A. M. Waas, C. D. Babcock-jr, and W. G. Knauss, An experimental study of compression failure of fibrous laminated composites in the presence of stress gradients, International Journal of Solids and Structures, vol.26, issue.9-10, pp.26-1071, 1990.
DOI : 10.1016/0020-7683(90)90017-P

C. Soutis, N. A. Fleck, and P. A. Smith, Failure prediction technique for compression loaded carbon fibre-epoxy laminate with open holes, Journal of Composite Materials, vol.25, pp.1476-1498, 1991.

A. M. Waas, Failure criteria for composites, Aerospace Engineering Department, 1999.

M. R. Wisnom, The effect of specimen size on the bending strength of unidirectional carbon fibre-epoxy, Composite Structures, vol.18, issue.1, pp.47-63, 1991.
DOI : 10.1016/0263-8223(91)90013-O

I. Grandsire-vincon, Compression des composites unidirectionnels: Méthodes d'essais et approche micromécanique, 1993.

M. R. Wisnom, Size effects in the testing of fibre-composite materials, Composites Science and Technology, vol.59, issue.13, pp.1937-1957, 1999.
DOI : 10.1016/S0266-3538(99)00053-6

I. Vincon, O. Allix, P. Sigety, and M. H. Auvray, Compressive performance of carbon fibres: experiment and analysis, Composites Science and Technology, vol.58, issue.10, pp.1649-1658, 1998.
DOI : 10.1016/S0266-3538(97)00235-2

W. J. Hart, R. Aoki, H. Bookholt, P. Curtis, I. Krober et al., Garteur compression behaviour of advanced CRFP, in: AGARD Report 785. The utilisation of advanced composites in military aircraft. 73rd meeting of the AGRAD structures and materials panel, 1991.

O. Anthoine, J. C. Grandidier, and L. Daridon, Pure compression testing of advanced fibre composites, Composite science and technology, pp.58-735, 1998.

B. W. Rosen, Mechanics of composite strengthening, Fiber composite materials, American Society for Metals Seminar, vol.3, pp.37-75, 1964.

A. S. Argon, Fracture of composites, Treatise of, Materials Science and Technology, vol.1, 1972.

B. Budiansky and M. , Micromechanics, Computers & Structures, vol.16, issue.1-4, pp.3-12, 1983.
DOI : 10.1016/0045-7949(83)90141-4

B. Budiansky and N. A. Fleck, Compressive failure of fibre composites, Journal of the Mechanics and Physics of Solids, vol.41, issue.1, pp.183-211, 1993.
DOI : 10.1016/0022-5096(93)90068-Q

S. Kyriakides, R. Arseculeratne, E. J. Perry, and K. M. Liechti, On the compressive failure of fiber reinforced composites, International Journal of Solids and Structures, vol.32, issue.6-7, pp.689-738, 1995.
DOI : 10.1016/0020-7683(94)00157-R

S. H. Lee and A. M. Waas, Compressive response and failure of fiber reinforced unidirectional composites, International Journal of Fracture, vol.100, issue.3, pp.275-306, 1999.
DOI : 10.1023/A:1018779307931

S. Drapier, J. C. Grandidier, and M. , A structural approach of plastic microbuckling in long fibre composites: comparison with theoretical and experimental results, International Journal of Solids and Structures, vol.38, issue.22-23, pp.3877-3904, 2001.
DOI : 10.1016/S0020-7683(00)00247-X

X. Martinez and S. Oller, Numerical Simulation of Matrix Reinforced Composite Materials Subjected to Compression Loads, Archives of Computational Methods in Engineering, vol.6, issue.5, pp.357-397, 2009.
DOI : 10.1007/s11831-009-9036-3

S. L. Lemanski and M. P. Sutcliffe, Compressive failure of finite size unidirectional composite laminates with a region of fibre waviness, Composites Part A: Applied Science and Manufacturing, vol.43, issue.3, pp.435-444, 2012.
DOI : 10.1016/j.compositesa.2011.11.007

N. Feld, O. Allix, E. Baranger, and J. M. Guimard, A micromechanics-based mesomodel for unidirectional laminates in compression up to failure, Journal of Composite Materials, vol.20, issue.23, pp.2893-2909, 2012.
DOI : 10.1177/0021998311434170

URL : https://hal.archives-ouvertes.fr/hal-00751319

J. C. Grandidier, P. Casari, and C. Jochum, A fibre direction compressive failure criterion for long fibre laminates at ply scale, including stacking sequence and laminate thickness effects, Composite Structures, vol.94, issue.12, pp.49-3799, 2012.
DOI : 10.1016/j.compstruct.2012.06.013

URL : https://hal.archives-ouvertes.fr/hal-01102021

S. Drapier, J. C. Grandidier, and M. , Towards a numerical model of the compressive strength for long fibre composites, European Journal of Mechanics - A/Solids, vol.18, issue.1, pp.69-92, 1999.
DOI : 10.1016/S0997-7538(99)80004-7

