P. Gosselet and C. Rey, Non-overlapping domain decomposition methods in structural mechanics, Archives of Computational Methods in Engineering, vol.48, issue.2, pp.515-572, 2006.
DOI : 10.1007/BF02905857

URL : https://hal.archives-ouvertes.fr/hal-01224408

T. J. Hughes, G. R. Feijoo, L. Mazzei, and J. B. Quincy, The variational multiscale method???a paradigm for computational mechanics, Computer Methods in Applied Mechanics and Engineering, vol.166, issue.1-2, pp.166-169, 1998.
DOI : 10.1016/S0045-7825(98)00079-6

H. B. Dhia and G. Rateau, The Arlequin method as a flexible engineering design tool, International Journal for Numerical Methods in Engineering, vol.193, issue.11, pp.1442-1462, 2005.
DOI : 10.1002/nme.1229

URL : https://hal.archives-ouvertes.fr/hal-00018915

E. Sanchez-palencia, Comportements local et macroscopique d'un type de milieux physiques heterogenes, International Journal of Engineering Science, vol.12, issue.4, pp.231-251, 1974.
DOI : 10.1016/0020-7225(74)90062-7

E. Sanchez-palencia, Non homogeneous media and vibration theory, Lecture Notes in Physics, vol.127, 1980.

F. Devries, H. Dumontet, G. Duvaut, and F. Léné, Homogenization and damage for composite structures, International Journal for Numerical Methods in Engineering, vol.11, issue.2, pp.285-298, 1989.
DOI : 10.1002/nme.1620270206

T. I. Zohdi, J. T. Oden, and G. J. Rodin, Hierarchical modeling of heterogeneous bodies, Computer Methods in Applied Mechanics and Engineering, vol.138, issue.1-4, pp.1-4, 1996.
DOI : 10.1016/S0045-7825(96)01106-1

J. T. Oden, K. Vemaganti, and N. Moës, Hierarchical modeling of heterogeneous solids, Computer Methods in Applied Mechanics and Engineering, vol.172, issue.1-4, pp.1-4, 1999.
DOI : 10.1016/S0045-7825(98)00224-2

URL : https://hal.archives-ouvertes.fr/hal-01006923

J. Fish, K. Shek, M. Pandheeradi, and M. S. Shephard, Computational plasticity for composite structures based on mathematical homogenization: Theory and practice, Computer Methods in Applied Mechanics and Engineering, vol.148, issue.1-2, pp.148-53, 1997.
DOI : 10.1016/S0045-7825(97)00030-3

M. Lefik and B. A. Schrefler, Modelling of nonstationary heat conduction problems in micro-periodic composites using homogenisation theory with corrective terms, Arch. Mech, vol.52, issue.2, pp.203-223, 2000.

D. Dureisseix and D. Néron, A multiscale computational approach with field transfer dedicated to coupled problems, Int. J. Multiscale Comput. Eng, vol.6, issue.3, pp.233-250, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00330016

H. Dumontet, Homogénéisation et effets de bords dans les composites, Thèse d'état, 1990.

M. Haboussi, H. Dumontet, and J. L. Billoët, On the modelling of interfacial transition behaviour in composite materials, Computational Materials Science, vol.20, issue.2, pp.251-266, 2001.
DOI : 10.1016/S0927-0256(00)00183-X

C. Huet, Application of variational concepts to size effects in elastic heterogeneous bodies, Journal of the Mechanics and Physics of Solids, vol.38, issue.6, pp.813-841, 1990.
DOI : 10.1016/0022-5096(90)90041-2

V. G. Kouznetsova, M. G. Geers, and W. A. Brekelmans, Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme, International Journal for Numerical Methods in Engineering, vol.42, issue.8, pp.1235-1260, 2002.
DOI : 10.1002/nme.541

T. Zohdi and P. Wriggers, Introduction to Computational Micromechanics, 2005.
DOI : 10.1007/978-3-540-32360-0

S. Ghosh, K. Lee, and S. Moorthy, Two scale analysis of heterogeneous elastic?plastic materials with asymptotic homogenization and voronoï cell finite element method, Comput. Methods Appl. Mech. Eng, pp.132-63, 1996.

R. Niekamp, D. Markovic, A. Ibrahimbegovic, H. G. Matthies, and R. L. Taylor, Multi-scale modeling of heterogeneous structures with inelastic constitutive behaviour?part ii: software coupling and implementation aspects, Eng. Comput, pp.26-32, 2009.

