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
Asymptotic numerical method for problems coupling several nonlinearities, Computer Methods in Applied Mechanics and Engineering, vol.191, issue.51-52, pp.5795-5810, 2002. ,
DOI : 10.1016/S0045-7825(02)00497-8
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
Méthode asymptotique numérique pour la plasticité, 2007. ,
Regularization and perturbation technique to solve plasticity problems, International Journal of Material Forming, vol.11, issue.1, pp.1-14, 2009. ,
DOI : 10.1007/978-1-349-02235-9_15
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 : 10.1007/978-3-642-81589-8_5
A modified corotational framework for triangular shell elements, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.13-16, pp.1905-1914, 2007. ,
DOI : 10.1016/j.cma.2006.10.006
The mechanics of size-dependent indentation, Journal of the Mechanics and Physics of Solids, vol.46, issue.10, pp.2949-2968, 1998. ,
DOI : 10.1016/S0022-5096(98)00018-0
Multiscale mechanical problems : the Arlequin method, Comptes Rendus Mathématique Académie des Sciences, vol.326, pp.899-904, 1998. ,
Asymptotic analysis for periodic structures, 1978. ,
An extension of the self-consistent scheme to plastically-flowing polycrystals, Journal of the Mechanics and Physics of Solids, vol.26, issue.5-6, pp.325-344, 1979. ,
DOI : 10.1016/0022-5096(78)90003-0
A theoretical derivation of the plastic properties of a polycrystalline face-center metal, Philosophical Magazine, vol.42, pp.1298-1307, 1951. ,
XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses., The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol.72, issue.327, pp.414-427, 1951. ,
DOI : 10.1098/rspa.1923.0023
Morphologically representative pattern-based bounding in elasticity, Journal of the Mechanics and Physics of Solids, vol.44, issue.3, pp.307-331, 1996. ,
DOI : 10.1016/0022-5096(95)00083-6
Bifurcation points and bifurcated branches by an asymptotic numerical method and Pad?? approximants, International Journal for Numerical Methods in Engineering, vol.60, issue.12, pp.1987-2012, 2004. ,
DOI : 10.1002/nme.1033
Méthode asymptotique numérique et et fortes non linéarités, Faculté des sciences Ben M'sik, 1995. ,
Simulation de la mise en forme à chaud par la méthode asymptotique numérique, Faculté des sciences Ben M'sik Casablanca, Maroc, 1999. ,
Micromechanics, Computers & Structures, vol.16, issue.1-4, pp.3-12, 1983. ,
DOI : 10.1016/0045-7949(83)90141-4
The Diamant Approach for an Efficient Automatic Differentiation of the Asymptotic Numerical Method, Comptes Rendus Mécanique, vol.336, pp.336-340, 2008. ,
DOI : 10.1007/978-3-540-68942-3_13
Plasticity for structural engineers, 1998. ,
DOI : 10.1007/978-1-4612-3864-5
Plastic behavior of composites and porous media under isotropic stress, International Journal of Engineering Science, vol.9, issue.10, pp.971-994, 1971. ,
DOI : 10.1016/0020-7225(71)90029-2
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
Asymptotic-numerical methods and Pade approximants for non-linear elastic structures, International Journal for Numerical Methods in Engineering, vol.5, issue.7, pp.1187-1213, 1994. ,
DOI : 10.1007/978-3-642-81589-8_5
Potier-Ferry. Méthode asymptotique numérique, 2007. ,
Experimentally tractable, pseudo-elastic constitutive caw for biomembranes : I. Theory, Journal of Biomechanical Engineering, vol.125, pp.94-99, 2003. ,
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
Variational Estimates for the Creep Behaviour of Polycrystals, Proceedings of the Royal Society A, pp.121-142, 1995. ,
DOI : 10.1098/rspa.1995.0009
Homogenization and damage for composite structures, International Journal for Numerical Methods in Engineering, vol.11, issue.2, pp.285-298, 1989. ,
DOI : 10.1002/nme.1620270206
Theoretical study of structural effects on the compressive strength of laminates composites. Compte Rendue de l, Académie des Sciences, vol.324, pp.219-227, 1997. ,
