C. Boutin and J. L. Auriault, Rayleigh scattering in elastic composite materials, International Journal of Engineering Science, vol.31, issue.12, pp.1669-1689, 1993.
DOI : 10.1016/0020-7225(93)90082-6

URL : https://hal.archives-ouvertes.fr/hal-00940461

C. Boutin, A. Rallu, and S. Hans, Large scale modulation of high frequency waves in periodic elastic composites, Journal of the Mechanics and Physics of Solids, vol.70, pp.362-381, 2014.
DOI : 10.1016/j.jmps.2014.05.015

H. Chen and C. T. Chan, Acoustic cloaking and transformation acoustics, Journal of Physics D: Applied Physics, vol.43, issue.11, 2010.
DOI : 10.1088/0022-3727/43/11/113001

D. J. Colquitt, R. V. Craster, T. Antonakakis, and S. Guenneau, Rayleigh-Bloch waves along elastic diffraction gratings, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, 2014.
DOI : 10.1098/rspa.2011.0652

URL : https://hal.archives-ouvertes.fr/hal-01283610

R. V. Craster, J. Kaplunov, and A. V. Pichugin, High-frequency homogenization for periodic media, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.26, issue.5685, pp.2341-2362, 2010.
DOI : 10.1126/science.1096796

E. Daya, B. Braikat, N. Damil, and M. Potier-ferry, Continuum modeling for the modulated vibration modes of large repetitive structures, Comptes Rendus M??canique, vol.330, issue.5, pp.333-338, 2002.
DOI : 10.1016/S1631-0721(02)01464-X

D. P. Divincenzo, Dispersive corrections to continuum elastic theory in cubic crystals, Physical Review B, vol.34, issue.8, pp.5450-5465, 1986.
DOI : 10.1103/PhysRevB.34.5450

J. H. Lee, J. P. Singer, and E. L. Thomas, Micro-/Nanostructured Mechanical Metamaterials, Advanced Materials, vol.106, issue.36, pp.4782-4810, 2012.
DOI : 10.1002/adma.201201644

Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang et al., Locally Resonant Sonic Materials, Science, vol.289, issue.5485, pp.1734-1736, 2000.
DOI : 10.1126/science.289.5485.1734

R. Maranganti and P. Sharma, A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies, Journal of the Mechanics and Physics of Solids, vol.55, issue.9, pp.1823-1852, 2007.
DOI : 10.1016/j.jmps.2007.02.011

G. W. Milton, M. Briane, and J. R. Willis, On cloaking for elasticity and physical equations with a transformation invariant form, New Journal of Physics, vol.8, issue.10, pp.248-267, 2006.
DOI : 10.1088/1367-2630/8/10/248

URL : https://hal.archives-ouvertes.fr/hal-00452194

G. W. Milton and J. R. Willis, On modifications of Newton's second law and linear continuum elastodynamics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.463, issue.2079, pp.855-880, 2007.
DOI : 10.1098/rspa.2006.1795

G. W. Milton and J. R. Willis, Minimum variational principles for time-harmonic waves in a dissipative medium and associated variational principles of Hashin-Shtrikman type, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.6, issue.2102, pp.3013-3032, 2010.
DOI : 10.1098/rspa.2008.0195

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

H. Nassar, Q. C. He, and N. Auffray, Willis elastodynamic homogenization theory revisited for periodic media, Journal of the Mechanics and Physics of Solids, vol.77, pp.158-178, 2015.
DOI : 10.1016/j.jmps.2014.12.011

URL : https://hal.archives-ouvertes.fr/hal-01112307

S. Nemat-nasser and A. Srivastava, Overall dynamic constitutive relations of layered elastic composites, Journal of the Mechanics and Physics of Solids, vol.59, issue.10, pp.1953-1965, 2011.
DOI : 10.1016/j.jmps.2011.07.008

S. Nemat-nasser and A. Srivastava, Homogenized dynamic constitutive relation for Bloch-wave propagation in periodic composites: structure and symmetries, Photonic and Phononic Properties of Engineered Nanostructures II, pp.82690-82690, 2012.
DOI : 10.1117/12.916572

S. Nemat-nasser and A. Srivastava, Bounds on effective dynamic properties of elastic composites, Journal of the Mechanics and Physics of Solids, vol.61, issue.1, pp.254-264, 2013.
DOI : 10.1016/j.jmps.2012.07.003

