, W. Brekelmans, and R. Peerlings, Strain-based transient-gradient damage model for failure analyses, Computer Methods in Applied Mechanics and Engineering, vol.160, issue.1-2, pp.133-153, 1998.
DOI : 10.1016/S0045-7825(98)80011-X

C. Giry, F. Dufour, and J. Mazars, Stress-based nonlocal damage model, International Journal of Solids and Structures, vol.48, issue.25-26, pp.25-26, 2011.
DOI : 10.1016/j.ijsolstr.2011.08.012

M. Jirásek, Comparison of integral-type nonlocal plasticity models for strain-softening materials, International Journal of Engineering Science, vol.41, issue.13-14, pp.1553-1602, 2003.
DOI : 10.1016/S0020-7225(03)00027-2

M. Jirásek and S. Marfia, Nonlocal damage models: displacement-based formulations, Euro-C conference Computational modelling of Concrete Structures, 2006.

M. Jirásek and J. Zeman, Localization study of a regularized energetic damage model, International Journal of Solids and Structures

A. Krayani, G. Pijaudier-cabot, and F. Dufour, Boundary effect on weight function in nonlocal damage model, Engineering Fracture Mechanics, vol.76, issue.14, pp.2217-2231, 2009.
DOI : 10.1016/j.engfracmech.2009.07.007
URL : https://hal.archives-ouvertes.fr/hal-00705454

L. Borderie, C. , and P. Unilatéraux-dans-un-matériau-endommageable, Modélisation et ApplicationàApplication`Applicationà l'Analyse de Structures en Béton, 1991.

D. C. Lagoudas, A gauge theory of damage, International Journal of Engineering Science, vol.29, issue.5, pp.597-606, 1991.
DOI : 10.1016/0020-7225(91)90064-A

D. C. Lagoudas and C. M. Huang, Finite element implementation of the gauge theory of damage, International Journal of Engineering Science, vol.32, issue.12, pp.12-1877, 1994.
DOI : 10.1016/0020-7225(94)90084-1

G. Lebon, Analyse de l'endommagement des structures de génie civil: techniques de sous-structuration hybrides coupléescouplées`coupléesà un modèle d'endommagement anisotrope, 2011.

J. Lemaitre and R. Desmorat, Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures, 2005.

J. Mazars, Y. Berthaud, and S. Ramtani, The unilateral behaviour of damaged concrete, Engineering Fracture Mechanics, vol.35, issue.4-5, pp.629-635, 1990.
DOI : 10.1016/0013-7944(90)90145-7

S. Murakami and N. Ohno, A constitutive equation of creep damage in polycrystalline metals, IUTAM Colloquium Euromech, vol.111, 1978.

S. Murakami, Mechanical Modeling of Material Damage, Journal of Applied Mechanics, vol.55, issue.2, pp.280-286, 1988.
DOI : 10.1115/1.3173673

A. Needleman, Material rate dependence and mesh sensitivity in localization problems, Computer Methods in Applied Mechanics and Engineering, vol.67, issue.1, pp.69-85, 1988.
DOI : 10.1016/0045-7825(88)90069-2

G. D. Nguyen, A damage model with evolving nonlocal interactions, International Journal of Solids and Structures, vol.48, issue.10, pp.1544-1559, 2011.
DOI : 10.1016/j.ijsolstr.2011.02.002

O. Nouailletas, Comportement d'une discontinuité dans un géomatériau sous sollicitations chemo-mécanique-expérimentations et modélisations, 2013.

B. Patzák and Z. Bittnar, Design of object oriented finite element code Advances in Engineering Software, pp.759-767, 2001.

B. Patzák, OOFEM ? an object-oriented simulation tool for advanced modeling of materials and structures, Acta Polytechnica, vol.52, pp.59-66, 2012.