Y. Maday and E. M. Ronquist, The Reduced Basis Element Method: Application to a Thermal Fin Problem, SIAM Journal on Scientific Computing, vol.26, issue.1, pp.240-258, 2004.
DOI : 10.1137/S1064827502419932

URL : https://hal.archives-ouvertes.fr/hal-00021699

K. Kunisch and L. Xie, POD-based feedback control of the burgers equation by solving the evolutionary HJB equation, Computers & Mathematics with Applications, vol.49, issue.7-8, pp.7-8, 2005.
DOI : 10.1016/j.camwa.2004.07.022

T. Lieu, C. Farhat, and A. Lesoinne, Reduced-order fluid/structure modeling of a complete aircraft configuration, Computer Methods in Applied Mechanics and Engineering, vol.195, issue.41-43, pp.41-43, 2006.
DOI : 10.1016/j.cma.2005.08.026

M. D. Gunzburger, J. S. Peterson, and J. N. Shadid, Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.4-6, pp.4-6, 2007.
DOI : 10.1016/j.cma.2006.08.004

M. Bergmann and L. L. Cordier, Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models, Journal of Computational Physics, vol.227, issue.16, pp.7813-7840, 2008.
DOI : 10.1016/j.jcp.2008.04.034

URL : https://hal.archives-ouvertes.fr/hal-00368500

G. Rozza, Abstract, Communications in Computational Physics, vol.32, issue.01, pp.1-48, 2011.
DOI : 10.1090/S0025-5718-1985-0804937-0

K. Carlberg, C. Bou-mosleh, and C. Farhat, Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations, International Journal for Numerical Methods in Engineering, vol.35, issue.2, pp.155-181, 2011.
DOI : 10.1002/nme.3050

J. A. Hernández, J. Oliver, A. E. Huespe, M. A. Caicedo, and J. C. Cante, High-performance model reduction techniques in computational multi scale homogenization, Comput. Methods Appl. Mech. Eng, 2013.

P. Ladevèze, Nonlinear Computational Structural Mechanics ? New Approaches and Non-incremental Methods of Calculation, 1999.

A. Nouy, A priori model reduction through Proper Generalized Decomposition for solving time-dependent partial differential equations, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.23-24, pp.23-24, 2010.
DOI : 10.1016/j.cma.2010.01.009

URL : https://hal.archives-ouvertes.fr/hal-00455635

B. Bognet, F. Bordeu, F. Chinesta, A. Leygue, and A. Poitou, Advanced simulation of models defined in plate geometries: 3D solutions with 2D computational complexity, Computer Methods in Applied Mechanics and Engineering, vol.201, issue.204, pp.1-12, 2012.
DOI : 10.1016/j.cma.2011.08.025

URL : https://hal.archives-ouvertes.fr/hal-01462825

A. Nouy, Recent Developments in Spectral Stochastic Methods for??the??Numerical Solution of Stochastic Partial Differential Equations, Archives of Computational Methods in Engineering, vol.24, issue.2, pp.251-285, 2009.
DOI : 10.1007/s11831-009-9034-5

URL : https://hal.archives-ouvertes.fr/hal-00366636

A. Ammar, F. Chinesta, E. Cueto, and M. Doblaré, Proper generalized decomposition of time-multiscale models, International Journal for Numerical Methods in Engineering, vol.26, issue.6, pp.569-596, 2012.
DOI : 10.1002/nme.3331

URL : https://hal.archives-ouvertes.fr/hal-01007223

. Ch, F. Ghnatios, A. Masson, A. Huerta, E. Leygue et al., Proper generalized decomposition based dynamic data-driven control of thermal processes, Comput. Methods Appl. Mech. Eng, pp.213-242, 2012.

