R. Abdelmoula, F. Krasucki, and J. Marigo, Microbuckling analysis of unidirectional fibred composites , Mecamat 93 -International Seminar on Micromechanics of Materials, pp.303-314, 1993.

R. Abeyaratne and N. Triantafyllidis, An Investigation of Localization in a Porous Elastic Material Using Homogenization Theory, Journal of Applied Mechanics, vol.51, issue.3, pp.481-486, 1984.
DOI : 10.1115/1.3167661

M. Agoras, O. Lopez-pamies, and P. P. Castaneda, A general hyperelastic model for incompressible fiber-reinforced elastomers, Journal of the Mechanics and Physics of Solids, vol.57, issue.2, pp.268-286, 2009.
DOI : 10.1016/j.jmps.2008.10.014

M. Agoras, O. Lopez-pamies, and P. P. Castaneda, Onset of macroscopic instabilities in fiber-reinforced elastomers at finite strain, Journal of the Mechanics and Physics of Solids, vol.57, issue.11, pp.1828-1850, 2009.
DOI : 10.1016/j.jmps.2009.08.001

S. Antman and C. Kenney, Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity, Archive for rational mechanics and analysis, 1981.

J. Argyris, Energy Theorems and Structural Analysis, Aircraft Engineering and Aerospace Technology, vol.26, issue.10, pp.347-356383, 1954.
DOI : 10.1108/eb032482

D. Arnold, Discretization by finite elements of a model parameter dependent problem, Numerische Mathematik, vol.5, issue.41, pp.405-421, 1981.
DOI : 10.1007/BF01400318

D. Arnold and F. Brezzi, Locking-free finite element methods for shells, Mathematics of Computation, vol.66, issue.217, pp.1-14, 1997.
DOI : 10.1090/S0025-5718-97-00785-0

I. Babuska, The finite element method with Lagrangian multipliers, Numerische Mathematik, vol.12, issue.3, pp.179-192, 1973.
DOI : 10.1007/BF01436561

J. Ball, Convexity conditions and existence theorems in nonlinear elasticity, Archive for Rational Mechanics and Analysis, vol.8, issue.4, pp.337-403, 1977.
DOI : 10.1007/BF00279992

A. Barbier, Note interne

K. Bathe, Finite Element Procedures, 1996.

K. Bathe, A. Iosilevich, and D. Chapelle, An inf-sup test for shell finite elements, Computers & Structures, vol.75, issue.5, pp.439-456, 2000.
DOI : 10.1016/S0045-7949(99)00213-8
URL : https://hal.archives-ouvertes.fr/hal-00839276

J. Batoz and G. Dhatt, Modélisation des Structures par Eléments Finis, 1990.

A. Benssousan, J. Lions, and G. Papanicoulan, Asymptotic analysis of periodic structures, 1978.

F. Bibliographie-bloch, Über die Quantenmechanik der Elektronen in Kristallgittern, Zeitschrift für Physik A Hadrons and Nuclei, pp.555-600, 1928.

M. Bonnet and A. Frangi, Analyse des solides déformables par la méthode des éléments finis, 2006.

M. Bornert, T. Bretheau, and P. Gilormini, Homogénéisation en mécanique des matériaux, Volumes 1 & 2, 2001.

J. Bourgat, P. L. Tallec, and S. Mani, Numerical simulation of the large displacements of an elastic rod in flexion and torsion, Journal of theoritical and applied mechanics, 1988.

J. Bramble and T. Sun, A locking-free finite element method for Naghdi shells, Journal of Computational and Applied Mathematics, vol.89, issue.1, pp.119-133, 1998.
DOI : 10.1016/S0377-0427(97)00234-3

F. Brezzi, On the existence, uniqueness and approximation of saddlepoint problems arising from Lagrangian multipliers, RAIRO Analyse Numérique, pp.129-151, 1974.

F. Brezzi and M. Fortin, Mixed and hybrid finite element mmethods, 1991.

M. Brun, O. Lopez-pamies, and P. P. Castaneda, Homogenization estimates for fiber-reinforced elastomers with periodic microstructures, International Journal of Solids and Structures, vol.44, issue.18-19, pp.5953-5979, 2007.
DOI : 10.1016/j.ijsolstr.2007.02.003

J. Cadou, M. Potier-ferry, and B. Cochelin, A numerical method for the computation of bifurcation points in fluid mechanics, European Journal of Mechanics - B/Fluids, vol.25, issue.2, pp.234-254, 2006.
DOI : 10.1016/j.euromechflu.2005.07.002
URL : https://hal.archives-ouvertes.fr/hal-00493902

J. Caillard, Note interne

A. Campos and F. Rochinha, Dynamics of rods : numerical formulation, Advances in Computational Techniques for Structural Engineering, 1996.

