A. Alliche and H. Dumontet, Anisotropic model of damage for geomaterials and concrete, International Journal for Numerical and Analytical Methods in Geomechanics, vol.26, issue.9, pp.969-979, 2011.
DOI : 10.1016/j.ijfatigue.2004.02.006

C. Amadio and M. Fragiacomo, A finite element model for the study of creep and shrinkage effects in composite beams with deformable shear connections, Costruzioni Metalliche, vol.4, pp.213-228, 1993.

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

P. Badel, V. Godard, and J. Leblond, Application of some anisotropic damage model to the prediction of the failure of some complex industrial concrete structure, International Journal of Solids and Structures, vol.44, issue.18-19, pp.5848-5874, 2007.
DOI : 10.1016/j.ijsolstr.2007.02.001

URL : https://hal.archives-ouvertes.fr/hal-00169822

H. Banon, H. M. Irvine, and J. M. Biggs, Seismic damage in reinforced concrete frames, J. Struct. Div, vol.107, issue.9, pp.1713-1729, 1981.

M. Brun, P. Labbé, D. Bertrand, and A. Courtois, Pseudo-dynamic tests on low-rise shear walls and simplified model based on the structural frequency drift, Engineering Structures, vol.33, issue.3, pp.796-812, 2010.
DOI : 10.1016/j.engstruct.2010.12.003

M. Brun, J. M. Reynouard, and L. Jezequel, A simple shear wall model taking into account stiffness degradation, Engineering Structures, vol.25, issue.1, pp.1-9, 2003.
DOI : 10.1016/S0141-0296(02)00084-6

D. Caillerie, Thin elastic and periodic plates, Mathematical Methods in the Applied Sciences, vol.2, issue.18, pp.159-191, 1984.
DOI : 10.1007/BFb0091528

D. Caillerie, 2D models of plate-like 3D elastic bodies In: Asymptotic Theories for Plates and Shells, Pitman Res. Notes in Math. S. Longman Sc. & Tech, vol.319, pp.28-34, 1995.

A. Carpinteri and A. Carpinteri, Hysteretic Behavior of RC Beams, Journal of Structural Engineering, vol.110, issue.9, pp.2073-2084, 1984.
DOI : 10.1061/(ASCE)0733-9445(1984)110:9(2073)

J. L. Chaboche, I. Milne, R. O. Ritchie, and B. Karihaloo, Damage Mechanics, Comprehensive Structural Integrity, pp.213-284, 2003.
DOI : 10.1016/B0-08-043749-4/02085-1

B. D. Coleman and M. Gurtin, Thermodynamics with internal variables, J. Chem. Phys, vol.48, issue.2, pp.597-613, 1967.
DOI : 10.1063/1.1711937

URL : http://repository.cmu.edu/cgi/viewcontent.cgi?article=1082&context=math

A. Dragon and Z. Mroz, A continuum model for plastic-brittle behaviour of rock and concrete, International Journal of Engineering Science, vol.17, issue.2, pp.121-137, 1979.
DOI : 10.1016/0020-7225(79)90058-2

M. N. Fardis, Seismic Design, Assessment and Retrofitting of Concrete Buildings, 2009.
DOI : 10.1007/978-1-4020-9842-0

C. R. Farrar and W. E. Baker, Measuring the stiffness of concrete shear walls during dynamic tests, Experimental Mechanics, vol.109, issue.5, pp.179-183, 1992.
DOI : 10.1007/BF02324730

P. H. Feenstra and R. De-borst, Constitutive Model for Reinforced Concrete, Journal of Engineering Mechanics, vol.121, issue.5, pp.587-595, 1995.
DOI : 10.1061/(ASCE)0733-9399(1995)121:5(587)

URL : https://repository.tudelft.nl/islandora/object/uuid%3A1524fa58-c77c-4f9c-8a78-c4ac66b519fa/datastream/OBJ/download

F. Gatuingt and G. Pijaudier-cabot, Coupled damage and plasticity modelling in transient dynamic analysis of concrete, International Journal for Numerical and Analytical Methods in Geomechanics, vol.37, issue.1, pp.1-24, 2002.
DOI : 10.1016/0029-5493(76)90015-7

URL : https://hal.archives-ouvertes.fr/hal-00994422

P. Germain, Mécanique des Milieux Continus, 1973.

P. Germain, The Method of Virtual Power in Continuum Mechanics. Part 2: Microstructure, SIAM Journal on Applied Mathematics, vol.25, issue.3, pp.556-575, 1973.
DOI : 10.1137/0125053

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

Y. Goto, Cracks formed in concrete around deformed tension bars, J. ACI, vol.68, issue.4, pp.224-251, 1971.

J. Guedes, P. Pegon, and A. Pinto, A fibre Timoshenko beam element in Castem2000, Special publication Nr. I.94.31, Joint Research Center, 1994.