M. Gologanu, J. B. Leblond, G. Perrin, and J. Devaux, Recent Extensions of Gurson???s Model for Porous Ductile Metals, Continuum Micromechanics , CISM Lectures Series, pp.61-130, 1997.
DOI : 10.1007/978-3-7091-2662-2_2

R. J. Smit, W. A. Brekelmans, and H. E. Meijer, Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling, Computer Methods in Applied Mechanics and Engineering, vol.155, issue.1-2, pp.181-192, 1998.
DOI : 10.1016/S0045-7825(97)00139-4

F. Feyel and J. L. 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

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

N. Triantafyllidis and B. N. , 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

G. Geymonat, S. Müller, 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

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

S. Nezamabadi, H. Zahrouni, J. Yvonnet, and M. , 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

N. Ohno, D. Okumura, and H. Noguchi, Microscopic symmetric bifurcation condition of cellular solids based on a homogenization theory of finite deformation, Journal of the Mechanics and Physics of Solids, vol.50, issue.5, pp.1125-1153, 2002.
DOI : 10.1016/S0022-5096(01)00106-5

C. Miehe, J. Schröder, and M. Becker, Computational homogenization analysis in finite elasticity: material and structural instabilities on the micro- and macro-scales of periodic composites and their interaction, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.44, pp.4971-5005, 2002.
DOI : 10.1016/S0045-7825(02)00391-2

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

O. Lopez-pamies and P. , Second-Order Estimates for the Macroscopic Response and Loss of Ellipticity in Porous Rubbers at Large Deformations, Journal of Elasticity, vol.21, issue.9, pp.247-287, 2005.
DOI : 10.1007/s10659-005-1405-z

URL : https://hal.archives-ouvertes.fr/hal-00111435

G. Debotton, I. Hariton, and E. A. 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. C. Michel, O. Lopez-pamies, and P. , 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

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

D. Okumura, A. Okada, and N. Ohno, Buckling behavior of Kelvin open-cell foams under [001], [011] and [111] compressive loads, International Journal of Solids and Structures, vol.45, issue.13, pp.3807-3820, 2008.
DOI : 10.1016/j.ijsolstr.2007.10.021

J. Hadamard, Lecons sur la Propagation des Ondes, Hermann et Cie, 1903.

J. W. Rudnicki and J. R. Rice, Conditions for the localization of deformation in pressure-sensitive dilatant materials, Journal of the Mechanics and Physics of Solids, vol.23, issue.6, pp.371-394, 1975.
DOI : 10.1016/0022-5096(75)90001-0

J. R. Rice, The localization of plastic deformation, Theoretical and Applied Mechanics (Proceedings of the 14th International Congress on Theoretical and Applied Mechanics), pp.207-220, 1976.

J. C. Grandidier, G. Ferron, and M. , Microbuckling and strength in long-fiber composites: theory and experiments, International Journal of Solids and Structures, vol.29, issue.14-15, pp.1753-1761, 1992.
DOI : 10.1016/0020-7683(92)90168-S

N. A. Fleck and J. Y. Shu, Microbuckle initiation in fibre composites : A finite element study, Journal of the Mechanics and Physics of Solids, vol.43, issue.12, pp.1887-1918, 1995.
DOI : 10.1016/0022-5096(95)00057-P

S. Forest and K. Sab, Cosserat overall modeling of heterogeneous materials, Mechanics Research Communications, vol.25, issue.4, pp.449-454, 1998.
DOI : 10.1016/S0093-6413(98)00059-7

V. G. Kousnetzova, 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

H. Hencky, Zur theorie deformationen und der hierdurch im material hervorgerufnen nebenspannungen, Zeitschrift Für Angewandte mathematik und Mechanik, pp.323-334, 1924.

W. F. Chen and D. J. Han, Plasticity for structural engineers, 1998.
DOI : 10.1007/978-1-4612-3864-5

H. Zahrouni, M. Potier-ferry, H. Elasmar, and N. , Asymptotic Numerical Method for Nonlinear Constitutive Laws, Revue Europ??enne des ??l??ments Finis, vol.10, issue.4, pp.841-869, 1998.
DOI : 10.1080/12506559.1998.10511344

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

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

J. M. Cadou, B. Cochelin, and M. , 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

H. Mottaqui, B. Braikat, and N. , Discussion about parameterization in the asymptotic numerical method: Application to nonlinear elastic shells, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.25-28, pp.1701-1709, 2010.
DOI : 10.1016/j.cma.2010.01.020

S. Drapier, J. C. Grandidier, and M. , Potier-Ferry, Structure effect and microbuckling , Composites science and technology, pp.56-861, 1996.
DOI : 10.1016/0266-3538(96)00033-4