R. Casciero, G. Salerno, and A. Lanzo, Finite element asymptotic analysis of slender elastic structures: A simple approach, International Journal for Numerical Methods in Engineering, vol.28, issue.7, pp.1397-1426, 1992.
DOI : 10.1002/nme.1620350703

P. Castaneda and E. Tiberio, A second-order homogenization method in finite elasticity and applications to black-filled elastomers, Journal of the Mechanics and Physics of Solids, vol.48, issue.6-7, pp.1389-1411, 2000.
DOI : 10.1016/S0022-5096(99)00087-3

D. Chapelle, Une formulation mixte de plaques où l'effort tranchant est approché dans son espace naturel, 1993.

D. Chapelle, Modèles de coques minces : comportements asymptotiques et méthodes numériques, 1996.

D. Chapelle, Etude des phénomènes de verrouillage numérique pour les problèmes de coques minces, 1996.

D. Chapelle, A locking-free approximation of curved rods by straight beam elements, Numerische Mathematik, vol.77, issue.3, pp.299-322, 1997.
DOI : 10.1007/s002110050288
URL : https://hal.archives-ouvertes.fr/hal-00839737

D. Chapelle and K. Bathe, Fundamental considerations for the finite element analysis of shell structures, Computers & Structures, vol.66, issue.1, pp.19-36, 1998.
DOI : 10.1016/S0045-7949(97)00078-3
URL : https://hal.archives-ouvertes.fr/hal-00839732

D. Chapelle and K. , Bathe, T he Finite Element Analysis of Shells -Fundamentals, 2003.

D. Chapelle and A. Ferent, MODELING OF THE INCLUSION OF A REINFORCING SHEET WITHIN A 3D MEDIUM, Mathematical Models and Methods in Applied Sciences, vol.13, issue.04, pp.573-595, 2003.
DOI : 10.1142/S0218202503002635
URL : https://hal.archives-ouvertes.fr/hal-00839241

M. Charlotte, Note interne

D. Chenais and J. Paumier, On the locking phenomenon for a class of elliptic problems, Numerische Mathematik, vol.67, issue.4, pp.427-440, 1994.
DOI : 10.1007/s002110050036

P. Ciarlet, T he finite element method for elliptic problems, 1978.

P. Ciarlet, Mathematical Elasticity -Volume I : 3-dim elasticity, North-Holland, 1988.

P. Ciarlet, Basic error estimates for elliptic problems, Handbook of Numerical Analysis, pp.17-351, 1991.

P. Ciarlet, Mathematical Elasticity -Volume III : Theory of Shells, North-Holland, 2000.

P. Clement and . Operationnelle, Approximation by finite element functions using local regularization, Revue fran??aise d'automatique, informatique, recherche op??rationnelle. Analyse num??rique, vol.9, issue.R2, pp.77-84, 1975.
DOI : 10.1051/m2an/197509R200771

R. Clough, The finite element method in plane stress analysis, Proceedings Second ASCE Conference on Electronic Computation, 1960.

B. Cochelin, A path-following technique via an asymptotic-numerical method, Computers & Structures, vol.53, issue.5, pp.1181-1192, 1994.
DOI : 10.1016/0045-7949(94)90165-1

C. Cornuault, Mise en oeuvre de logiciels performants pour l'analyse non linéaire en calcul de structures , Calcul des structures et intelligence artificielle, 1988.

N. Damil and M. 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

G. Debotton, I. Hariton, and E. Socolsky, Neo-Hookean fiber-reinforced composites in finite elasticity, Journal of the Mechanics and Physics of Solids, vol.54, issue.3, pp.533-559, 2006.
DOI : 10.1016/j.jmps.2005.10.001

J. Dejonghe, Note interne

S. Drapier, C. Gardin, J. C. Grandidier, M. Potierferry, and V. , Structure effect and microbuckling, Structure effect and microbuckling, pp.861-867, 1996.
DOI : 10.1016/0266-3538(96)00033-4

