W. Aggoune, H. Zahrouni, and M. Potier-ferry, Asymptotic numerical methods for unilateral contact, International Journal for Numerical Methods in Engineering, vol.1, issue.6, pp.605-631, 2006.
DOI : 10.1002/nme.1714

G. Alfano, M. A. Et, and . Crisfield, Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues, International Journal for Numerical Methods in Engineering, vol.26, issue.7, pp.1701-1736, 2001.
DOI : 10.1002/nme.93

G. Alfano, M. A. Et, and . Crisfield, Solution strategies for the delamination analysis based on a combination of local-control arc-length and line searches, International Journal for Numerical Methods in Engineering, vol.26, issue.7, pp.999-1048, 2003.
DOI : 10.1002/nme.806

O. Allix, Délaminage : approche par la mécanique de l'endommagement, 1987.

J. Dans, P. Fouet, E. R. Ladevèze, and . Ohayon, First Colloquium GRECO- GIS Calcul des Structures Giens, Calcul des Structures et Intelligence Artificielle, pp.39-53, 1987.

O. Allix, The damage mesomodel for laminates : Interface identification and application to delamination, Course of Emerging Techniques for Damage Prediction and Failure Analysis of Composite Structures. Cépaduès éditions, 2008.

O. Allix, A. Et, and . Corigliano, Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens, International Journal of Fracture, vol.13, issue.1, pp.111-140, 1996.
DOI : 10.1007/BF00037233

O. Allix, A. Et, and . Corigliano, Geometrical and interfacial non-linearities in the analysis of delamination in composites, International Journal of Solids and Structures, vol.36, issue.15, pp.2189-2216, 1999.
DOI : 10.1016/S0020-7683(98)00079-1

O. Allix, P. Kerfriden, and E. P. Gosselet, On the control of the load increments for a proper description of multiple delamination in a domain decomposition framework, International Journal for Numerical Methods in Engineering, vol.77, issue.6, pp.1518-1540, 2010.
DOI : 10.1002/nme.2884
URL : https://hal.archives-ouvertes.fr/hal-00537803

O. Allix, P. Et, and . Ladevèze, Interlaminar interface modelling for the prediction of delamination, Composite Structures, vol.22, issue.4, pp.235-242, 1992.
DOI : 10.1016/0263-8223(92)90060-P

O. Allix, P. Ladevèze, and E. A. Corigliano, Damage analysis of interlaminar fracture specimens, Composite Structures, vol.31, issue.1, pp.61-74, 1995.
DOI : 10.1016/0263-8223(95)00002-X

O. Allix, D. Lévêque, and E. L. Perret, Identification and forecast of delamination in composite laminates by an interlaminar interface model, Composites Science and Technology, vol.58, issue.5, pp.671-678, 1998.
DOI : 10.1016/S0266-3538(97)00144-9

J. S. Arora, A. I. Chahande, and J. K. Paeng, Multiplier methods for engineering optimization, International Journal for Numerical Methods in Engineering, vol.27, issue.7, pp.1485-1525, 1991.
DOI : 10.1002/nme.1620320706
URL : https://hal.archives-ouvertes.fr/hal-01352827

L. Azrar, B. Cochelin, N. Damil, and M. Potier-ferry, An asymptotic-numerical method to compute the postbuckling behaviour of elastic plates and shells, International Journal for Numerical Methods in Engineering, vol.13, issue.8, pp.1251-1277, 1993.
DOI : 10.1002/nme.1620360802

G. I. Barenblatt, The Mathematical Theory of Equilibrium Cracks in Brittle Fracture, pp.55-129, 1962.
DOI : 10.1016/S0065-2156(08)70121-2

K. J. Bathe, Finite Element Procedures, 2007.

K. J. Bathe, E. Ramm, and E. L. Wilson, Finite element formulations for large deformation dynamic analysis, International Journal for Numerical Methods in Engineering, vol.7, issue.2, pp.353-386, 1975.
DOI : 10.1002/nme.1620090207
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.208.5272

J. L. Batoz, G. Et, and . Dhatt, Incremental displacement algorithms for nonlinear problems, International Journal for Numerical Methods in Engineering, vol.14, issue.8, pp.1262-1267, 1979.
DOI : 10.1002/nme.1620140811

T. Belytschko, L. W. Et, and . Glaum, Applications of higher order corotational stretch theories to nonlinear finite element analysis, Computers & Structures, vol.10, issue.1-2, pp.175-182, 1979.
DOI : 10.1016/0045-7949(79)90085-3

T. Belytschko, W. Liu, and E. B. Moran, Nonlinear finite elements for continua and structures, 2000.

B. Dhia and H. , Problèmes mécaniques multi-échelles : la méthode arlequin. Comptes Rendus de l, Académie des Sciences, vol.326, pp.899-904, 1998.

B. Dhia, H. Et, and O. Jamond, On the use of XFEM within the Arlequin framework for the simulation of crack propagation, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.1403-1414, 2010.
DOI : 10.1016/j.cma.2009.11.014
URL : https://hal.archives-ouvertes.fr/hal-00422595

J. Bernoulli, Curvatura laminae elasticae, Acta Eruditorum Lipsiae, pp.262-276, 1694.

M. Biot, Theory of elasticity with large displacements and rotations, Proc. 5th Int, p.117, 1938.
URL : https://hal.archives-ouvertes.fr/hal-01369405

P. Boisse, P. Ladevèze, and E. P. Rougée, A large time increment method for elastoplastic problems, European Journal of Mechanics -A/Solids, vol.8, issue.4, pp.257-275, 1989.

V. V. Bolotin, Mechanics of delaminations in laminate composite structures, Mechanics of Composite Materials, vol.37, issue.5/6, pp.367-380, 2001.
DOI : 10.1023/A:1014210527476

W. J. Bottega, A. Et, and . Maewal, Delamination Buckling and Growth in Laminates, Journal of Applied Mechanics, vol.50, issue.1, pp.184-189, 1983.
DOI : 10.1115/1.3166988

P. Boucard, P. Ladevèze, M. Poss, and E. P. Rougée, A nonincremental approach for large displacement problems, Computers & Structures, vol.64, issue.1-4, pp.1-4, 1997.
DOI : 10.1016/S0045-7949(96)00165-4

A. Brandt, Guide to multigrid development, Conference on Multigrid Methods, pp.220-312, 1982.
DOI : 10.1016/0146-664X(81)90046-0

J. C. Brewer, P. A. Et, and . Lagace, Quadratic Stress Criterion for Initiation of Delamination, Journal of Composite Materials, vol.8, issue.12, pp.1141-1155, 1988.
DOI : 10.1177/002199838802201205

D. Bruno, F. Et, and . Greco, An asymptotic analysis of delamination buckling and growth in layered plates, International Journal of Solids and Structures, vol.37, issue.43, pp.6239-6276, 2000.
DOI : 10.1016/S0020-7683(99)00281-4

D. Bruno, A. Et, and . Grimaldi, Delamination failure of layered composite plates loaded in compression, International Journal of Solids and Structures, vol.26, issue.3, pp.313-330, 1990.
DOI : 10.1016/0020-7683(90)90043-U

G. H. Bryan, On the stability of elastic systems, Proc. Cambr, 0199.

G. H. Bryan, On the buckling of simply supported rectangular plates uniformly compressed in one direction, Proc. London Math. Soc. 22, p.54, 1891.

B. Budiansky, J. W. Et, and . Hutchinson, Dynamic buckling of imperfectionsensitive structures, of Engineering and applied physics, 1964.

P. Bussy, P. Rougée, and E. P. Vauchez, The large time increment method for numerical simulation of metal fonning processes, Dans Numerical Methods in Engineering, pp.102-109, 1990.

N. J. Carpenter, R. L. Taylor, and M. G. Katona, Lagrange constraints for transient finite element surface contact, International Journal for Numerical Methods in Engineering, vol.1, issue.1, pp.103-128, 1991.
DOI : 10.1002/nme.1620320107
URL : https://hal.archives-ouvertes.fr/hal-01389918

H. Chai, C. D. Babcock, and W. G. Knauss, One dimensional modelling of failure in laminated plates by delamination buckling, International Journal of Solids and Structures, vol.17, issue.11, pp.1069-1083, 1981.
DOI : 10.1016/0020-7683(81)90014-7

L. Champaney, J. Y. Cognard, and E. P. Ladèveze, Modular analysis of assemblages of three-dimensional structures with unilateral contact conditions, Computers & Structures, vol.73, issue.1-5, pp.1-5, 1999.
DOI : 10.1016/S0045-7949(98)00285-5

Z. Chen and H. L. Schreyer, A numerical solution scheme for softening problems involving total strain control, Computers & Structures, vol.37, issue.6, pp.1043-1050, 1990.
DOI : 10.1016/0045-7949(90)90016-U

G. P. Cherepanov, Crack propagation in continuous media, Journal of Applied Mathematics and Mechanics, vol.31, issue.3, pp.476-488, 1967.
DOI : 10.1016/0021-8928(67)90034-2

B. Cochelin and N. Damil, Méthode asymptotique numérique, 1997.

B. Cochelin, M. Et, and . Potier-ferry, A numerical model for buckling and growth of delaminations in composite laminates, Computer Methods in Applied Mechanics and Engineering, vol.89, issue.1-3, pp.1-3, 1991.
DOI : 10.1016/0045-7825(91)90048-B

J. Cognard, Une nouvelle approche des problèmes de plasticité et de viscoplasticité : la Méthode à Grand Incrément de Temps, Thèse de doctorat, 1989.