A non-linear numerical approach to the analysis of microbuckling, Composites Science and Technology, vol.58, issue.5, pp.785-790, 1998. ,
DOI : 10.1016/S0266-3538(97)00170-X
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
On the Optimality of the Discrete Karhunen--Lo??ve Expansion, SIAM Journal on Control and Optimization, vol.36, issue.6, pp.1937-1939, 1998. ,
DOI : 10.1137/S0363012997315750
The modeling of inelastic composite materials with the transformation field analysis, Modelling and Simulation in Materials Science and Engineering, vol.2, issue.3A, pp.571-586, 1994. ,
DOI : 10.1088/0965-0393/2/3A/011
A numerical continuation method based on Pad?? approximants, International Journal of Solids and Structures, vol.37, issue.46-47, pp.6981-7001, 2000. ,
DOI : 10.1016/S0020-7683(99)00323-6
Long-wave in-plane buckling of elastoplastic square honeycombs, International Journal of Plasticity, vol.22, issue.9, pp.1569-1585, 2006. ,
DOI : 10.1016/j.ijplas.2005.09.003
Derivatives of tangential stiffness matrices for equilibrium path descriptions, International Journal for Numerical Methods in Engineering, vol.XVII, issue.5, pp.1093-1113, 1991. ,
DOI : 10.1115/1.3422829
On step size adjustments in structural continuation problems, Computers & Structures, vol.55, issue.3, pp.495-506, 1995. ,
DOI : 10.1016/0045-7949(95)98875-Q
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
Computational damage mechanics for composite materials based on mathematical homogenization, International Journal for Numerical Methods in Engineering, vol.25, issue.11, pp.1657-1679, 1999. ,
DOI : 10.1016/0013-7944(86)90035-4
Strain gradient plasticity Advances in applied mechanics, pp.295-361, 1997. ,
Asymptotic analysis of heterogeneous Cosserat media, International Journal of Solids and Structures, vol.38, issue.26-27, pp.4585-4608, 2001. ,
DOI : 10.1016/S0020-7683(00)00295-X
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
Elastoviscoplastic constitutive frameworks for generalized continua, Acta Mechanica, vol.160, issue.1-2, pp.71-111, 2003. ,
DOI : 10.1007/s00707-002-0975-0
Theory and practice of enginnering with rubber, 1978. ,
Strongly non-local gradient-enhanced finite strain elastoplasticity, International Journal for Numerical Methods in Engineering, vol.36, issue.14, pp.2039-2068, 2003. ,
DOI : 10.1016/S0020-7225(97)00116-X
Rubber and rubber elasticity: A review, Journal of Polymer Science: Polymer Symposia, vol.6, issue.1, pp.1-17, 1974. ,
DOI : 10.1002/polc.5070160221
A new constitutive relation for rubber. Rubber chemistry and technology, pp.59-61, 1996. ,
La méthode des puissances virtuelles en mécanique des milieux continus, première partie : théorie du second gradient, Journal de Mécanique, vol.12, pp.235-274, 1973. ,
Homogenization of nonlinearly elastic materials : microscopic bifurcation and macroscopic loss of rank-one convexity. Archive for Rational Mechanics and Analysis, pp.231-290, 1993. ,
A multi-level computational model for multi-scale damage analysis in composite and porous materials, International Journal of Solids and Structures, vol.38, issue.14, pp.2335-2385, 2001. ,
DOI : 10.1016/S0020-7683(00)00167-0
Approximate Models for Ductile Metals Containing Nonspherical Voids???Case of Axisymmetric Oblate Ellipsoidal Cavities, Journal of Engineering Materials and Technology, vol.116, issue.3, pp.290-297, 1994. ,
DOI : 10.1115/1.2904290
Approximate models for ductile metals containing non-spherical voids???Case of axisymmetric prolate ellipsoidal cavities, Journal of the Mechanics and Physics of Solids, vol.41, issue.11, pp.1723-1754, 1994. ,
DOI : 10.1016/0022-5096(93)90029-F
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
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
Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods, Computer Methods in Applied Mechanics and Engineering, vol.83, issue.2, pp.143-198, 1990. ,
DOI : 10.1016/0045-7825(90)90148-F
Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I???Yield Criteria and Flow Rules for Porous Ductile Media, Journal of Engineering Materials and Technology, vol.99, issue.1, pp.2-15, 1977. ,
DOI : 10.1115/1.3443401
The Elastic Moduli of Heterogeneous Materials, Journal of Applied Mechanics, vol.29, issue.1, pp.143-150, 1962. ,
DOI : 10.1115/1.3636446
On some variational principles in anisotropic and nonhomogeneous elasticity, Journal of the Mechanics and Physics of Solids, vol.10, issue.4, pp.335-342, 1962. ,
DOI : 10.1016/0022-5096(62)90004-2
A variational approach to the theory of the elastic behaviour of polycrystals, Journal of the Mechanics and Physics of Solids, vol.10, issue.4, pp.343-352, 1962. ,
DOI : 10.1016/0022-5096(62)90005-4
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
Zur theorie deformationen und der hierdurch im material hervorgerufnen nebenspannungen. Zeitschrift Für Angewandte mathematik und Mechanik, pp.323-334, 1924. ,
DOI : 10.1002/zamm.19240040405
The elastic behavior of a crystalline aggregate, Proceedings of the Physical Society A, pp.349-354, 1952. ,
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
A self-consistent mechanics of composite materials, Journal of the Mechanics and Physics of Solids, vol.13, issue.4, pp.213-222, 1965. ,
DOI : 10.1016/0022-5096(65)90010-4
On macroscopic effects of heterogeneity in elastoplastic media at finite strain, Mathematical Proceedings of the Cambridge Philosophical Society, vol.290, issue.03, pp.481-494, 1984. ,
DOI : 10.1016/0022-5096(67)90018-X
A comparison of homogenization and standard mechanics analyses for periodic porous composites, Computational Mechanics, vol.34, issue.2, pp.73-95, 1992. ,
DOI : 10.1007/3-540-17616-0
Turbulence, Coherent Structures, Dynamical Systems and Symmetry, 1998. ,
A new Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models, Journal of Elasticity, vol.61, pp.1-48, 2000. ,
DOI : 10.1007/0-306-48389-0_1
URL : https://hal.archives-ouvertes.fr/hal-01297725
Analysis of a complex of statistical variables into principal components., Journal of Educational Psychology, vol.24, issue.7, pp.498-520, 1933. ,
DOI : 10.1037/h0070888
Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, Applied Mechanics Reviews, vol.55, issue.5, 2002. ,
DOI : 10.1115/1.1497492
Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials, Proceedings of the Royal Society A, pp.101-127, 1976. ,
DOI : 10.1098/rspa.1976.0027
Fields in nonlinear composites : I. Theory, Proceedings of the Royal Society A, pp.183-202, 2007. ,
Some problems of the theory of plastic deformation, Prikl. Mat. Mekh, vol.7, 1943. ,
The elasto-plastic stability of plates. National Advisory Commitee for Aeronautics, Technical Memorandum, p.1188, 1947. ,
Quelques techniques pour appliquer la MAN aux structures plastiques et aux grands systèmes, 2001. ,
A general constitutive theory for linear and nonlinear particulate media with microstructure evolution, Journal of the Mechanics and Physics of Solids, vol.46, issue.3, pp.427-465, 1998. ,
DOI : 10.1016/S0022-5096(97)00095-1
Multiscale Methods for Composites: A Review, Archives of Computational Methods in Engineering, vol.69, issue.1, pp.31-75, 2009. ,
DOI : 10.1007/978-1-4613-8646-9_12
Zur spektraltheorie stochastischer prozesse, Annales Academiae Scientiarum Fennicae-Mathematica, vol.34, pp.1-7, 1946. ,
Techniques for the analysis of non-linear systems with applications to solids and structural mechanics. PhD thesis, In the series 'Acta Polytechnica Scandinavia, 1999. ,
Stabilized forms of orthogonal residual and constant incremental work control path following methods, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.13-16, pp.1389-1396, 2008. ,
