N. Auffray, F. Dell-'isola, V. A. Eremeyev, A. Madeo, and G. Rosi, Hamilton???Piola least action principle for second gradient continua and capillary fluids, Mathematics and Mechanics of Solids, vol.309, issue.4, pp.375-417, 2015.
DOI : 10.1137/0125053

URL : https://hal.archives-ouvertes.fr/hal-00836085

J. Louis, A. , and C. Boutin, Long wavelength inner-resonance cut-off frequencies in elastic composite materials, International Journal of Solids and Structures, vol.49, pp.23-243269, 2012.

G. Barbagallo, A. Madeo, M. Valerio-d-'agostino, and R. Abreu, Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics, International Journal of Solids and Structures, vol.120, pp.7-30, 2017.
DOI : 10.1016/j.ijsolstr.2017.01.030

URL : https://hal.archives-ouvertes.fr/hal-01719592

S. Bauer, P. Neff, D. Pauly, and G. Starke, New Poincar??-type inequalities, Comptes Rendus Mathematique, vol.352, issue.2, pp.163-166, 2014.
DOI : 10.1016/j.crma.2013.11.017

S. Bauer, P. Neff, D. Pauly, and G. Starke, Dev-Div-and DevSym-DevCurl-inequalities for incompatible square tensor fields with mixed boundary conditions. ESAIM: Control, Optimisation and Calculus of Variations, pp.112-133, 2016.
DOI : 10.1051/cocv/2014068

C. Boutin and S. Hans, Homogenisation of periodic discrete medium: Application to dynamics of framed structures, Computers and Geotechnics, vol.30, issue.4, pp.303-320, 2003.
DOI : 10.1016/S0266-352X(03)00005-3

C. Boutin, S. Hans, and C. Chesnais, Generalized Beams and Continua, Dynamics of Reticulated Structures, pp.131-141, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00941153

C. Boutin and J. Soubestre, Generalized inner bending continua for linear fiber reinforced materials, International Journal of Solids and Structures, vol.48, issue.3-4, pp.517-534, 2011.
DOI : 10.1016/j.ijsolstr.2010.10.017

URL : https://hal.archives-ouvertes.fr/hal-00941247

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, vol.468, issue.2141, pp.47120140465-20140465, 2014.
DOI : 10.1098/rspa.2011.0652

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

M. Valerio-d-'agostino, G. Barbagallo, A. Ghiba, P. