H. Ammari and H. Kang, Polarization and Moment Tensors with Applications to Inverse Problems and Effective Medium Theory, Appl. Math. Sci, vol.162, 2007.

H. Ammari, H. Kang, and K. Touibi, Boundary layer techniques for deriving the effective properties of composite materials, Asymptotic Anal, pp.41-119, 2005.

S. Amstutz, S. M. Giusti, A. A. Novotny, E. A. De-souza, and . Neto, Topological derivative for multi-scale linear elasticity models applied to the synthesis of microstructures, International Journal for Numerical Methods in Engineering, vol.78, issue.3, pp.733-756, 2010.
DOI : 10.1126/science.238.4826.551-a

I. V. Andrianov, V. I. Bolshakov, V. V. Danishevs-'kyy, and D. Weichert, Higher order asymptotic homogenization and wave propagation in periodic composite materials, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.191, issue.2024, pp.1181-1201, 2008.
DOI : 10.1070/SM2000v191n07ABEH000491

H. Askes and E. C. , Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results, International Journal of Solids and Structures, vol.48, issue.13, p.1962, 1990.
DOI : 10.1016/j.ijsolstr.2011.03.006

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

M. Bonnet, Higher-order topological sensitivity for 2-D potential problems. Application to fast identification of inclusions, International Journal of Solids and Structures, vol.46, issue.11-12, pp.2275-2292, 2009.
DOI : 10.1016/j.ijsolstr.2009.01.021
URL : https://hal.archives-ouvertes.fr/hal-00495407

M. Bonnet and R. Cornaggia, Higher order topological derivatives for three-dimensional anisotropic elasticity, ESAIM: Mathematical Modelling and Numerical Analysis, vol.244, issue.6, pp.2069-2092, 2017.
DOI : 10.1002/pssb.200572719
URL : https://hal.archives-ouvertes.fr/hal-01499498

L. Brioullin, Wave Propagation in Periodic Structures, 1953.

D. J. Cedio-fengya, S. Moskow, and M. Vogelius, Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction, Inverse Problems, vol.14, issue.3, pp.553-595, 1998.
DOI : 10.1088/0266-5611/14/3/011

R. Craster, J. Kaplunov, E. Nolde, and S. Guenneau, Bloch dispersion and high frequency homogenization for separable doubly-periodic structures, Wave Motion, vol.49, issue.2, pp.333-346, 2012.
DOI : 10.1016/j.wavemoti.2011.11.005
URL : https://hal.archives-ouvertes.fr/hal-00761147

J. F. Douglas and E. J. Garboczi, Intrinsic Viscosity and the Polarizability of Particles Having a Wide Range of Shapes, Adv. Chem. Phys, vol.43, issue.1, pp.91-85, 1995.
DOI : 10.1103/PhysRevA.43.6473

M. Farhat, S. Guenneau, S. Enoch, A. Movchan, F. Zolla et al., A homogenization route towards square cylindrical acoustic cloaks, New Journal of Physics, vol.10, issue.11, p.115030, 2008.
DOI : 10.1088/1367-2630/10/11/115030
URL : https://hal.archives-ouvertes.fr/hal-00468908

M. Giusti, A. A. Novotny, E. A. De-souza, and . Neto, Sensitivity of the macroscopic response of elastic microstructures to the insertion of inclusions, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.192, issue.12, p.466, 2010.
DOI : 10.1016/j.jbiomech.2008.06.020

B. Guzina and M. Bonnet, Small-inclusion asymptotic of misfit functionals for inverse problems in acoustics, Inverse Problems, vol.22, issue.5, pp.1761-1786, 2006.
DOI : 10.1088/0266-5611/22/5/014
URL : https://hal.archives-ouvertes.fr/hal-00111266

F. Hecht, New development in freefem++, Journal of Numerical Mathematics, vol.20, issue.3-4, pp.251-265, 2012.
DOI : 10.1515/jnum-2012-0013
URL : https://hal.archives-ouvertes.fr/hal-01476313

G. C. Hsiao and W. L. Wendland, Boundary Integral Equations, 2008.

D. Joyce, W. J. Parnell, R. C. Assier, and I. D. Abrahams, An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems, Soc. Proc. Lond. Ser. A Math, 2017.
DOI : 10.3732/ajb.90.3.333

A. and L. Hyaric, Introduction to FreeFem++-cs, preprint, https://hal.archives-ouvertes, p.1169630, 2015.

M. Maldovan, Sound and heat revolutions in phononics, Nature, vol.84, issue.7475, pp.503-209, 2013.
DOI : 10.1103/PhysRevE.84.065701

G. Milton, M. Briane, and J. Willis, On cloaking for elasticity and physical equations with a transformation invariant form, New Journal of Physics, vol.8, issue.10, p.248, 2006.
DOI : 10.1088/1367-2630/8/10/248
URL : https://hal.archives-ouvertes.fr/hal-00452194

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.109-1240020, 1968.
DOI : 10.1016/0020-7683(68)90036-X

H. Nassar, Q. He, and N. Auffray, Willis elastodynamic homogenization theory revisited for periodic media, Journal of the Mechanics and Physics of Solids, vol.77, pp.77-158, 2015.
DOI : 10.1016/j.jmps.2014.12.011
URL : https://hal.archives-ouvertes.fr/hal-01112307

A. A. Novotny and J. Sokoo-lowski, Topological Derivatives in Shape Optimization
DOI : 10.1007/978-3-642-35245-4
URL : https://hal.archives-ouvertes.fr/hal-01304757

M. Otomori, T. Yamada, K. Izui, S. Nishiwaki, and J. Andkjaer, A topology optimization method based on the level set method for the design of negative permeability dielectric metamaterials, Computer Methods in Applied Mechanics and Engineering, vol.237, issue.240, pp.192-211, 2012.
DOI : 10.1016/j.cma.2012.04.022

A. Toader, The Topological Derivative of Homogenized Elastic Coefficients of Periodic Microstructures, SIAM Journal on Control and Optimization, vol.49, issue.4, pp.1607-1628, 2011.
DOI : 10.1137/100782772

A. Wautier and B. B. Guzina, On the second-order homogenization of wave motion in periodic media and the sound of a chessboard, Journal of the Mechanics and Physics of Solids, vol.78, pp.78-382, 2015.
DOI : 10.1016/j.jmps.2015.03.001
URL : https://hal.archives-ouvertes.fr/hal-01984505

J. R. Willis, Dynamics of Composites, Continuum Micromechanics, pp.265-290, 1997.
DOI : 10.1007/978-3-7091-2662-2_5

J. Zhu, J. Christensen, J. Jung, L. Martin-moreno, X. Yin et al., A holey-structured metamaterial for acoustic deep-subwavelength imaging, Nature Physics, vol.7, issue.1, pp.52-55, 2011.
DOI : 10.1103/PhysRevLett.104.164301
URL : https://www.nature.com/articles/nphys1804.pdf