DOI : 10.1016/j.cma.2007.11.002
Computational homogenization for the multi-scale analysis of multiphase materials, 2002. ,
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 : 10.1016/0956-7151(94)90502-9
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
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
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/(SICI)1097-0207(19991010)46:4<501::AID-NME685>3.0.CO;2-7
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.3061-3087, 2003. ,
DOI : 10.1016/S0045-7825(03)00341-4
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
Nonlinear composites: a linearization procedure, exact to second-order in contrast and for which the strain-energy and affine formulations coincide, Comptes Rendus M??canique, vol.332, issue.9, pp.693-700, 2004. ,
DOI : 10.1016/j.crme.2004.04.004
URL : https://hal.archives-ouvertes.fr/hal-00088254
On the effective behavior of nonlinear inelastic composites: II, Journal of the Mechanics and Physics of Solids, vol.55, issue.9, pp.1964-1992, 2007. ,
DOI : 10.1016/j.jmps.2007.02.004
URL : https://hal.archives-ouvertes.fr/hal-00214215
High-order predictor-corrector algorithms, International Journal for Numerical Methods in Engineering, vol.72, issue.6, pp.685-704, 2002. ,
DOI : 10.1016/S0045-7949(98)00336-8
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
PROPER ORTHOGONAL DECOMPOSITION AND ITS APPLICATIONS???PART I: THEORY, Journal of Sound and Vibration, vol.252, issue.3, pp.527-544, 2002. ,
DOI : 10.1006/jsvi.2001.4041
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/BF02417888
URL : https://hal.archives-ouvertes.fr/hal-00111435
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
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
Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I???Analysis, Journal of the Mechanics and Physics of Solids, vol.55, issue.8, pp.1677-1701, 2007. ,
DOI : 10.1016/j.jmps.2007.01.007
URL : https://hal.archives-ouvertes.fr/hal-00311891
Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: II???Results, Journal of the Mechanics and Physics of Solids, vol.55, issue.8, pp.1702-1728, 2007. ,
DOI : 10.1016/j.jmps.2007.01.008
URL : https://hal.archives-ouvertes.fr/hal-00311892
Empirical orthogonal eigenfunctions and statistical weather prediction, 1956. ,
Probability theory. Van Nostrand, 1955. ,
An iterative process based on homotopy and perturbation techniques, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.13-14, pp.1845-1858, 2000. ,
DOI : 10.1016/S0045-7825(00)00198-5
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
Large strain finite element analysis of a local second gradient model: application to localization, International Journal for Numerical Methods in Engineering, vol.28, issue.4, pp.499-521, 2002. ,
DOI : 10.1016/0020-7683(91)90004-Y
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
Nonuniform transformation field analysis, International Journal of Solids and Structures, vol.40, issue.25, pp.6937-6955, 2003. ,
DOI : 10.1016/S0020-7683(03)00346-9
URL : https://hal.archives-ouvertes.fr/hal-00088331
Computational analysis of nonlinear composite structures using the nonuniform transformation field analysis, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.48-51, pp.5477-5502, 2004. ,
DOI : 10.1016/j.cma.2003.12.071
URL : https://hal.archives-ouvertes.fr/hal-00088245
Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy, Computer Methods in Applied Mechanics and Engineering, vol.192, issue.5-6, pp.559-591, 2003. ,
DOI : 10.1016/S0045-7825(02)00564-9
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
Variational bounds on the effective moduli of anisotropic composites, Journal of the Mechanics and Physics of Solids, vol.36, issue.6, pp.597-629, 1988. ,
DOI : 10.1016/0022-5096(88)90001-4
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