D. Gonzalez, F. Masson, F. Poulhaon, A. Leygue, E. Cueto et al., Proper Generalized Decomposition based dynamic data driven inverse identification, Mathematics and Computers in Simulation, vol.82, issue.9, pp.1677-1695, 2012.
DOI : 10.1016/j.matcom.2012.04.001

F. Chinesta, P. Ladevèze, and E. Cueto, A Short Review on Model Order Reduction Based on Proper Generalized Decomposition, Archives of Computational Methods in Engineering, vol.69, issue.9, pp.395-404, 2011.
DOI : 10.1007/s11831-011-9064-7

URL : https://hal.archives-ouvertes.fr/hal-01004940

P. Ladevèze and A. Nouy, On a multiscale computational strategy with time and space homogenization for structural mechanics, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.28-30, 2003.
DOI : 10.1016/S0045-7825(03)00341-4

P. Ladevèze, J. Passieux, and D. Néron, The LATIN multiscale computational method and the Proper Generalized Decomposition, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.21-22, 2010.
DOI : 10.1016/j.cma.2009.06.023

J. Dolbow, N. Moes, and T. Belytschko, An extended finite element method for modeling crack growth with frictional contact, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.51-52, pp.51-52, 2001.
DOI : 10.1016/S0045-7825(01)00260-2

URL : https://hal.archives-ouvertes.fr/hal-01461932

R. Ribeaucourt, M. Baietto-dubourg, and A. , A new fatigue frictional contact crack propagation model with the coupled X-FEM/LATIN method, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.33-34, pp.33-34, 2007.
DOI : 10.1016/j.cma.2007.03.004

URL : https://hal.archives-ouvertes.fr/hal-00380802

D. Néron and D. , A computational strategy for poroelastic problems with a time interface between coupled physics, International Journal for Numerical Methods in Engineering, vol.195, issue.44-47, pp.783-804, 2008.
DOI : 10.1002/nme.2091

D. Néron and D. Dureisseix, A computational strategy for thermo-poroelastic structures with a time-space interface coupling, International Journal for Numerical Methods in Engineering, vol.15, issue.4, pp.1053-1084, 2008.
DOI : 10.1002/nme.2283

. Ch, P. Heyberger, D. Boucard, and . Néron, A rational strategy for the resolution of parametrized problems in the PGD framework, Comput. Methods Appl. Mech. Eng, vol.259, pp.40-49, 2013.

A. Nouy and P. Ladevèze, Multiscale Computational Strategy With Time and Space Homogenization: A Radial-Type Approximation Technique for Solving Microproblems, International Journal for Multiscale Computational Engineering, vol.2, issue.4, pp.557-574, 2004.
DOI : 10.1615/IntJMultCompEng.v2.i4.40

URL : https://hal.archives-ouvertes.fr/hal-00368058

D. Néron and P. Ladevèze, Proper Generalized Decomposition for Multiscale and??Multiphysics Problems, Archives of Computational Methods in Engineering, vol.193, issue.1???4, pp.351-372, 2010.
DOI : 10.1007/s11831-010-9053-2

H. Lamari, A. Ammar, P. Cartraud, G. Legrain, F. Chinesta et al., Routes for Efficient Computational Homogenization of??Nonlinear Materials Using the??Proper Generalized Decompositions, Archives of Computational Methods in Engineering, vol.198, issue.33???36, pp.373-391, 2010.
DOI : 10.1007/s11831-010-9051-4

F. Halabi, D. González, A. Chico, and M. Doblaré, FE2 multiscale in linear elasticity based on parametrized microscale models using proper generalized decomposition, Computer Methods in Applied Mechanics and Engineering, vol.257, pp.257-183, 2013.
DOI : 10.1016/j.cma.2013.01.011

N. Relun, D. Néron, and P. A. Boucard, Multiscale elastic-viscoplastic computational analysis. A detailed example, Revue europ??enne de m??canique num??rique, vol.20, issue.7-8, pp.7-8
DOI : 10.3166/ejcm.20.379-409

N. Relun, D. Néron, and P. Boucard, A model reduction technique based on the PGD for elastic-viscoplastic computational analysis, Computational Mechanics, vol.20, issue.7???8, pp.83-92, 2013.
DOI : 10.1007/s00466-012-0706-x

R. Glowinski and P. L. Tallec, Augmented lagrangian interpretation of the nonoverlapping Schwartz alternating method, Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, pp.224-231, 1990.

J. Passieux, P. Ladevèze, and D. Néron, A scalable time???space multiscale domain decomposition method: adaptive time scale separation, Computational Mechanics, vol.39, issue.32???33, pp.621-633, 2010.
DOI : 10.1007/s00466-010-0504-2

P. A. Guidault, O. Allix, L. Champaney, and C. Cornuault, A multiscale extended finite element method for crack propagation, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.5, pp.381-399, 2008.
DOI : 10.1016/j.cma.2007.07.023