H. Dumontet, . Rairo-mathematical, . Modelling, . Numerical-analysis-modelisation-mathematique, . Et et al., Study of a boundary layer problem in elastic composite materials, ESAIM: Mathematical Modelling and Numerical Analysis, vol.20, issue.2, pp.265-286, 1986.
DOI : 10.1051/m2an/1986200202651

J. D. Eshelby, The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.241, issue.1226, pp.376-396, 1957.
DOI : 10.1098/rspa.1957.0133

F. Feyel, A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.3233-3244, 2003.
DOI : 10.1016/S0045-7825(03)00348-7

F. Feyel, J. L. Chaboche, and V. , 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

C. Gardin, J. Grandidier, and P. M. , Homogenized models for compressive behaviour of long fibre composite materials, T ech. rep, 1998.

M. G. Geers, E. W. Coenen, V. G. Kouznetsova, and R. , Multi-scale computational homogenization of structured thin sheets, Modelling and Simulation in Materials Science and Engineering, vol.15, issue.4, pp.393-404, 2007.
DOI : 10.1088/0965-0393/15/4/S06

M. G. Geers, V. G. Kouznetsova, and W. A. Brekelmans, Multi-scale computational homogenization: Trends and challenges, 4th International Conference on Advanced Computational Methods in Engineering, pp.2175-2182, 2008.
DOI : 10.1016/j.cam.2009.08.077
URL : http://doi.org/10.1016/j.cam.2009.08.077

G. Geymonat, S. Muller, and N. Triantafyllidis, Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity, Archive for Rational Mechanics and Analysis, vol.52, issue.3, pp.231-290, 1993.
DOI : 10.1007/BF00380256

V. Girault and P. Raviart, Finite element approximation of the Navier-Stokes equations, Lecture Notes in Mathematics, vol.749, 1981.
DOI : 10.1007/BFb0063447

A. Gloria, Modélisation et méthodes numériques multi-échelles en élasticité non linéaire (multiscale modeling and numerical methods in nonlinear elasticity, Ecole Nationale des Ponts et Chaussées, 2007.

L. Gong, S. Kyriakides, and N. Triantafyllidis, On the stability of Kelvin cell foams under compressive loads, Journal of the Mechanics and Physics of Solids, vol.53, issue.4, pp.771-794, 2005.
DOI : 10.1016/j.jmps.2004.10.007

J. Grandidier, Résistance en compression des composites à fibres longues, T ech. rep., Dossier d'habilitation à diriger les recherches, 1998.

J. Grandidier and M. Potier-ferry, Microflambage des fibres dans un matériau composite à fibres longues, Comptes rendus de l'Académie des sciences, pp.1-6, 1990.

Z. Y. Guo, X. Q. Peng, and B. Moran, A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus, Journal of the Mechanics and Physics of Solids, vol.54, issue.9, pp.1952-1971, 2006.
DOI : 10.1016/j.jmps.2006.02.006

Z. Hashin, The Elastic Moduli of Heterogeneous Materials, Journal of Applied Mechanics, vol.29, issue.1, pp.143-150, 1962.
DOI : 10.1115/1.3636446

Z. Hashin and S. Shtrikman, A variational approach to the theory of the elastic behaviour of multiphase materials, Journal of the Mechanics and Physics of Solids, vol.11, issue.2, pp.127-140, 1963.
DOI : 10.1016/0022-5096(63)90060-7

Q. C. He, H. L. Quang, and Z. Q. Feng, Exact Results for the Homogenization of Elastic Fiber-Reinforced Solids at Finite Strain, Journal of Elasticity, vol.52, issue.2, pp.153-177, 2006.
DOI : 10.1007/s10659-006-9049-1
URL : https://hal.archives-ouvertes.fr/hal-01179043

R. Hill, A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, vol.6, issue.3, 1958.
DOI : 10.1016/0022-5096(58)90029-2

R. Hill, Elastic properties of reinforced solids: Some theoretical principles, Journal of the Mechanics and Physics of Solids, vol.11, issue.5, pp.357-372, 1963.
DOI : 10.1016/0022-5096(63)90036-X

G. Holzapfel, Nonlinear solid mechanics, 2000.

C. Horgan and G. Saccomandi, A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids, Journal of the Mechanics and Physics of Solids, vol.53, issue.9, 1985.
DOI : 10.1016/j.jmps.2005.04.004