A Theory of Large Elastic Deformation, Journal of Applied Physics, vol.92, issue.9, pp.582-592, 1940. ,
DOI : 10.1021/ie50271a013
The chemistery and physics of rubber-like substances, 1963. ,
A critical review of asymptotic numerical methods, Archives of Computational Methods in Engineering, vol.16, issue.Supp., pp.31-50, 1998. ,
DOI : 10.1080/12506559.1996.11509512
Variational self-consistent estimates for cubic viscoplastic polycrystals: the effects of grain anisotropy and shape, Journal of the Mechanics and Physics of Solids, vol.49, issue.2, pp.313-340, 2001. ,
DOI : 10.1016/S0022-5096(00)00037-5
Averaging theorems in finite deformation plasticity, Mechanics of Materials, vol.31, issue.8, pp.493-523, 1999. ,
DOI : 10.1016/S0167-6636(98)00073-8
Micromechanics : Overall properties of heterogeneous materials . North-Holland Series, Applied Mathematics and Mechanics, vol.37, 1993. ,
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
Potier-Ferry. A multiscale finite element approach for buckling analysis of elastoplastic long fiber composites, International Journal for Multiscale Computational Engineering, 2009. ,
Biaxial Testing of Membrane Biomaterials: Testing Equipment and Procedures, Journal of Biomechanical Engineering, vol.113, issue.3, pp.295-300, 1991. ,
DOI : 10.1115/1.2894887
Finite elements of non-linear continua, 1972. ,
Finite element methods for constrained problems in elasticity, International Journal for Numerical Methods in Engineering, vol.3, issue.5, pp.701-725, 1982. ,
DOI : 10.1016/0045-7825(78)90005-1
Large Deformation Isotropic Elasticity - On the Correlation of Theory and Experiment for Incompressible Rubberlike Solids, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.326, issue.1567, pp.565-584, 1972. ,
DOI : 10.1098/rspa.1972.0026
Elastic deformation of rubber-like solids. Mechanics of Solids, The Rondey Hill 60th Anniversary Volume, 1982. ,
Non-linear elastic deformations, 1984. ,
Long-wave buckling of elastic square honeycombs subject to in-plane biaxial compression, International Journal of Mechanical Sciences, vol.46, issue.11, pp.1697-1713, 2004. ,
DOI : 10.1016/j.ijmecsci.2004.09.011
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
Post-buckling analysis of elastic honeycombs subject to in-plane biaxial compression, International Journal of Solids and Structures, vol.39, issue.13-14, pp.3487-3503, 2002. ,
DOI : 10.1016/S0020-7683(02)00165-8
Elastoplastic microscopic bifurcation and post-bifurcation behavior of periodic cellular solids, Journal of the Mechanics and Physics of Solids, vol.52, issue.3, pp.641-666, 2004. ,
DOI : 10.1016/j.jmps.2003.07.002
Buckling behavior of Kelvin open-cell foams under ,
Improvements on Taylor's upper bound for rigid-plastic composites, Materials Science and Engineering: A, vol.175, issue.1-2, pp.15-19, 1994. ,
DOI : 10.1016/0921-5093(94)91039-1
Sur la représentation approchée d'une fonction par des fractions rationnelles. Annales scientifiques de l'École Normale Supérieure, pp.3-93 ,
Prediction of the elastic constants of multiphase materials, Trans. Am. Inst. Min. Metail. Pet. Engng, vol.218, pp.36-41, 1960. ,
GRADIENT ENHANCED DAMAGE FOR QUASI-BRITTLE MATERIALS, International Journal for Numerical Methods in Engineering, vol.23, issue.19, pp.3391-3403, 1996. ,
DOI : 10.1016/0020-7683(87)90083-7
The effective mechanical properties of nonlinear isotropic composites, Journal of the Mechanics and Physics of Solids, vol.39, issue.1, pp.45-71, 1991. ,
DOI : 10.1016/0022-5096(91)90030-R
New variational principles in plasticity and their application to composite materials, Journal of the Mechanics and Physics of Solids, vol.40, issue.8, pp.1757-1788, 1992. ,
DOI : 10.1016/0022-5096(92)90050-C
Exact second-order estimates for the effective mechanical properties of nonlinear composite materials, Journal of the Mechanics and Physics of Solids, vol.44, issue.6, pp.827-862, 1996. ,