J. Cognard, D. Dureisseix, P. Lavedèze, and E. P. Lorong, Exp??rimentation d'une approche parall??le en calcul des structures, Revue Europ??enne des ??l??ments Finis, vol.49, issue.6, pp.197-220, 1996.
DOI : 10.1080/12506559.1996.10511217

A. Combescure, Etude de la stabilité non-linéaire géométrique et non-linéaire matériau des coques minces. Application aux coques de révolution avec imperfections soumises à des chargements complexes, 1995.

A. Corigliano, Formulation, identification and use of interface models in the numerical analysis of composite delamination, International Journal of Solids and Structures, vol.30, issue.20, pp.2779-2811, 1993.
DOI : 10.1016/0020-7683(93)90154-Y

A. Corigliano and O. Allix, Some aspects of interlaminar degradation in composites, Computer Methods in Applied Mechanics and Engineering, vol.185, issue.2-4, pp.2-4, 2000.
DOI : 10.1016/S0045-7825(99)00260-1

P. Cornetti, N. Pugno, A. Carpinteri, and E. D. Taylor, Finite fracture mechanics: A coupled stress and energy failure criterion, Engineering Fracture Mechanics, vol.73, issue.14, pp.2021-2033, 2006.
DOI : 10.1016/j.engfracmech.2006.03.010
URL : http://porto.polito.it/1398750/1/EFM5.pdf

H. L. Cox, The buckling of thin plates in compression, Aeron. Res. Comm., R. and M, p.1554, 1934.

P. Cresta, O. Allix, C. Rey, and E. S. Guinard, Nonlinear localization strategies for domain decomposition methods: Application to post-buckling analyses, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.8, pp.1436-1446, 2007.
DOI : 10.1016/j.cma.2006.03.013
URL : https://hal.archives-ouvertes.fr/hal-00118192

M. A. Crisfield, A fast incremental/iterative solution procedure that handles ???snap-through???, Computers & Structures, vol.13, issue.1-3, pp.55-62, 1981.
DOI : 10.1016/0045-7949(81)90108-5

M. A. Crisfield, A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements, Computer Methods in Applied Mechanics and Engineering, vol.81, issue.2, pp.131-150, 1990.
DOI : 10.1016/0045-7825(90)90106-V

N. Damil, M. Et, and . Potier-ferry, A New method to compute perturbed bifurcations: Application to the buckling of imperfect elastic structures, International Journal of Engineering Science, vol.28, issue.9, pp.943-957, 1990.
DOI : 10.1016/0020-7225(90)90043-I

L. Daridon, K. Et, and . Zidani, The stabilizing effects of fiber bridges on delamination cracks, Composites Science and Technology, vol.62, issue.1, pp.83-90, 2002.
DOI : 10.1016/S0266-3538(01)00181-6

L. Daudeville, P. Et, and . Ladevèze, A damage mechanics tool for laminate delamination, Composite Structures, vol.25, issue.1-4, pp.547-555, 1993.
DOI : 10.1016/0263-8223(93)90203-3

D. Borst and R. , Computation of post-bifurcation and post-failure behavior of strain-softening solids, Computers & Structures, vol.25, issue.2, pp.211-224, 1987.
DOI : 10.1016/0045-7949(87)90144-1

P. Destuynder, P. E. Djaoua, L. Chesnay, and J. C. Nedelec, Sur une Interpr??tation Math??matique de l'Int??grale de Rice en Th??orie de la Rupture Fragile, Mathematical Methods in the Applied Sciences, vol.III, issue.1, pp.70-87, 1981.
DOI : 10.1002/mma.1670030106

C. Dohrmann, A Preconditioner for Substructuring Based on Constrained Energy Minimization, SIAM Journal on Scientific Computing, vol.25, issue.1, pp.246-258, 2003.
DOI : 10.1137/S1064827502412887

L. H. Donnell, C. C. Et, and . Wan, Effect of imperfections on buckling of thin cylinders and columns under axial compression, Journal of Applied Mechanics, vol.17, pp.73-83, 1950.

D. S. Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids, vol.8, issue.2, pp.100-104, 1960.
DOI : 10.1016/0022-5096(60)90013-2

D. Dureisseix, P. Et, and . Ladevèze, Une approche parall??le et multi-??chelles en calcul des structures : exemples et performances, Revue Europ??enne des ??l??ments Finis, vol.7, issue.1-3, pp.73-87, 1997.
DOI : 10.1080/12506559.1998.11690466

G. Duvaut, J. L. Et, and . Lions, Les inéquations en mécanique et en physique, 1972.

L. Euler, Methodus inveniendi lineas curvas : maximi minimive propietate gaudentes, sive solutio problematis isoperimetrici latissimo sensu accepti, 1744.