M. Hori and S. Nemat-nasser, On two micromechanics theories for determining micro???macro relations in heterogeneous solids, Mechanics of Materials, vol.31, issue.10, pp.667-682, 1999.
DOI : 10.1016/S0167-6636(99)00020-4

T. Hughes, The Finite Element Method, 1987.

T. Hughes and J. Winget, Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis, International Journal for Numerical Methods in Engineering, vol.101, issue.12, 1980.
DOI : 10.1002/nme.1620151210

A. Ibrahimbegovic and D. Markovic, Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.28-30, pp.3089-3107, 2003.
DOI : 10.1016/S0045-7825(03)00342-6

H. Keller, The Bordering Algorithm and Path Following Near Singular Points of Higher Nullity, SIAM Journal on Scientific and Statistical Computing, vol.4, issue.4, pp.573-582, 1983.
DOI : 10.1137/0904039

. Kirchhoff, Uber die Gleichungen des Gleichgewichts eines elastischeen Korpers bei nicht unendlich kleinen Verschiebungen seiner Theile, Sitzungsber.Akad.Wiss.Wien, vol.9, pp.762-773

W. Koiter, Over de stabiliteit van het elastisch evenwicht, 1945.

V. Kouznetsova, Computational homogenization for the multi-scale analysis of multi-phase materials, 2002.

V. Kouznetsova, M. G. Geers, W. A. Brekelmans, &. Jv, . Sons et al., 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

V. Kouznetsova, W. Brekelmans, and F. Baaijens, An approach to micro-macro modeling of heterogeneous materials, Computational Mechanics, vol.27, issue.1, pp.37-48, 2001.
DOI : 10.1007/s004660000212

V. G. Kouznetsova, M. G. Geers, W. A. Brekelmans, and E. , 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.5525-5550, 2004.
DOI : 10.1016/j.cma.2003.12.073

H. Lahman, J. Cadou, H. Zahrouni, N. Damil, and M. , High-order predictor-corrector algorithms, International Journal for Numerical Methods in Engineering, vol.72, issue.6, pp.685-704, 2002.
DOI : 10.1002/nme.524

L. Bris and C. , Systèmes multi-échelles, Modélisation et simulation, Mathématiques & applications, vol.47, 2005.

L. Tallec and P. , Existence and approximation results for nonlinear mixed problems: Application to incompressible finite elasticity, Numerische Mathematik, vol.11, issue.3, pp.365-382, 1982.
DOI : 10.1007/BF01396438

L. Tallec and P. , Numerical methods for nonlinear three dimensional elasticity, Handbook of Numerical Analysis, pp.465-624, 1994.

L. Tallec and P. , Modélisation et calcul des milieux continus, Editions de l'Ecole Polytechnique, 2009.

L. Tallec, P. , S. Mani, and F. Rochinha, Finite element computation of hyperelastic rods in large displacements , Mathematical modelling and numerical analysis, 1991.

S. Loehnert and P. Wriggers, Effective behaviour of elastic heterogeneous thin structures at finite deformations, COMPUTATIONAL MECHANICS, pp.595-606, 2008.

O. Lopez-pamies, On the effective behavior, microstruture evolution, and macroscopic stability of elastomeric composites, 2006.

O. Lopez-pamies and P. Castaneda, Second-Order Homogenization Estimates Incorporating Field Fluctuations in Finite Elasticity, Mathematics and Mechanics of Solids, vol.9, issue.3, pp.243-270, 2004.
DOI : 10.1177/1081286504038467

O. Lopez-pamies and P. Castaneda, On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: I???Theory, Journal of the Mechanics and Physics of Solids, vol.54, issue.4, pp.807-830, 2006.
DOI : 10.1016/j.jmps.2005.10.006
URL : https://hal.archives-ouvertes.fr/hal-00111466

O. Lopez-pamies and P. Castaneda, On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations: II???Application to cylindrical fibers, Journal of the Mechanics and Physics of Solids, vol.54, issue.4, pp.831-863, 2006.
DOI : 10.1016/j.jmps.2005.10.010
URL : https://hal.archives-ouvertes.fr/hal-00111467

O. Lopez-pamies and P. P. Castaneda, Microstructure evolution in hyperelastic laminates and implications for overall behavior and macroscopic stability, 44th Annual Technical Meeting of the Society-of-Engineering-Science, pp.364-374, 2007.
DOI : 10.1016/j.mechmat.2009.01.006

