. Bibliographie and . Abdelkhalek, Coupled approach for atness prediction in cold rolling of thin strip, International Journal of Mechanical Sciences, vol.53, issue.9, p.661675, 2011.

. Abdoun, Forced harmonic response of viscoelastic structures by an asymptotic numerical method, Computers & Structures, vol.87, issue.1-2, p.91100, 2009.
DOI : 10.1016/j.compstruc.2008.08.006

. Attipou, Thermal wrinkling of thin membranes using a Fourier, p.532544, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01514967

. Attipou, A multiscale approach for the vibration analysis of heterogeneous materials: Application to passive damping, Journal of Sound and Vibration, vol.332, issue.4, p.725739, 2013.
DOI : 10.1016/j.jsv.2012.10.020

URL : https://hal.archives-ouvertes.fr/hal-00858653

G. Baker, G. A. Baker, and P. R. Graves-morris, The Pad?? approximant, Journal of Mathematical Analysis and Applications, vol.2, issue.1, 1996.
DOI : 10.1016/0022-247X(61)90042-7

K. Bathe, Finite element procedures, 2006.

F. Bechet and H. Boudaoud, Résolution de problemes de contact et de frottement avec la Méthode Asymptotique Numérique, Mathserv.Cnam.Fr, p.16, 2009.

[. Dhia and H. , Problèmes mécaniques multi-échelles : la méthode Arlequin . Comptes Rendus de l'Academie de Sciences -Serie IIb : Mécanique, p.326899904, 1998.

B. Dhia, H. Jamond, and O. , 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.199-220, 2010.
DOI : 10.1016/j.cma.2009.11.014

URL : https://hal.archives-ouvertes.fr/hal-00422595

B. Dhia, R. Dhia, H. Rateau, and G. , Analyse mathématique de la méthode Arlequin mixte, Comptes Rendus de l'Academie des Sciences -Series I : Mathematics, p.332649654, 2001.

B. Dhia, R. Dhia, H. Rateau, and G. , The Arlequin method as a exible engineering design tool, International Journal for Numerical Methods in Engineering, vol.62, p.14421462, 2005.

. Bilasse, A generic approach for the solution of nonlinear residual equations. Part II: Homotopy and complex nonlinear eigenvalue method, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.49-52, pp.49-5239994004, 2009.
DOI : 10.1016/j.cma.2009.09.015

V. Birman, Thermomechanical Wrinkling in Composite Sandwich Structures, AIAA Journal, vol.42, issue.7, p.14741479, 2004.
DOI : 10.2514/8.2071

V. Birman, Thermally induced bending and wrinkling in large aspect ratio sandwich panels, Composites Part A: Applied Science and Manufacturing, vol.36, issue.10, p.14121420, 2005.
DOI : 10.1016/j.compositesa.2004.11.013

. Blandino, The eect of asymmetric mechanical and thermal loading on membrane wrinkling, 2002.

. Blandino, Thin film membrane wrinkling due to mechanical and thermal loads, 19th AIAA Applied Aerodynamics Conference, p.111, 2001.
DOI : 10.1007/BF02321658

. Boudaoud, A numerical method for nonlinear complex modes with application to active???passive damped sandwich structures, Engineering Structures, vol.31, issue.2, p.31284291, 2009.
DOI : 10.1016/j.engstruct.2008.08.008

. Boumediene, Nonlinear forced vibration of damped plates coupling asymptotic numerical method and reduction models, Computational Mechanics, vol.88, issue.3, p.359377, 2011.
DOI : 10.1016/j.compstruc.2010.06.003

URL : https://hal.archives-ouvertes.fr/hal-00987126

. Brau, Multiple-length-scale elastic instability mimics parametric resonance of nonlinear oscillators, Nature Physics, vol.23, issue.1, p.5660, 2010.
DOI : 10.1119/1.13798

C. Brebbia, C. Brebbia, and J. Connor, Geometrically nonlinear niteelement analysis, Journal of the Engineering Mechanics Division, vol.95, issue.2, p.463486, 1969.

R. Brezinski, C. Brezinski, and M. Redivo-zaglia, New representations of Pad??, Pad??-type, and partial Pad?? approximants, Journal of Computational and Applied Mathematics, vol.284, p.6977, 2015.
DOI : 10.1016/j.cam.2014.07.007

. Brush, . Almroth, D. O. Brush, and B. O. Almroth, Buckling of Bars, Plates, and Shells, Journal of Applied Mechanics, vol.42, issue.4, 1975.
DOI : 10.1115/1.3423755

. Carter, Growth and branching of wrinkles in deposited lms, Thin Solid Films, vol.287, issue.12, p.275279, 1996.