A. G. Evans, J. W. Et, and . Hutchinson, On the mechanics of delamination and spalling in compressed films, International Journal of Solids and Structures, vol.20, issue.5, pp.455-466, 1984.
DOI : 10.1016/0020-7683(84)90012-X

C. Farhat, M. Lesoinne, and E. K. Pierson, A scalable dual-primal domain decomposition method, Numerical Linear Algebra with Applications, vol.46, issue.7-8, pp.687-714, 2000.
DOI : 10.1002/1099-1506(200010/12)7:7/8<687::AID-NLA219>3.0.CO;2-S

C. Farhat, F. Et, and . Roux, A method of finite element tearing and interconnecting and its parallel solution algorithm, International Journal for Numerical Methods in Engineering, vol.28, issue.6, pp.1205-1227, 1991.
DOI : 10.1002/nme.1620320604

C. Farhat, F. X. Et, and . Roux, An Unconventional Domain Decomposition Method for an Efficient Parallel Solution of Large-Scale Finite Element Systems, SIAM Journal on Scientific and Statistical Computing, vol.13, issue.1, pp.379-396, 1992.
DOI : 10.1137/0913020

C. Farhat, F. X. Et, and . Roux, Implicit parallel processing in structural mechanics, Comput. Mech. Adv, vol.2, pp.1-124, 1994.

R. Fedorenko, The speed of convergence of one iterative process, USSR Computational Mathematics and Mathematical Physics, vol.4, issue.3, pp.227-235, 1964.
DOI : 10.1016/0041-5553(64)90253-8

C. A. Felippa and B. Haugen, A unified formulation of small-strain corotational finite elements: I. Theory, Computer Methods in Applied Mechanics and Engineering, vol.194, issue.21-24, pp.21-24, 2005.
DOI : 10.1016/j.cma.2004.07.035

F. Feyel, J. Et, and . Chaboche, FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials, Computer Methods in Applied Mechanics and Engineering, vol.183, issue.3-4, pp.309-330, 2000.
DOI : 10.1016/S0045-7825(99)00224-8

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.53-73, 1997.
DOI : 10.1016/S0045-7825(97)00030-3

G. Francfort, J. Et, and . Marigo, Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, vol.46, issue.8, pp.1319-1342, 1998.
DOI : 10.1016/S0022-5096(98)00034-9

K. O. Friedrichs, J. J. Et, and . Stoker, The Non-Linear Boundary Value Problem of the Buckled Plate, American Journal of Mathematics, vol.63, issue.4, pp.839-888, 1941.
DOI : 10.2307/2371625

M. Geers, V. Kouznetsova, and E. W. Brekelmans, Multi-scale computational homogenization: Trends and challenges, Journal of Computational and Applied Mathematics, vol.234, issue.7, pp.2175-2182, 2010.
DOI : 10.1016/j.cam.2009.08.077

M. G. Geers, Enhanced solution control for physically and geometrically non-linear problems. Part I?the subplane control approach, International Journal for Numerical Methods in Engineering, vol.160, issue.2, pp.177-204, 1999.
DOI : 10.1002/(SICI)1097-0207(19990920)46:2<177::AID-NME668>3.0.CO;2-L
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.524.3318

L. Gendre, O. Allix, P. Gosselet, and E. F. Comte, Non-intrusive and exact global/local techniques for structural problems with local plasticity, Computational Mechanics, vol.36, issue.1, pp.233-245, 2009.
DOI : 10.1007/s00466-009-0372-9
URL : https://hal.archives-ouvertes.fr/hal-00437023

P. Germain, Introduction à la mécanique des milieux continus, 1968.

S. Ghosh, K. Lee, and E. S. Moorthy, Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method, International Journal of Solids and Structures, vol.32, issue.1, pp.27-62, 1995.
DOI : 10.1016/0020-7683(94)00097-G

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

P. Gosselet, C. Et, and . Rey, On a selective reuse of Krylov subspaces in Newton- Krylov approaches for nonlinear elasticity, 14th Conference on Domain Decomposition methods, pp.419-426, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00277780

P. Gosselet, C. Et, and . 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

A. A. Griffith, The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.221, issue.582-593, pp.163-198, 1921.
DOI : 10.1098/rsta.1921.0006

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

Z. Hashin, Finite thermoelastic fracture criterion with application to laminate cracking analysis, Journal of the Mechanics and Physics of Solids, vol.44, issue.7, pp.1129-1145, 1996.
DOI : 10.1016/0022-5096(95)00080-1

T. K. Hellen, On the method of virtual crack extensions, International Journal for Numerical Methods in Engineering, vol.85, issue.1, pp.187-207, 1975.
DOI : 10.1002/nme.1620090114

M. R. Hestenes, Multiplier and gradient methods, Journal of Optimization Theory and Applications, vol.4, issue.5, pp.303-320, 1969.
DOI : 10.1007/BF00927673

A. Hillerborg, M. Modéer, and P. E. 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.773-781, 1976.
DOI : 10.1016/0008-8846(76)90007-7

J. Hinojosa, O. Allix, P. A. Guidault, and E. P. Cresta, On the robustness of a mixed domain decomposition method with nonlinear relocalization for handling geometrical instabilities, Comp. Meth. in Applied Mech, 2011.
URL : https://hal.archives-ouvertes.fr/tel-00745225

J. W. Hutchinson, W. T. Et, and . Koiter, Postbuckling theory, Applied Mechanics Reviews, vol.23, issue.12, pp.1353-1366, 1970.