DOI : 10.1016/0022-5096(96)00015-4
Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I???theory, Journal of the Mechanics and Physics of Solids, vol.50, issue.4, pp.737-757, 2002. ,
DOI : 10.1016/S0022-5096(01)00099-0
Variational estimates of the self-consistent type for some model nonlinear polycrystals, Proceedings of the Royal Society A, vol.453, pp.2715-2724, 1997. ,
Nonlinear composites Advances in Applied Mechanics, pp.171-302, 1998. ,
Constitutive models for porous materials with evolving microstructure, Journal of the Mechanics and Physics of Solids, vol.42, pp.1459-1497, 1994. ,
Strategies for tracing the nonlinear response near limit points éditeurs, Nonlinear Finite Element Analysis in Structural Mechanics, pp.63-89, 1981. ,
Etude de l'initiation de l'endommagement dans la matrice d'un matériau composite par une méthode d'homogénisation, Aerospace Science and Technology, vol.9, pp.37-51, 1987. ,
Some computational aspects of the stability analysis of nonlinear structures, Computer Methods in Applied Mechanics and Engineering, vol.47, issue.3, pp.219-259, 1984. ,
DOI : 10.1016/0045-7825(84)90078-1
Large Elastic Deformations of Isotropic Materials. IV. Further Developments of the General Theory, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.241, issue.835, pp.379-397, 1948. ,
DOI : 10.1098/rsta.1948.0024
Mechanics of composite strengthening. Fiber composite materials, American Society for Metals Seminar, pp.37-75, 1964. ,
A priori hyperreduction method: an adaptive approach, Journal of Computational Physics, vol.202, issue.1, pp.346-366, 2005. ,
DOI : 10.1016/j.jcp.2004.07.015
Incorporation of Experimentally-Derived Fiber Orientation into a Structural Constitutive Model for Planar Collagenous Tissues, Journal of Biomechanical Engineering, vol.21, issue.2, pp.280-287, 2003. ,
DOI : 10.1007/s004660050294
Non-homogeneous media and vibration theory, In : Lecture Notes in Physics, p.127, 1980. ,
Scale Effects in Media With Periodic and Nearly Periodic Microstructures, Part II: Failure Mechanisms, Journal of Applied Mechanics, vol.41, issue.4, pp.763-771, 1997. ,
DOI : 10.1115/1.2788980
Finite elements for materials with strain gradient effects, International Journal for Numerical Methods in Engineering, vol.9, issue.3, pp.373-391, 1999. ,
DOI : 10.1002/nme.1620090117
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
Turbulence and the dynamics of coherent structures. I. Coherent structures, Quarterly of Applied Mathematics, vol.45, issue.3, pp.561-590, 1987. ,
DOI : 10.1090/qam/910462
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
Multiscale aggregating discontinuities method for micro???macro failure of composites, Composites Part B: Engineering, vol.40, issue.6, pp.417-426, 2009. ,
DOI : 10.1016/j.compositesb.2009.01.007
Analyse limite et homogénéisation Comptes Rendus de l'Académie des sciences, pp.1355-1358, 1983. ,
Local and global aspects in the mathematical theory of plasticity. Dans A. Sawczuk et G. Bianchi, éditeurs, Plasticity today : modelling, methods and applications, pp.279-310, 1985. ,
Overall potentials and extremal surfaces of power law or ideally plastic composites, Journal of the Mechanics and Physics of Solids, vol.41, issue.6, pp.981-1002, 1993. ,
DOI : 10.1016/0022-5096(93)90051-G
Variational Principles for Inhomogeneous Non-linear Media, IMA Journal of Applied Mathematics, vol.35, issue.1, pp.39-54, 1986. ,
DOI : 10.1093/imamat/35.1.39
Some simple explicit bounds for the overall behaviour of nonlinear composites, International Journal of Solids and Structures, vol.29, issue.14-15, pp.1981-1987, 1992. ,
DOI : 10.1016/0020-7683(92)90188-Y
A Theory of Particle-Reinforced Plasticity, Journal of Applied Mechanics, vol.55, issue.1, pp.126-135, 1988. ,
DOI : 10.1115/1.3173618
Plastic strains in metals, Journal Institute of Metals, vol.62, pp.307-324, 1938. ,