B. Halphen and Q. S. Nguyen, Sur les matériaux standards généralisés, J. de Mécanique, vol.14, pp.39-63, 1975.

R. Hill, On Constitutive Macro-Variables for Heterogeneous Solids at Finite Strain, Proc. R. Soc. London, pp.131-147, 1972.
DOI : 10.1098/rspa.1972.0001

A. R. Ingraffea, W. H. Gerstk, P. Gergely, and V. Saouma, Fracture Mechanics of Bond in Reinforced Concrete, Journal of Structural Engineering, vol.110, issue.4, pp.871-890, 1984.
DOI : 10.1061/(ASCE)0733-9445(1984)110:4(871)

A. S. Kobayashi, N. M. Hawkins, Y. A. Chan, and I. J. Lin, A feasibility study of detecting reinforcing-bar debonding by acoustic-emission technique, Experimental Mechanics, vol.68, issue.4, pp.301-308, 1980.
DOI : 10.1007/BF02328623

P. Koechlin and S. Potapov, Global Constitutive Model for Reinforced Concrete Plates, Journal of Engineering Mechanics, vol.133, issue.3, pp.257-266, 2007.
DOI : 10.1061/(ASCE)0733-9399(2007)133:3(257)

URL : https://hal.archives-ouvertes.fr/hal-00086333

P. Kotronis, J. Mazars, and L. Davenne, The equivalent reinforced concrete model for simulating the behavior of walls under dynamic shear loading, Engineering Fracture Mechanics, vol.70, issue.7-8, pp.7-8, 2003.
DOI : 10.1016/S0013-7944(02)00167-4

URL : https://hal.archives-ouvertes.fr/hal-01009018

W. Krätzig and R. Polling, An elasto-plastic damage model for reinforced concrete with minimum number of material parameters, Computers & Structures, vol.82, issue.15-16, pp.1201-1215, 2004.
DOI : 10.1016/j.compstruc.2004.03.002

H. P. Lee, Shell finite element of reinforced concrete for internal pressure analysis of nuclear containment building, Nuclear Engineering and Design, vol.241, issue.2, pp.515-525, 2011.
DOI : 10.1016/j.nucengdes.2010.11.008

E. Lorentz and S. Andrieux, Analysis of nonlocal models through energetic formulations, Int. J. Solids Struct, vol.42, issue.12, pp.2905-2936, 2003.

E. Lorentz and V. Godard, Gradient damage models: Toward full-scale computations, Computer Methods in Applied Mechanics and Engineering, vol.200, issue.21-22, pp.21-221927, 1944.
DOI : 10.1016/j.cma.2010.06.025

K. Maekawa, A. Pimanmas, and H. Okamura, Nonlinear Mechanics of Reinforced Concrete, 2003.

D. Markovic, P. Koechlin, and F. Voldoire, Reinforced concrete structures under extreme loading: Stress resultant Global Reinforced Concrete Models (GLRC) In: COMPDYN, Comput. Meth. in Struct. Dyn. and Earthq. Eng, 2007.

P. Marti, M. Alvarez, W. Kaufmann, and V. Sigrist, Tension Chord Model for Structural Concrete, Structural Engineering International, vol.8, issue.4, pp.287-298, 1998.
DOI : 10.2749/101686698780488875

J. Mazars, P. Kotronis, and L. Davenne, A new modelling strategy for the behaviour of shear walls under dynamic loading, Earthquake Engineering & Structural Dynamics, vol.25, issue.4, pp.937-954, 2002.
DOI : 10.1080/12795119.1997.9692120

URL : https://hal.archives-ouvertes.fr/hal-01004915

E. Mörsch, Concrete-Steel Construction, 1909.

B. Nedjar, Elastoplastic-damage modelling including the gradient of damage: formulation and computational aspects, International Journal of Solids and Structures, vol.38, issue.30-31, pp.5421-5451, 2001.
DOI : 10.1016/S0020-7683(00)00358-9

D. Ngo and A. C. Scoderlis, Finite element analysis of reinforced concrete beams, ACI J, vol.64, pp.152-163, 1967.

H. Okamura and I. H. Kim, Seismic performance check and size effect FEM analysis of reinforced concrete, Engineering Fracture Mechanics, vol.65, issue.2-3, pp.369-389, 2000.
DOI : 10.1016/S0013-7944(99)00122-8

I. R. Pascu, Contribution à l'analyse d'éléments en béton armé sollicités en membrane et flexion bi-axiale, 1995.

P. Peric´, D. De-souza-neto, E. A. Feijóo, R. A. Partovi, M. et al., On micro-to-macro transitions for multi-scale analysis of non-linear heterogeneous materials: unified variational basis and finite element implementation, Int. J. Numer. Methods Eng, vol.87, pp.1-5, 2011.