. Cerda, Thin lms : wrinkling of an elastic sheet under tension, Nature, issue.6907, p.419579580, 2002.

. Cheng, Wrinkling behavior of laminated steel sheets, Journal of Materials Processing Technology, vol.151, issue.1-3, p.133140, 2004.
DOI : 10.1016/j.jmatprotec.2004.04.028

. Chiu, Mechanical and Thermal Wrinkling of Polymer Membranes, Journal of Applied Mechanics, vol.61, issue.1, pp.6167-70, 1994.
DOI : 10.1115/1.2901423

. Cochelin, M??thode asymptotique num??rique, European Journal of Computational Mechanics, vol.17, issue.4, 2007.
DOI : 10.1080/17797179.2008.9737353

M. A. Criseld, A fast incremental/iterative solution procedure that handles "snap-through, Computers & Structures, vol.13, p.5562, 1981.

. Cuong, Experimental and numerical modelling of atness defects in strip cold rolling, International Journal of Solids and Structures, pp.69-70111, 2015.

D. A. Dadeppo and R. Schmidt, Instability of Clamped-Hinged Circular Arches Subjected to a Point Load, Journal of Applied Mechanics, vol.42, issue.4, pp.894-896, 1975.
DOI : 10.1115/1.3423734

P. Damil, N. Damil, and M. Potier-ferry, A generalized continuum approach to describe instability pattern formation by a multiple scale analysis, Comptes Rendus M??canique, vol.334, issue.11, p.334674678, 2006.
DOI : 10.1016/j.crme.2006.09.002

N. Damil and M. Potier-ferry, Inuence of local wrinkling on membrane behaviour : A new approach by the technique of slowly variable Fourier coecients, Journal of the Mechanics and Physics of Solids, issue.8, p.5811391153, 2010.

. Damil, New nonlinear multi-scale models for wrinkled membranes, Comptes Rendus M??canique, vol.341, issue.8, p.341616624, 2013.
DOI : 10.1016/j.crme.2013.06.001

. Damil, Membrane wrinkling revisited from a multi-scale point of view, Advanced Modeling and Simulation in Engineering Sciences, vol.1, issue.1, p.6, 2014.
DOI : 10.1016/j.crme.2005.10.013

URL : https://hal.archives-ouvertes.fr/hal-01515214

P. Daya, E. Daya, and M. Potier-ferry, A numerical method for nonlinear eigenvalue problems application to vibrations of viscoelastic structures, Computers & Structures, vol.79, issue.5, p.79533541, 2001.
DOI : 10.1016/S0045-7949(00)00151-6

A. Diaby, Contribution à l'étude du ambement des structures gonables, 2005.

. Diaby, Buckling and wrinkling of prestressed membranes, Finite Elements in Analysis and Design, vol.42, issue.11, p.429921001, 2006.
DOI : 10.1016/j.finel.2006.03.003

URL : https://hal.archives-ouvertes.fr/hal-01005295

. Ed-dinari, Large torsion analysis of thin-walled open sections beams by the Asymptotic Numerical Method, Engineering Structures, vol.81, p.240255, 2014.
DOI : 10.1016/j.engstruct.2014.09.045

URL : https://hal.archives-ouvertes.fr/hal-01503893

. Friedl, Buckling of stretched strips, Computers & Structures, vol.78, issue.1-3, p.185190, 2000.
DOI : 10.1016/S0045-7949(00)00072-9

. Gilabert, Buckling instability and pattern around holes or cracks in thin plates under a tensile load, European journal of mechanics. A. Solids, vol.11, issue.1, p.6589, 1992.

. Goyal, On instability-induced debond initiation in thin lm systems, Engineering Fracture Mechanics, issue.8, p.7712981313, 2010.

A. Gu, P. Gu, and R. J. Asaro, Wrinkling of sandwich polymer matrix composite panels under transverse thermal gradients, Fire Safety Journal, vol.43, issue.2, p.151160, 2008.
DOI : 10.1016/j.firesaf.2007.06.003

N. Halphen, B. Halphen, and Q. S. Nguyen, Sur les matériaux standard généralisés, Journal de mécanique, vol.14, p.3963, 1975.

. Healey, Wrinkling behavior of highly stretched rectangular elastic lms via parametric global bifurcation, Journal of Nonlinear Science, vol.23, issue.5, p.777805, 2013.