G. Irwin, Analysis of stresses and strains near the end of crack traversing a plate, Journal of Applied Mechanics, vol.24, pp.361-364, 1957.

M. Jamal, L. Lahlou, M. Midani, H. Zahrouni, A. Limam et al., A semi-analytical buckling analysis of imperfect cylindrical shells under axial compression, International Journal of Solids and Structures, vol.40, issue.5, pp.1311-1327, 2003.
DOI : 10.1016/S0020-7683(02)00583-8

P. Jetteur, S. Cescotto, V. De-ville-de-goyet, and E. F. Frey, Improved nonlinear finite elements for oriented bodies using an extension of marguerre's theory, Computers & Structures, vol.17, issue.1, pp.129-137, 1983.
DOI : 10.1016/0045-7949(83)90037-8

L. M. Kachanov, Separation failure of composite materials, Polymer Mechanics, vol.12, issue.5, pp.812-815, 1976.
DOI : 10.1007/BF00856347

M. F. Kanninen, 03) An augmented double cantilever beam model for studying crack propagation and arrest, International Journal of Fracture, vol.9, issue.1, pp.83-92, 1973.

P. Kerfriden, Stratégie de décomposition de domaine à trois échelles pour la simulation du délaminage dans les stratifiés, Thèse de doctorat, 2008.

P. Kerfriden, O. Allix, and E. P. Gosselet, A three-scale domain decomposition method for the 3D analysis of debonding in laminates, Computational Mechanics, vol.150, issue.1, pp.343-362, 2009.
DOI : 10.1007/s00466-009-0378-3
URL : https://hal.archives-ouvertes.fr/hal-00437026

N. Kikuchi, Penalty/finite element approximations of a class of unilateral contact problems Penalty method and finite element method, 1982.

W. T. Koiter, On the stability of Elastic Equilibrium (in Dutch) Thèse de doctorat, Wright-Patterson Air Force Base, Hollande. English translation issued as NASA TT-F-10833, 1945.

V. 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

P. Ladevèze, Sur une famille d'algorithmes en mécanique des structures. Comptes-rendus des séances de l'Académie des sciences. Série 2, Mécaniquephysique , chimie, sciences de l'univers, sciences de la terre 300, pp.41-44, 1985.

P. Ladevèze, Sur la mécanique de l'endommagement des composites, Proc. of the 8éme Journées Nationales sur les Composites, pp.667-683, 1986.

P. Ladevèze, A damage computational method for composite structures, Computers & Structures, vol.44, issue.1-2, pp.79-87, 1992.
DOI : 10.1016/0045-7949(92)90226-P

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

P. Ladevèze, O. Loiseau, and E. D. Dureisseix, A micro???macro and parallel computational strategy for highly heterogeneous structures, International Journal for Numerical Methods in Engineering, vol.46, issue.12, pp.121-138, 2001.
DOI : 10.1002/nme.274

P. Ladevèze, G. Lubineau, and E. D. Violeau, A Computational Damage Micromodel of Laminated Composites, International Journal of Fracture, vol.155, issue.10, pp.139-150, 2006.
DOI : 10.1007/s10704-005-3077-x

P. Ladevèze, A. Et, and . 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, A. Nouy, and E. O. Loiseau, A multiscale computational approach for contact problems, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.43, pp.4869-4891, 2002.
DOI : 10.1016/S0045-7825(02)00406-1

P. Ladevèze, J. Passieux, and E. 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

L. Tallec, P. , J. Mandel, and E. M. Vidrascu, A Neumann--Neumann Domain Decomposition Algorithm for Solving Plate and Shell Problems, SIAM Journal on Numerical Analysis, vol.35, issue.2, pp.836-867, 1998.
DOI : 10.1137/S0036142995291019
URL : https://hal.archives-ouvertes.fr/inria-00077196

A. Legay, A. Et, and . Combescure, Efficient algorithms for parametric non-linear instability analysis, International Journal of Non-Linear Mechanics, vol.37, issue.4-5, pp.4-5, 2002.
DOI : 10.1016/S0020-7462(01)00094-4
URL : https://hal.archives-ouvertes.fr/hal-01422436

D. Leguillon, A method based on singularity theory to predict edge delamination of laminates, International Journal of Fracture, vol.100, issue.1, pp.105-120, 1999.
DOI : 10.1023/A:1018382422833

D. Leguillon, Strength or toughness? A criterion for crack onset at a notch, European Journal of Mechanics - A/Solids, vol.21, issue.1, pp.61-72, 2002.
DOI : 10.1016/S0997-7538(01)01184-6

D. Leguillon, E. Et, and . Sanchez-palencia, Effets de bords et singularités dans les matériaux composites, Annales des Composites, Effets de bords et singularités dans les matériaux composites stratifiés, pp.7-20, 1987.