A class of general algorithms for multi-scale analyses of heterogeneous media, Computer Methods in Applied Mechanics and Engineering, vol.190, issue.40-41, pp.5427-5464, 2001. ,
DOI : 10.1016/S0045-7825(01)00179-7
A high-order mixture model for periodic particulate composites, International Journal of Solids and Structures, vol.23, pp.989-1002, 1987. ,
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
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
Failure Surfaces for Finitely Strained Two-Phase Periodic Solids Under General In-Plane Loading, Journal of Applied Mechanics, vol.331, issue.3, pp.505-515, 2006. ,
DOI : 10.1016/0022-5096(89)90028-8
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
The Strain???Energy Function of a Hyperelastic Material in Terms of the Extension Ratios, Journal of Applied Physics, vol.38, issue.7, pp.2997-3002, 1967. ,
DOI : 10.1098/rsta.1951.0005
An asymptotic-numerical method to compute bifurcating branches, International Journal for Numerical Methods in Engineering, vol.288, issue.8, pp.1365-1389, 1998. ,
DOI : 10.1007/BFb0009197
On bounds for the overall elastic moduli of inhomogeneous systems???II, Journal of the Mechanics and Physics of Solids, vol.14, issue.5, pp.151-162, 1986. ,
DOI : 10.1016/0022-5096(66)90025-1
Elasticity theory of compositesA. Hopkins et M.I. Sewell, éditeurs , Mechanics of Solids, The Rodney Hill 60th Anniversary Volume, pp.653-686, 1982. ,
The Overall Elastic Response of Composite Materials, Journal of Applied Mechanics, vol.50, issue.4b, pp.1202-1209, 1983. ,
DOI : 10.1115/1.3167202
Variational estimates for the overall response of an inhomogeneous media ,
The overall response of nonlinear composite media, European Journal of Mechanics A, Solids, vol.19, pp.165-184, 2000. ,
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
A quadratically convergent procedure for the calculation of stability points in finite element analysis, Computer Methods in Applied Mechanics and Engineering, vol.70, issue.3, pp.329-347, 1988. ,
DOI : 10.1016/0045-7825(88)90024-2
Crack tip fields in strain gradient plasticity, Journal of the Mechanics and Physics of Solids, vol.44, issue.10, pp.1621-1648, 1996. ,
DOI : 10.1016/0022-5096(96)00035-X
A bridging domain method for coupling continua with molecular dynamics, Computer Methods in Applied Mechanics and Engineering, vol.193, issue.17-20, pp.1645-1669, 2004. ,
DOI : 10.1016/j.cma.2003.12.053
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
The reduced model multiscale method (R3M) for the non-linear homogenization of hyperelastic media at finite strains, Journal of Computational Physics, vol.223, issue.1, pp.341-368, 2007. ,
DOI : 10.1016/j.jcp.2006.09.019
URL : https://hal.archives-ouvertes.fr/hal-00693621
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
Méthode asymptotique numérique pour les coques en grandes rotations, 1998. ,
Asymptotic numerical method for strong nonlinearities. Revue Européenne des Eléments Finis, pp.13-97, 2004. ,
Solving plasticity problems by a perturbation technique, PAMM, vol.II b, issue.1, pp.455-456, 2005. ,
DOI : 10.1002/pamm.200510204
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
Asymptotic Numerical Method for Nonlinear Constitutive Laws, Revue Europ??enne des ??l??ments Finis, vol.10, issue.4, pp.841-869, 1998. ,
DOI : 10.1002/nme.1620100303
A finite element displacement formulation for gradient elastoplasticity, International Journal for Numerical Methods in Engineering, vol.5, issue.6, pp.1369-1388, 2001. ,
DOI : 10.1002/nme.1620050111
A strain energy function for arteries accounting for wall composition and structure, Journal of Biomechanics, vol.37, issue.7, pp.989-1000, 2004. ,
DOI : 10.1016/j.jbiomech.2003.11.026
Diagrammes contraintes-déformations pour les problèmes de traction et de compression pour le modèle compressible, p.122 ,