D. Markovic, Modélisation multiéchelles de structures hétérogènes aux comportements anélastiques non linéaires, 2004.

D. Markovic and A. Ibrahimbegovic, On micro???macro interface conditions for micro scale based FEM for inelastic behavior of heterogeneous materials, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.48-51, pp.5503-5523, 2004.
DOI : 10.1016/j.cma.2003.12.072

P. Mchugh, R. Asaro, and C. Shih, Computational modeling of metal matrix composite materials???III. Comparisons with phenomenological models, Acta Metallurgica et Materialia, vol.41, issue.5, pp.1489-1499, 1993.
DOI : 10.1016/0956-7151(93)90257-S

J. Merodio and R. Ogden, Mechanical response of fiber-reinforced incompressible non-linearly elastic solids, International Journal of Non-Linear Mechanics, vol.40, issue.2-3, pp.213-227, 2005.
DOI : 10.1016/j.ijnonlinmec.2004.05.003

P. A. Michailidis, N. Triantafyllidis, J. A. Shaw, and G. D. , Superelasticity and stability of a shape memory alloy hexagonal honeycomb under in-plane compression, International Journal of Solids and Structures, vol.46, issue.13, 2009.
DOI : 10.1016/j.ijsolstr.2009.03.013
URL : https://hal.archives-ouvertes.fr/hal-00870869

J. Michel, H. Moulinec, and P. Suquet, Effective properties of composite materials with periodic microstructure: a computational approach, Computer Methods in Applied Mechanics and Engineering, vol.172, issue.1-4, pp.109-143, 1999.
DOI : 10.1016/S0045-7825(98)00227-8

J. Michel, O. Lopez-pamies, and P. , Ponte Castañeda, and N. Triantafyllidis, Microscopic and macroscopic instabilities in finitely strained fiber-reinforced elastomers, 2010.

J. C. Michel, O. Lopez-pamies, P. P. Castaneda, and N. Triantafyllidis, Microscopic and macroscopic instabilities in finitely strained porous elastomers, Journal of the Mechanics and Physics of Solids, vol.55, issue.5, pp.900-938, 2007.
DOI : 10.1016/j.jmps.2006.11.006
URL : https://hal.archives-ouvertes.fr/hal-00111501

C. Miehe, J. Schroder, and J. Schotte, Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials, Computer Methods in Applied Mechanics and Engineering, vol.171, issue.3-4, pp.387-418, 1999.
DOI : 10.1016/S0045-7825(98)00218-7

A. Mielke, Energetic formulation of multiplicative elasto-plasticity using dissipation distances, Continuum Mechanics and Thermodynamics, vol.15, issue.4, pp.351-382, 2003.
DOI : 10.1007/s00161-003-0120-x

E. Monteiro, J. Yvonnet, and Q. C. He, Computational homogenization for nonlinear conduction in heterogeneous materials using model reduction, Computational Materials Science, vol.42, issue.4, pp.704-712, 2008.
DOI : 10.1016/j.commatsci.2007.11.001
URL : https://hal.archives-ouvertes.fr/hal-00692239

T. Mori and K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metallurgica, vol.21, issue.5, pp.571-574, 1973.
DOI : 10.1016/0001-6160(73)90064-3

H. Moulinec, P. Suquet, R. De, . Academie, . Sciences-se-rie et al., A fast numerical-method for computing the linear and nonlinear mechanical-properties of composites, COMPTES, vol.318, pp.1417-1423, 1994.

H. Moulinec and P. Suquet, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Computer Methods in Applied Mechanics and Engineering, vol.157, issue.1-2, pp.69-94, 1998.
DOI : 10.1016/S0045-7825(97)00218-1
URL : https://hal.archives-ouvertes.fr/hal-01282728

S. Muller, Homogenization of nonconvex integral functionals and cellular elastic-materials, AR- CHIVE FOR RATIONAL MECHANICS AND ANALYSIS, pp.189-212, 1987.

S. Nemat-nasser and M. Hori, Micromechanics : overall properties of heterogeneous materials, North-Holland series in applied mathematics and mechanics, 1993.