R. Levien, The elastica : a mathematical history, 2008.

S. Levy, Bending of rectangular plates with large deflections, 1945.

O. Loiseau, Une stratégie de calcul multiéchelle pour les structures hétérogènes, Thèse de doctorat, 2001.

A. M. Lyapunov, Problème général de la stabilité du mouvement, Mathematics Society of Kharkov, 1892.

J. Mandel, Introduction à la mécanique des milieux continus déformables, Éditions scientifiques de Pologne, 1974.

J. Mandel, Balancing domain decomposition, Communications in Numerical Methods in Engineering, vol.13, issue.3, pp.233-241, 1993.
DOI : 10.1002/cnm.1640090307
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.44.876

H. Matthies, G. Et, and . Strang, The solution of nonlinear finite element equations, International Journal for Numerical Methods in Engineering, vol.5, issue.11, pp.1613-1626, 1979.
DOI : 10.1002/nme.1620141104

I. M. May, Y. Et, and . Duan, A local arc-length procedure for strain softening, Computers & Structures, vol.64, issue.1-4, pp.1-4, 1997.
DOI : 10.1016/S0045-7949(96)00172-1

J. Melenk, I. Et, and . Babu?ka, The partition of unity finite element method: Basic theory and applications, Computer Methods in Applied Mechanics and Engineering, vol.139, issue.1-4, pp.289-314, 1996.
DOI : 10.1016/S0045-7825(96)01087-0

R. Michalowski, Z. Et, and . Mroz, Associated and non-associated sliding rules in contact friction problems, Archiwum Mechaniki Stosowanej, vol.30, issue.3, pp.259-276, 1978.

N. Moës, J. Dolbow, and E. 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

M. Mooney, A Theory of Large Elastic Deformation, Journal of Applied Physics, vol.11, issue.9, pp.582-592, 1940.
DOI : 10.1063/1.1712836

A. Needleman, A Continuum Model for Void Nucleation by Inclusion Debonding, Journal of Applied Mechanics, vol.54, issue.3, pp.525-531, 1987.
DOI : 10.1115/1.3173064

D. Néron, D. Et, and . 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

S. Nezamabadi, H. Zahrouni, J. Yvonnet, and M. Potier-ferry, A Multiscale Finite Element Approach for Buckling Analysis of Elastoplastic Long Fiber Composites, International Journal for Multiscale Computational Engineering, vol.8, issue.3, pp.287-301, 2010.
DOI : 10.1615/IntJMultCompEng.v8.i3.50
URL : https://hal.archives-ouvertes.fr/hal-01468352

Q. S. Nguyen, Stabilité des structures élastiques, Mathématiques & Applications 18, 1995.

K. Nilsson, A. E. Et, M. H. Giannakopoulos, C. A. Aliabadi, D. J. Brebbia et al., Finite element simulation of delamination growth, Proc. of the first International Conference on Computer-Aided Assesment and Control of Localized Damage, pp.299-313, 1990.

A. Nouy, Une stratégie de calcul multiéchelle avec homogénéisation en temps et en espace pour le calcul de structures fortement hétérogènes, Thèse de doctorat, 2003.

R. J. Nuismer, J. M. Et, and . Whitney, Stress fracture criteria for laminated composites containing stress concentrations, Journal of Composite Materials, vol.8, pp.253-265, 1974.

J. T. Oden, E. B. Et, and . Pires, Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity, Journal of Applied Mechanics, vol.50, issue.1, pp.67-76, 1983.
DOI : 10.1115/1.3167019

R. W. Ogden, Non-Linear Elastic Deformations, 1984.

J. Pebrel, C. Rey, and E. P. Gosselet, A Nonlinear Dual-Domain Decomposition Method: Application to Structural Problems with Damage, International Journal for Multiscale Computational Engineering, vol.6, issue.3, pp.251-262, 2008.
DOI : 10.1615/IntJMultCompEng.v6.i3.50
URL : https://hal.archives-ouvertes.fr/hal-00344445

R. B. Pipes, N. J. Et, and . Pagano, Interlaminar Stresses in Composite Laminates Under Uniform Axial Extension, Journal of Composites Materials, vol.4, p.538, 1970.
DOI : 10.1007/978-94-017-2233-9_19

M. Potier-ferry, Perturbed bifurcation theory, Journal of Differential Equations, vol.33, issue.1, pp.112-146, 1979.
DOI : 10.1016/0022-0396(79)90083-4
URL : http://doi.org/10.1016/0022-0396(79)90083-4

M. J. Powell, A method for nonlinear constraints in minimization problems, Optimization, pp.283-298, 1969.

P. Duval and R. , Quasi-static evolution of delaminated structures: analysis of stability and bifurcation, International Journal of Solids and Structures, vol.41, issue.1, pp.103-130, 2004.
DOI : 10.1016/j.ijsolstr.2003.07.006
URL : https://hal.archives-ouvertes.fr/hal-00111398

J. S. Przemieniecki, MATRIX STRUCTURAL ANALYSIS OF SUBSTRUCTURES, AIAA Journal, vol.1, issue.1, pp.138-147, 1963.
DOI : 10.2514/3.1483