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)

M. Pimentel, E. Brüwhiler, and J. Figueiras, Extended cracked membrane model for the analysis of RC panels, Engineering Structures, vol.32, issue.8, pp.1964-1975, 2010.
DOI : 10.1016/j.engstruct.2010.02.030

H. Reinhardt, H. Cornelissen, and D. Hordijk, Tensile Tests and Failure Analysis of Concrete, Journal of Structural Engineering, vol.112, issue.11, pp.2462-2477, 1986.
DOI : 10.1061/(ASCE)0733-9445(1986)112:11(2462)

E. Rumanus and G. Meschke, Homogenization-based modeling of reinforced concrete in the context of durability-oriented analyses, ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, 2007.

E. Rumanus and G. Meschke, Modeling of reinforced concrete by means of homogenization approach including steel?concrete interactions, p.8, 2008.

A. Rutenberg, Simplified P-Delta analysis for asymmetric structures, ASCE J. Struct. Div, vol.1089, 1982.

E. Sanchez-palencia, Non-Homogeneous Media and Vibration Theory, 1980.

E. Sanchez-palencia, A. Zaoui, and P. Suquet, Homogenization Technique for Composite Media, 1987.
DOI : 10.1007/3-540-17616-0

S. A. Sheikh and S. M. Uzumeri, Analytical model for concrete confinement in tied columns, ASCE J. Struct. Div, vol.108, issue.12, pp.2703-2722, 1982.

R. G. Selby and F. J. Vecchio, A constitutive model for analysis of reinforced concrete solids. Can, J. Civ. Eng, vol.24, pp.460-470, 1997.

J. F. Shao, Y. Jia, D. Kondo, and A. S. Chiarelli, A coupled elastoplastic damage model for semi-brittle materials and extension to unsaturated conditions, Mechanics of Materials, vol.38, issue.3, pp.218-232, 2006.
DOI : 10.1016/j.mechmat.2005.07.002

URL : https://hal.archives-ouvertes.fr/hal-00021987

M. Soltani, X. An, and K. Maekawa, Computational model for post cracking analysis of RC membrane elements based on local stress???strain characteristics, Engineering Structures, vol.25, issue.8, pp.993-1007, 2003.
DOI : 10.1016/S0141-0296(03)00042-7

M. Soltani, X. An, and K. Maekawa, Localized nonlinearity and size-dependent mechanics of in-plane RC element in shear, Engineering Structures, vol.27, issue.6, pp.891-908, 2005.
DOI : 10.1016/j.engstruct.2005.01.011

E. Spacone, F. C. Filippou, and F. F. Taucer, FIBRE BEAM-COLUMN MODEL FOR NON-LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION, Earthquake Engineering & Structural Dynamics, vol.25, issue.7, pp.711-725, 1996.
DOI : 10.1002/(SICI)1096-9845(199607)25:7<711::AID-EQE576>3.0.CO;2-9

E. Spacone and S. El-tawil, Nonlinear Analysis of Steel-Concrete Composite Structures: State of the Art, Journal of Structural Engineering, vol.130, issue.2, pp.159-168, 2004.
DOI : 10.1061/(ASCE)0733-9445(2004)130:2(159)

C. Stolz, On Micro-Macro Transition in Non-Linear Mechanics, Materials, vol.21, issue.12, pp.296-317, 2010.
DOI : 10.1016/S0065-2156(08)70330-2

URL : https://hal.archives-ouvertes.fr/hal-00456089

P. Suquet, Overall potentials and extremal surfaces of power law or ideally plastic composites, Journal of the Mechanics and Physics of Solids, vol.41, issue.6, pp.981-1002, 1993.
DOI : 10.1016/0022-5096(93)90051-G

F. J. Vecchio and M. P. Collins, Modified compression field theory for reinforced concrete elements subjected to shear, ACI J, vol.83, pp.219-231, 1986.

T. Takeda, M. A. Sozen, and N. Nielsen, Reinforced concrete response to simulated earthquakes, J. Struct. Div, vol.96, issue.12, pp.2557-2573, 1970.