M. Nestorovic and N. Triantafyllidis, Onset of failure in finitely strained layered composites subjected to combined normal and shear loading, Journal of the Mechanics and Physics of Solids, vol.52, issue.4, pp.941-974, 2004.
DOI : 10.1016/j.jmps.2003.06.001

S. Nezamabadi, J. Yvonnet, H. Zahrouni, and M. , A multilevel computational strategy for handling microscopic and macroscopic instabilities, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.27-29, pp.2099-2110, 2009.
DOI : 10.1016/j.cma.2009.02.026
URL : https://hal.archives-ouvertes.fr/hal-00692235

J. Oden, Finite elements for nonlinear continua, 1972.

I. Oezdemir, W. A. Brekelmans, and M. G. , computational homogenization for the thermo-mechanical analysis of heterogeneous solids, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.3-4, pp.602-613, 2008.
DOI : 10.1016/j.cma.2008.09.008

R. Ogden, Large Deformation Isotropic Elasticity: On the Correlation of Theory and Experiment for Compressible Rubberlike Solids, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.328, issue.1575, pp.567-583, 1972.
DOI : 10.1098/rspa.1972.0096

R. Ogden, Volume changes associated with the deformation of rubber-like solids, Journal of the Mechanics and Physics of Solids, vol.24, issue.6, pp.323-338, 1976.
DOI : 10.1016/0022-5096(76)90007-7

R. Ogden, Nonlinear Elastic Deformations, Journal of Applied Mechanics, vol.52, issue.3, 1997.
DOI : 10.1115/1.3169137
URL : https://hal.archives-ouvertes.fr/hal-01303324

R. Peek and N. Triantafyllidis, Worst shapes of imperfections for space trusses with many simultaneously buckling members, International Journal of Solids and Structures, vol.29, issue.19, pp.2385-2402, 1992.
DOI : 10.1016/0020-7683(92)90222-F

J. Pitkäranta, The problem of membrane locking in finite element analysis of cylindrical shells, pp.523-542, 1992.

J. Pitkäranta, Y. Leino, O. Ovaskainen, and J. Piila, Shell deformation states and the finite element method: A benchmark study of cylindrical shells, Computer Methods in Applied Mechanics and Engineering, vol.128, issue.1-2, pp.81-121, 1995.
DOI : 10.1016/0045-7825(95)00870-X

P. Castaneda, P. , and P. Suquet, Nonlinear Composites, ADVANCES IN APPLIED MECHANICS, pp.171-302, 1998.
DOI : 10.1016/S0065-2156(08)70321-1
URL : https://hal.archives-ouvertes.fr/hal-00311888

M. Potier-ferry, Méthodes asymptotiques numériques, Revue Européenne des Eléments Finis, 2004.

G. Qiu and T. Pence, Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids, Journal of Elasticity, vol.49, issue.1, pp.1-30, 1997.
DOI : 10.1023/A:1007410321319

N. Quoc-son, Stabilité et mécanique non linéaire, 2000.

A. Reuss, Berechnung der Flie??grenze von Mischkristallen auf Grund der Plastizit??tsbedingung f??r Einkristalle ., ZAMM - Zeitschrift f??r Angewandte Mathematik und Mechanik, vol.8, issue.1, pp.49-58, 1929.
DOI : 10.1002/zamm.19290090104

P. Saad, Modélisation et identification du comportement non linéaire des cales en caoutchouc, 2003.

S. Saint?venant and A. D. , Sur les pressions qui se développent à l'intérieur des corps solides lorsque les déplacements de leurs points, sans altérer l'élasticité, nepeuvent cependant pas être considérés comme très petits, Bull. Soc. Philomath, vol.5, pp.26-28

J. Sanchez-hubert and E. Sanchez-palencia, Introduction aux méthodes asymptotiques et à l'homogénéisation :application à la mécanique des milieux continus, 1992.

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

E. Sanchez-palencia, Statique et dynamique des coques minces. I : Cas de flexion pure non inhibée, Comptes rendus de l'Académie des sciences, Mathématique, vol.1, issue.309, pp.411-417, 1989.

E. Sanchez-palencia, Statique et dynamique des coques minces. II : Cas de flexion pure inhibée, Comptes rendus de l'Académie des sciences, Mathématique, vol.1, issue.309, pp.531-537, 1989.

J. Simo and L. Vu-quoc, A three-dimensional finite-strain rod model. part ii : computational aspects , Computer methods in applied mechanics and engineering, 1986.