Y. Qiu, M. A. Crisfield, and E. G. Alfano, An interface element formulation for the simulation of delamination with buckling, Engineering Fracture Mechanics, vol.68, issue.16, pp.1755-1776, 2001.
DOI : 10.1016/S0013-7944(01)00052-2

I. S. Raju, Calculation of strain-energy release rates with higher order and singular finite elements, Engineering Fracture Mechanics, vol.28, issue.3, pp.251-274, 1987.
DOI : 10.1016/0013-7944(87)90220-7

E. Ramm, A plate/shell element for large deflections and rotations. Dans US-Germany Symp. on Formulations and Computational Algorithms in Finite Element, 1976.

E. W. Ramm, E. Wunderlish, K. J. Stein, and . Bathe, Strategies for Tracing the Nonlinear Response Near Limit Points, Proceedings of the Europe -US Workshop on Nonlinear Finite Element Analysis in Structural Mechanics, pp.63-89, 1980.
DOI : 10.1007/978-3-642-81589-8_5

E. Ramm, D. R. Hinton, E. C. Owen, and . Taylor, The Riks/Wempner approach -an extension of the displacement control method in non-linear analysis, Recent advances in non-linear computational mechanics, pp.63-86, 1982.

J. Rannou, A. Gravouil, and M. Baïetto-dubourg, A local multigrid X-FEM strategy for 3-D crack propagation, International Journal for Numerical Methods in Engineering, vol.41, issue.11-12, pp.581-600, 2009.
DOI : 10.1002/nme.2427
URL : https://hal.archives-ouvertes.fr/hal-00938285

C. Rey, Une technique d'accélération de la résolution de problèmes d'élasticité non-linéaire par décomposition de domaine, Compte rendu de l'Académie des Sciences 322 série IIb, pp.601-606, 1996.

J. R. Rice, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, Journal of Applied Mechanics, vol.35, issue.2, p.379, 1968.
DOI : 10.1115/1.3601206

E. Riks, The Application of Newton???s Method to the Problem of Elastic Stability, Journal of Applied Mechanics, vol.39, issue.4, pp.1060-1065, 1972.
DOI : 10.1115/1.3422829

E. Riks, An incremental approach to the solution of snapping and buckling problems, International Journal of Solids and Structures, vol.15, issue.7, pp.524-551, 1979.
DOI : 10.1016/0020-7683(79)90081-7

F. Risler, C. Et, and . Rey, Iterative accelerating algorithms with krylov subspaces for the solution to large-scale nonlinear problems, Numerical Algorithms, vol.23, issue.1, pp.1-30, 2000.
DOI : 10.1023/A:1019187614377

V. Roulet, L. Champaney, and P. Boucard, A parallel strategy for the multiparametric analysis of structures with large contact and friction surfaces, Advances in Engineering Software, vol.42, issue.6, pp.347-358, 2011.
DOI : 10.1016/j.advengsoft.2011.02.013

E. F. Rybicki, M. F. Et, and . Kanninen, A finite element calculation of stress intensity factors by a modified crack closure integral, Engineering Fracture Mechanics, vol.9, issue.4, pp.931-938, 1977.
DOI : 10.1016/0013-7944(77)90013-3

Y. Saad, Iterative methods for sparse linear systems (2e éd, 2003.

J. Salençon, Mécanique des milieux continus Tome 1 : Concepts Généraux, 2005.

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

J. C. Schellekens, R. Et, and . De-borst, Application of linear and nonlinear fracture mechanics options to free edge delamination in laminated composites, HERON, vol.36, issue.2, pp.37-48, 1991.

J. C. Schellekens, R. D. Et, and . Borst, A non-linear finite element approach for the analysis of mode-I free edge delamination in composites, International Journal of Solids and Structures, vol.30, issue.9, pp.1239-1253, 1993.
DOI : 10.1016/0020-7683(93)90014-X

H. A. Schwarz, Ueber einige Abbildungsaufgaben., Journal f??r die reine und angewandte Mathematik (Crelles Journal), vol.1869, issue.70, pp.65-83, 1869.
DOI : 10.1515/crll.1869.70.105
URL : http://www.digizeitschriften.de/download/PPN243919689_0070/PPN243919689_0070___log10.pdf

L. Series, F. Feyel, and F. Roux, Une méthode de décomposition de domaine avec deux multiplicateurs de Lagrange, application au calcul de structure, cas du contact, 2003.