R. Peerlings, R. De-borst, W. Brekelmans, and J. De-vree, Gradient-enhanced damage model for quasi-brittle materials, Int. J. Numer. Methods Engng, vol.39, pp.391-403, 1996.

R. H. Peerlings, M. D. Geers, R. De-borst, and W. A. 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

K. Pham and J. J. Marigo, From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models, Continuum Mechanics and Thermodynamics, vol.30, issue.6, pp.147-171, 2013.
DOI : 10.1007/s00161-011-0228-3
URL : https://hal.archives-ouvertes.fr/hal-00647860

G. Pijaudier-cabot and Z. Ba?ant, Nonlocal Damage Theory, Journal of Engineering Mechanics, vol.113, issue.10, pp.1512-1545, 1987.
DOI : 10.1061/(ASCE)0733-9399(1987)113:10(1512)

G. Pijaudier-cabot, K. Haidar, and J. Dubé, Non-local damage model with evolving internal length, International Journal for Numerical and Analytical Methods in Geomechanics, vol.28, issue.78, pp.633-652, 2004.
DOI : 10.1002/nag.367

G. Pijaudier-cabot, A. Krayani, and F. Dufour, Comments on boundary effects in non local damage based models, chapter, Nonlocal Modeling of Materials, 2007.

G. Pijaudier-cabot and F. Dufour, Non local damage model, European Journal of Environmental and Civil Engineering, vol.310, issue.6-7, pp.6-7, 2010.
DOI : 10.1016/S0020-7683(98)00226-1
URL : https://hal.archives-ouvertes.fr/hal-00867880

F. Ragueneau, L. Borderie, C. Mazars, and J. , Damage model for concrete-like materials coupling cracking and friction, contribution towards structural damping: first uniaxial applications, Mechanics of Cohesive-frictional Materials, vol.3, issue.8, pp.607-626, 2000.
DOI : 10.1002/1099-1484(200011)5:8<607::AID-CFM108>3.0.CO;2-K

B. Richard and F. Ragueneau, Continuum damage mechanics based model for quasi brittle materials subjected to cyclic loadings: Formulation, numerical implementation and applications, Engineering Fracture Mechanics, vol.98, pp.383-406, 2013.
DOI : 10.1016/j.engfracmech.2012.11.013

L. Rojas-solano, D. Grégoire, and G. Pijaudier-cabot, Interaction-based non-local damage model for failure in quasi-brittle materials, Mechanics Research Communications, vol.54, pp.56-62, 2013.
DOI : 10.1016/j.mechrescom.2013.09.011
URL : https://hal.archives-ouvertes.fr/hal-00867464

A. Simone, G. N. Wells, and L. J. Sluys, From continuous to discontinuous failure in a gradient-enhanced continuum damage model, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.41-42, pp.41-424581, 2004.
DOI : 10.1016/S0045-7825(03)00428-6

S. Saroukhani, R. Vafadari, and A. Simone, A simplified implementation of a gradient-enhanced damage model with transient length scale effects, Computational Mechanics, vol.42, issue.14, pp.899-909, 2013.
DOI : 10.1007/s00466-012-0769-8

J. A. Sethian, Level set methods and Fast Marching Methods: evolving interfaces in computational geometry, Fluid Mechanics, Computer Vision and Materials Science, 1999.

A. Souid, F. Ragueneau, A. Delaplace, and R. Desmorat, Pseudodynamic testing and nonlinear substructuring of damaging structures under earthquake loading, Engineering Structures, pp.1102-1110, 2009.

R. Sheriff and L. Geldart, Exploration Seismology, 1995.
DOI : 10.1017/CBO9781139168359

N. Tsitsiklis, Efficient algorithms for globally optimal trajectories, IEEE Transactions on Automatic Control, vol.40, issue.9, pp.1528-1538, 1995.
DOI : 10.1109/9.412624

G. Wentzel, Eine Verallgemeinerung der Quantenbedingungen für die Zwecke der Wellenmechanik, pp.518-529, 1926.