S. B. Altan and E. C. Aifantis, On the structure of the mode III crack-tip in gradient elasticity, Scripta Metallurgica et Materialia, vol.26, issue.2, pp.319-324, 1992.
DOI : 10.1016/0956-716X(92)90194-J

A. Bensoussan, J. Lions, and G. C. Papanicolaou, Asymptotic Analysis for Periodic Structures, 1978.

C. Boutin, Microstructural effects in elastic composites, International Journal of Solids and Structures, vol.33, issue.7, pp.1023-1051, 1996.
DOI : 10.1016/0020-7683(95)00089-5

URL : https://hal.archives-ouvertes.fr/hal-00940462

F. Bouyge, I. Jasiuk, and M. Ostoja-starzewski, A micromechanically based couple???stress model of an elastic two-phase composite, International Journal of Solids and Structures, vol.38, issue.10-13, pp.1721-1735, 2001.
DOI : 10.1016/S0020-7683(00)00132-3

F. Bouyge, I. Jasiuk, and M. Ostoja-starzewski, A micromechanically based couple-stress model of an elastic orthotropic twophase composite, Eur. J. Mech. A, vol.21, p.465481, 2002.

R. Chambon, D. Caillerie, and T. Matsuchima, Plastic continuum with microstructure, local second gradient theories for geomaterials: localization studies, International Journal of Solids and Structures, vol.38, issue.46-47, pp.8503-8527, 2001.
DOI : 10.1016/S0020-7683(01)00057-9

G. Diener, C. Raabe, and J. Weissbarth, Bounds for the non-local effective properties of random media, Journal of the Mechanics and Physics of Solids, vol.29, issue.3, pp.181-198, 1981.
DOI : 10.1016/0022-5096(81)90025-9

G. Diener, C. Raabe, and J. Weissbarth, Bounds for the non-local effective properties of random media???II, Journal of the Mechanics and Physics of Solids, vol.30, issue.5, pp.305-322, 1982.
DOI : 10.1016/0022-5096(82)90002-3

G. Diener, A. Hurrich, and J. Weissbarth, Bounds on the non-local effective elastic properties of composites, Journal of the Mechanics and Physics of Solids, vol.32, issue.1, pp.21-39, 1984.
DOI : 10.1016/0022-5096(84)90003-6

W. J. Drugan and J. R. Willis, A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites, Journal of the Mechanics and Physics of Solids, vol.44, issue.4, pp.497-524, 1996.
DOI : 10.1016/0022-5096(96)00007-5

R. A. Engelen, N. A. Fleck, R. H. Peerlings, and M. G. Geers, An evaluation of higher-order plasticity theories for predicting size effects and localisation, International Journal of Solids and Structures, vol.43, issue.7-8, pp.1857-1877, 2006.
DOI : 10.1016/j.ijsolstr.2004.05.072

G. Exadaktylos, Gradient elasticity with surface energy: Mode-I crack problem, International Journal of Solids and Structures, vol.35, issue.5-6, pp.5-6, 1998.
DOI : 10.1016/S0020-7683(97)00036-X

N. A. Fleck and J. W. Hutchinson, A phenomenological theory for strain gradient effects in plasticity, Journal of the Mechanics and Physics of Solids, vol.41, issue.12, pp.1825-1857, 1993.
DOI : 10.1016/0022-5096(93)90072-N

N. A. Fleck, G. M. Muller, M. F. Ashby, and J. W. Hutchinson, Strain gradient plasticity: Theory and experiment, Acta Metallurgica et Materialia, vol.42, issue.2, pp.475-487, 1994.
DOI : 10.1016/0956-7151(94)90502-9

]. S. Forest, Mechanics of generalized continua: construction by homogenizaton, Le Journal de Physique IV, vol.08, issue.PR4, pp.39-48, 1998.
DOI : 10.1051/jp4:1998405

]. S. Forest, Milieux continus généralisés et matériaux hétérogènes, 2006.

]. B. Gambin and E. Kroner, Higher-Order Terms in the Homogenized Stress-Strain Relation of Periodic Elastic Media, physica status solidi (b), vol.7, issue.2, pp.513-519
DOI : 10.1002/pssb.2221510211

H. G. Georgiadis and C. G. Grentzelou, Energy theorems and the J-integral in dipolar gradient elasticity, International Journal of Solids and Structures, vol.43, issue.18-19, pp.18-19, 2006.
DOI : 10.1016/j.ijsolstr.2005.08.009

]. A. Green and R. S. Rivlin, Multipolar continuum mechanics, Arch. Rat. Mech. Anal, vol.17, pp.113-147, 1964.
DOI : 10.1007/bf00253051

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.469.5709

V. Kouznetsova, M. G. Geers, and W. A. Brekelmans, 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

R. D. Mindlin, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis, vol.16, issue.1, pp.51-78, 1964.
DOI : 10.1007/BF00248490

R. D. Mindlin, Second gradient of strain and surface-tension in linear elasticity, International Journal of Solids and Structures, vol.1, issue.4, pp.417-438, 1965.
DOI : 10.1016/0020-7683(65)90006-5

R. D. Mindlin and N. N. , On first strain-gradient theories in linear elasticity, International Journal of Solids and Structures, vol.4, issue.1, pp.109-124, 1968.
DOI : 10.1016/0020-7683(68)90036-X

]. H. Moulinec and P. Suquet, A fast numerical method for computing the linear and nonlinear mechanical properties of composites, C. R. Acad. Sci, issue.11, pp.318-1417, 1994.

H. B. Mühlhaus and E. C. Aifantis, A variational principle for gradient plasticity, International Journal of Solids and Structures, vol.28, issue.7, pp.845-857, 1991.
DOI : 10.1016/0020-7683(91)90004-Y

V. P. Smyshlyaev and K. D. Cherednichenko, On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media, Journal of the Mechanics and Physics of Solids, vol.48, issue.6-7, pp.1325-1357, 2000.
DOI : 10.1016/S0022-5096(99)00090-3

]. R. Toupin, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis, vol.38, issue.1, pp.385-414, 1962.
DOI : 10.1007/BF00253945

URL : https://hal.archives-ouvertes.fr/hal-00852443

]. R. Toupin, Theories of elasticity with couple-stress, Archive for Rational Mechanics and Analysis, vol.17, issue.2, pp.85-112, 1964.
DOI : 10.1007/BF00253050

URL : https://hal.archives-ouvertes.fr/hal-00853382

N. Triantafyllidis and E. C. Aifantis, A gradient approach to localization of deformation. I. Hyperelastic materials, Journal of Elasticity, vol.5, issue.3, pp.225-237, 1986.
DOI : 10.1007/BF00040814

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

I. Vardoulakis, G. Exadaktylos, and E. Aifantis, Gradient elasticity with surface energy: mode-III crack problem, International Journal of Solids and Structures, vol.33, issue.30, pp.4531-4559, 1996.
DOI : 10.1016/0020-7683(95)00277-4

X. Yuan, Y. Tomita, and T. Andou, A micromechanical approach of nonlocal modeling for media with periodic microstructures, Mechanics Research Communications, vol.35, issue.1-2, p.126133, 2008.
DOI : 10.1016/j.mechrescom.2007.07.004