J. C. Simo, L. Et, and . Vu-quoc, A three-dimensional finite-strain rod model. part II: Computational aspects, Computer Methods in Applied Mechanics and Engineering, vol.58, issue.1, pp.79-116, 1986.
DOI : 10.1016/0045-7825(86)90079-4

B. Storåkers, B. Et, and . Andersson, Nonlinear plate theory applied to delamination in composites, Journal of the Mechanics and Physics of Solids, vol.36, issue.6, pp.689-718, 1988.
DOI : 10.1016/0022-5096(88)90004-X

T. Strouboulis, K. Coops, and I. Babu?ka, The generalized finite element method, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.32-33, pp.32-33, 2001.
DOI : 10.1016/S0045-7825(01)00188-8

J. M. Thompson, A. C. Et, and . Walker, The non-linear perturbation analysis of discrete structural systems, International Journal of Solids and Structures, vol.4, issue.8, pp.757-768, 1968.
DOI : 10.1016/0020-7683(68)90054-1

S. P. Timoshenko, History of Strength of Materials, 1953.

S. P. Timoshenko, J. M. Et, and . Gere, Theory of Elastic Stability, 1936.

E. Trefftz, K. Et, and . Marguerre, Über die tragfähigkeit eines längsbelasteten plattenstreifens nach überschreiten der beullast, Zeitschrift fur Angewandte Mathematik und Mechanik, pp.85-100, 1937.

C. Truesdell, R. A. Et, and . Toupin, The classic field theories, Handbuch Der Physik, pp.226-790, 1960.

M. J. Turner, E. H. Dill, H. C. Martin, and R. J. Melosh, Large deflections of structures subjected to heating and external loads, Journal of the Aeronautical Sciences, vol.27, issue.2, pp.97-106, 1960.

V. Tvergaard, Effect of fibre debonding in a whisker-reinforced metal, Materials Science and Engineering: A, vol.125, issue.2, pp.203-213, 1990.
DOI : 10.1016/0921-5093(90)90170-8

M. A. Tzaferopoulos and P. D. Panagiotopoulos, Delamination of composites as a substationarity problem: Numerical approximation and algorithms, Computer Methods in Applied Mechanics and Engineering, vol.110, issue.1-2, pp.63-85, 1993.
DOI : 10.1016/0045-7825(93)90020-X

P. Vannucci, B. Cochelin, N. Damil, and M. Potier-ferry, An asymptotic-numerical method to compute bifurcating branches, International Journal for Numerical Methods in Engineering, vol.288, issue.8, pp.1365-1389, 1998.
DOI : 10.1002/(SICI)1097-0207(19980430)41:8<1365::AID-NME332>3.0.CO;2-Y

D. Violeau, Une stratégie de calcul pour l'analyse à l'échelle "micro" des endommagements jusqu'à rupture des composites stratifiés, Thèse de doctorat, 2007.

T. Von-kármán, E. E. Sechler, and L. H. Donnell, The strength of thin plates in compression, Transactions of the ASME, vol.54, pp.53-58, 1932.

T. Von-kármán and H. Tsien, The Buckling of Spherical Shells by External Pressure, Journal of the Aeronautical Sciences, vol.7, p.43, 1939.
DOI : 10.1016/B978-0-12-398277-3.50006-3

T. Von-kármán and H. Tsien, The Buckling of Thin Cylindrical Shells under Axial Compression, Journal of the Aeronautical Sciences, vol.8, p.303, 1941.
DOI : 10.1016/B978-0-12-398277-3.50009-9

G. Wempner, Finite elements, finite rotations and small strains of flexible shells, International Journal of Solids and Structures, vol.5, issue.2, pp.117-153, 1969.
DOI : 10.1016/0020-7683(69)90025-0

G. A. Wempner, Discrete approximations related to nonlinear theories of solids, International Journal of Solids and Structures, vol.7, issue.11, pp.1581-1599, 1971.
DOI : 10.1016/0020-7683(71)90038-2

J. D. Whitcomb, Three-Dimensional Analysis of a Postbuckled Embedded Delamination, Journal of Composite Materials, vol.11, issue.4, pp.862-889, 1989.
DOI : 10.1177/002199838902300901

J. D. Whitcomb, Iterative global/local finite element analysis, Computers & Structures, vol.40, issue.4, pp.1027-1031, 1991.
DOI : 10.1016/0045-7949(91)90334-I

R. D. Wood, O. C. Et, and . Zienkiewicz, Geometrically nonlinear finite element analysis of beams, frames, arches and axisymmetric shells, Computers & Structures, vol.7, issue.6, pp.725-735, 1977.
DOI : 10.1016/0045-7949(77)90027-X

P. Wriggers, Computational Contact Mechanics (2e éd, 2006.

S. Yaghmai, E. P. Et, and . Popov, Incremental analysis of large deflections of shells of revolution, International Journal of Solids and Structures, vol.7, issue.10, pp.1375-1393, 1971.
DOI : 10.1016/0020-7683(71)90052-7

H. Zahrouni, B. Cochelin, and M. Potier-ferry, Computing finite rotations of shells by an asymptotic-numerical method, Computer Methods in Applied Mechanics and Engineering, vol.175, issue.1-2, pp.71-85, 1999.
DOI : 10.1016/S0045-7825(98)00320-X

O. C. Zienkiewicz, The Finite Element Method (3e éd.), 1977.

T. Zohdi, J. Oden, and E. G. 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