A. Spencer, Deformations of fibre-reinforced materials, 1972.

A. Spencer, Continuum theory of the mechanics of fibre-reinforced composites, 1984.

C. Stolz, Stabilité des matériaux et des structures, 2003.

G. Strang, Variational crimes in the finite element method, Mathematical Foundations of the Finite Element Method, 1972.

J. Sulem and I. Vardoulakis, Bifurcation analysis of the triaxial test on rock specimens. A theoretical model for shape and size effect, Acta Mechanica, vol.8, issue.3-4, pp.195-212, 1990.
DOI : 10.1007/BF01172981

P. M. Suquet, Local and global aspects in the mathematical theory of plasticity, Plasticity today : modelling, methods and applications, pp.279-310, 1985.

R. Temam, Navier Stokes Equations: Theory and Numerical Analysis, Journal of Applied Mechanics, vol.45, issue.2, 2001.
DOI : 10.1115/1.3424338

I. Temizer and P. Wriggers, An adaptive method for homogenization in orthotropic nonlinear elasticity, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.35-36, pp.3409-3423, 2007.
DOI : 10.1016/j.cma.2007.03.017

K. Terada, M. Hori, T. Kyoya, and N. Kikuchi, Simulation of the multi-scale convergence in computational homogenization approaches, International Journal of Solids and Structures, vol.37, issue.16, pp.2285-2311, 2000.
DOI : 10.1016/S0020-7683(98)00341-2

N. Triantafyllidis and R. Abeyaratne, Instabilities of a Finitely Deformed Fiber-Reinforced Elastic Material, Journal of Applied Mechanics, vol.50, issue.1, pp.149-156, 1983.
DOI : 10.1115/1.3166983

N. Triantafyllidis and S. Bardenhagen, The influence of scale size on the stability of periodic solids and the role of associated higher order gradient continuum models, Journal of the Mechanics and Physics of Solids, vol.44, issue.11, pp.1891-1928, 1996.
DOI : 10.1016/0022-5096(96)00047-6

N. Triantafyllidis and B. Maker, On the Comparison Between Microscopic and Macroscopic Instability Mechanisms in a Class of Fiber-Reinforced Composites, Journal of Applied Mechanics, vol.52, issue.4, pp.794-800, 1985.
DOI : 10.1115/1.3169148

N. Triantafyllidis and R. Peek, On stability and the worst imperfection shape in solids with nearly simultaneous eigenmodes, International Journal of Solids and Structures, vol.29, issue.18, pp.2281-2299, 1992.
DOI : 10.1016/0020-7683(92)90216-G

N. Triantafyllidis and M. Schraad, Onset of failure in aluminum honeycombs under general in-plane loading, Journal of the Mechanics and Physics of Solids, vol.46, issue.6, pp.1089-1124, 1998.
DOI : 10.1016/S0022-5096(97)00060-4

N. Triantafyllidis, M. Nestorovic, and M. Schraad, Failure surfaces for finitely strained twophase periodic solids under general in-plane loading, JOURNAL OF APPLIED MECHANICS- TRANSACTIONS OF THE ASMEJSME Joint Fluids Engineering Conference, vol.73, pp.505-515, 2003.

O. Van-der-sluis, P. Schreurs, W. Brekelmans, and H. Meijer, Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling, Mechanics of Materials, vol.32, issue.8, pp.449-462, 2000.
DOI : 10.1016/S0167-6636(00)00019-3

W. Voigt, Theoretische Studien über die Elasticitätsverhältnisse der Krystalle, Abh.Kgl.Ges.Wiss.Göttingen, Math.Kl, vol.34, pp.3-51, 1887.

K. Washizu, Variational Methods in Elasticity and Plasticity, 1975.

B. Wohlmuth, Discretization Methods and Iterative Solvers Based on Domain Decomposition, 2001.
DOI : 10.1007/978-3-642-56767-4

J. Yvonnet and Q. C. He, The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains, Proceedings of computational physics, 2006.
DOI : 10.1016/j.jcp.2006.09.019
URL : https://hal.archives-ouvertes.fr/hal-00693621

J. Yvonnet, H. Zahrouni, and M. Potier-ferry, A model reduction method for the post-buckling analysis of cellular microstructures, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.1-4, pp.265-280, 2007.
DOI : 10.1016/j.cma.2007.07.026
URL : https://hal.archives-ouvertes.fr/hal-00711330

J. Yvonnet, D. Gonzalez, and Q. C. He, Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials, Computer Methods in Applied Mechanics and Engineering, vol.198, issue.33-36, pp.2723-2737, 2009.
DOI : 10.1016/j.cma.2009.03.017
URL : https://hal.archives-ouvertes.fr/hal-00692234

O. Zienkiewicz, The finite element method in engineering science, 1971.