. Hornig, Wrinkling Analysis of ThermoElastic Membranes, p.3343, 2006.

. Hu, Multi-scale modelling of sandwich structures using the Arlequin method Part I : Linear modelling. Finite Elements in Analysis and Design, p.3751, 2008.

. Hu, A bridging technique to analyze the inuence of boundary conditions on instability patterns, Journal of Computational Physics, issue.10, p.23037533764, 2011.

. Huang, Macroscopic simulation of membrane, International Journal of Solids & Structures, pp.64-65246258, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01514739

. Iyer, Buckling patterns in diamond-like carbon lms, Thin Solid Films, vol.256, issue.12, p.94100, 1995.

P. Jacques, N. Jacques, and M. Potier-ferry, On mode localisation in tensile plate buckling, Comptes Rendus M??canique, vol.333, issue.11, p.333804809, 2005.
DOI : 10.1016/j.crme.2005.10.013

URL : https://hal.archives-ouvertes.fr/hal-00455508

. Jenkins, Experimental measurement of wrinkling in membranes undergoing planar deformation, Experimental Mechanics, vol.43, issue.10, p.147152, 1998.
DOI : 10.1007/BF02321658

R. M. Jones, Buckling of bars, plates, and shells, 2006.

. Kim, Wrinkling initiation and growth in modi " ed Yoshida buckling test : Finite element analysis and experimental comparison, International Journal of Mechanical Sciences, vol.42, p.16831714, 2000.

. Koutsawa, Sensitivities of eective properties computed using micromechanics dierential schemes and high-order Taylor series : Application to piezo-polymer composites, Mechanics Research Communications, vol.37, issue.5, p.489494, 2010.

. Kouznetsova, Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.48-51, pp.48-5155255550, 2004.
DOI : 10.1016/j.cma.2003.12.073

. Lahmam, High-order predictor-corrector algorithms, International Journal for Numerical Methods in Engineering, vol.72, issue.6, p.55685704, 2002.
DOI : 10.1016/S0045-7949(98)00336-8

. Lecieux, . Bouzidi, Y. Lecieux, and R. Bouzidi, Experimental analysis on membrane wrinkling under biaxial load ??? Comparison with bifurcation analysis, International Journal of Solids and Structures, vol.47, issue.18-19, pp.18-1924592475, 2010.
DOI : 10.1016/j.ijsolstr.2010.05.005

URL : https://hal.archives-ouvertes.fr/hal-01006831

. Lecieux, . Bouzidi, Y. Lecieux, and R. Bouzidi, Numerical wrinkling prediction of thin hyperelastic structures by direct energy minimization, Advances in Engineering Software, vol.50, issue.1, p.5768, 2012.
DOI : 10.1016/j.advengsoft.2012.02.010

URL : https://hal.archives-ouvertes.fr/hal-01007136

. Li, Surface wrinkling of mucosa induced by volumetric growth: Theory, simulation and experiment, Journal of the Mechanics and Physics of Solids, vol.59, issue.4, p.758774, 2011.
DOI : 10.1016/j.jmps.2011.01.010

. Lougou, Vibration modeling of large repetitive sandwich structures with viscoelastic core, Mechanics of Advanced Materials and Structures, vol.44, issue.4, p.0, 2014.
DOI : 10.1016/j.cma.2008.09.003

URL : https://hal.archives-ouvertes.fr/hal-01514954

. Miller, Finite element analysis of partly wrinkled membranes, p.631639, 1985.

W. Murray, D. W. Murray, and E. L. Wilson, Finite-element postbuckling analysis of thin elastic plates, AIAA Journal, vol.89, issue.10, p.19151920, 1969.
DOI : 10.2514/3.1825

R. Nakhoul, Méthode multi-échelle pour la modélisation du ambage des tôles minces sous contraintes résiduelles-Application au laminage, CSMA 2013-11ème Colloque National en Calcul des Structures, p.18, 2013.

S. Nezamabadi, Méthode Asymptotique Numérique pour l'étude multi échelle des instabilités dans les matériaux hétérogènes, 2009.

. Nezamabadi, Stratégie numérique pour modéliser des plis dans les membranes minces, p.14, 2013.

S. Orszulik, R. R. Orszulik, and J. Shan, Fuzzy logic active atness control of a space membrane structure, Acta Astronautica, vol.77, p.6876, 2012.