S. Nemat-nasser, J. R. Willis, A. Srivastava, and A. V. Amirkhizi, Homogenization of periodic elastic composites and locally resonant sonic materials, Physical Review B, vol.83, issue.10, 2011.
DOI : 10.1103/PhysRevB.83.104103

E. Nolde, R. V. Craster, and J. Kaplunov, High frequency homogenization for structural mechanics, Journal of the Mechanics and Physics of Solids, vol.59, issue.3, pp.651-671, 2011.
DOI : 10.1016/j.jmps.2010.12.004

A. N. Norris, Acoustic cloaking theory, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.43, issue.5801, pp.2411-2434, 2008.
DOI : 10.1126/science.1133628

URL : http://arxiv.org/abs/0805.0080

A. N. Norris and A. L. Shuvalov, Elastic cloaking theory, Wave Motion, vol.48, issue.6, pp.525-538, 2011.
DOI : 10.1016/j.wavemoti.2011.03.002

URL : http://arxiv.org/abs/1103.6045

A. N. Norris, A. L. Shuvalov, and A. A. Kutsenko, Analytical formulation of three-dimensional dynamic homogenization for periodic elastic systems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.467, issue.2131, pp.1629-1651, 2012.
DOI : 10.1098/rspa.2010.0620

A. V. Pichugin, H. Askes, and A. Tyas, Asymptotic equivalence of homogenisation procedures and fine-tuning of continuum theories, Journal of Sound and Vibration, vol.313, issue.3-5, pp.858-874, 2008.
DOI : 10.1016/j.jsv.2007.12.005

E. Sanchez-palencia, Non-homogeneous media and vibration theory, 1980.

A. L. Shuvalov, A. A. Kutsenko, A. N. Norris, and O. Poncelet, Effective Willis constitutive equations for periodically stratified anisotropic elastic media, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.41, issue.1, pp.1749-1769, 2011.
DOI : 10.1121/1.1488942

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

A. Srivastava and S. Nemat-nasser, Overall dynamic properties of three-dimensional periodic elastic composites, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.467, issue.2131, pp.269-287, 2011.
DOI : 10.1098/rspa.2010.0620

N. Turbé, Applications of bloch expansion to periodic elastic and viscoelastic media, Mathematical Methods in the Applied Sciences, vol.33, issue.1, pp.433-449, 1982.
DOI : 10.1002/mma.1670040128

N. Turbé, Bloch expansion in generalized thermoelasticity, International Journal of Engineering Science, vol.27, issue.1, pp.55-62, 1989.
DOI : 10.1016/0020-7225(89)90167-5

J. R. Willis, Polarization approach to the scattering of elastic waves???I. Scattering by a single inclusion, Journal of the Mechanics and Physics of Solids, vol.28, issue.5-6, pp.287-305, 1980.
DOI : 10.1016/0022-5096(80)90021-6

J. R. Willis, A polarization approach to the scattering of elastic waves???II. Multiple scattering from inclusions, Journal of the Mechanics and Physics of Solids, vol.28, issue.5-6, pp.307-327, 1980.
DOI : 10.1016/0022-5096(80)90022-8

J. R. Willis, Variational principles for dynamic problems for inhomogeneous elastic media, Wave Motion, vol.3, issue.1, pp.1-11, 1981.
DOI : 10.1016/0165-2125(81)90008-1

J. R. Willis, The nonlocal influence of density variations in a composite, International Journal of Solids and Structures, vol.21, issue.7, pp.805-817, 1985.
DOI : 10.1016/0020-7683(85)90084-8

J. R. Willis, Exact effective relations for dynamics of a laminated body, Mechanics of Materials, vol.41, issue.4, pp.385-393, 2009.
DOI : 10.1016/j.mechmat.2009.01.010

J. R. Willis, Effective constitutive relations for waves in composites and metamaterials, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.41, issue.2079, pp.1865-1879, 2011.
DOI : 10.1098/rspa.2006.1795

J. R. Willis, The construction of effective relations for waves in a composite, Comptes Rendus M??canique, vol.340, issue.4-5, pp.181-192, 2012.
DOI : 10.1016/j.crme.2012.02.001