H. Padé, Sur la repr??sentation approch??e d'une fonction par des fractions rationnelles, Annales scientifiques de l'??cole normale sup??rieure, vol.9, 1892.
DOI : 10.24033/asens.378

M. Plassa, Eects of elastic instability of thin germanium lms, Thin Solid Films, vol.3, issue.5, p.305314, 1969.

G. Rateau, Méthode Arlequin pour les problèmes mécaniques multiéchelles, 2003.

E. Riks, An incremental approach to the solution of snapping and buckling problems, International Journal of Solids and Structures, vol.15, issue.7, p.529551, 1979.
DOI : 10.1016/0020-7683(79)90081-7

. Roddeman, The Wrinkling of Thin Membranes: Part I???Theory, Journal of Applied Mechanics, vol.54, issue.4, p.884887, 1987.
DOI : 10.1115/1.3173133

. Roddeman, The wrinkling of thin membranes : Part IInumerical analysis, Journal of Applied Mechanics, vol.54, issue.4, p.888892, 1987.

. Shaw, . Huang, D. Shaw, and Y. Huang, Buckling behavior of a central cracked thin plate under tension, Engineering Fracture Mechanics, vol.35, issue.6, p.3510191027, 1990.
DOI : 10.1016/0013-7944(90)90129-5

. Shimizu, Buckling of plates with a hole under tension. Thin-Walled Structures, p.3549, 1991.

V. Simo, J. Simo, and L. Vu-quoc, A three-dimensional nite-strain rod model. part II : Computational aspects, Computer Methods in Applied Mechanics and Engineering, vol.58, issue.1, p.79116, 1986.

. Singha, Thermal postbuckling analysis of laminated composite plates, Composite Structures, vol.54, issue.4, p.453458, 2001.
DOI : 10.1016/S0263-8223(01)00117-9

G. Timoshenko, S. Timoshenko, and J. Gere, Theory of Elastic Stability, 2009.

G. Timoshenko, S. Timoshenko, and J. N. Goodier, Theory of elasticity, 1951.

W. Timoshenko, S. Timoshenko, and S. Woinowsky-krieger, Theory of plates and shells, 1959.

S. Tomita, Y. Tomita, and . Shindo, Onset and growth of wrinkles in thin square plates subjected to diagonal tension, International Journal of Mechanical Sciences, vol.30, issue.12, p.30921931, 1988.
DOI : 10.1016/0020-7403(88)90074-4

H. Wagner, Flat sheet metal girders with very thin webs, Part I -General theories and assumptions, National Advisory Commitee for Aeronautics, issue.604, 1931.

B. Wagner, H. Wagner, and W. Ballerstedt, Tension elds in originally curved, thin sheets during shearing stresses, National Advisory Commitee for Aeronautics, vol.774, 1935.

. Wang, A new computational method for wrinkling analysis of gossamer space structures, International Journal of Solids and Structures, vol.46, issue.6, p.4615161526, 2009.
DOI : 10.1016/j.ijsolstr.2008.11.018

. Wang, Wrinkling prediction of rectangular shell-membrane under transverse in-plane displacement, International Journal of Solids and Structures, vol.44, issue.20, p.4465076516, 2007.
DOI : 10.1016/j.ijsolstr.2007.02.036

. Wesfreid, . Zaleski, J. E. Wesfreid, and S. Zaleski, Cellular structures in instabilities, Cellular Structures in Instabilities, 1984.
DOI : 10.1007/3-540-13879-X

P. Wong, Y. W. Wong, and S. Pellegrino, Wrinkled membranes Part III : Numerical simulations, Journal of Mechanics of Materials and Structures, vol.1, issue.1, p.6395, 2006.

. Xu, Bridging techniques in a multi-scale modeling of pattern formation, International Journal of Solids and Structures, vol.51, issue.18, p.5131193134, 2014.
DOI : 10.1016/j.ijsolstr.2014.05.011

URL : https://hal.archives-ouvertes.fr/hal-01503453

. Xu, Instabilities in thin lms on hyperelastic substrates by 3D nite elements, International Journal of Solids and Structures, pp.69-707185, 2015.

. Xu, 3D nite element modeling for instabilities in thin lms on soft substrates, International Journal of Solids and Structures, pp.51-72, 2014.

. Xu, Multiple bifurcations in wrinkling analysis of thin lms on compliant substrates, International Journal of Non-Linear Mechanics, vol.76, p.203222, 2015.

L. Zheng, Wrinkling of Dielectric Elastomer Membranes, 2009.

T. Zienkiewicz, O. C. Zienkiewicz, and R. L. Taylor, The nite element method, 1991.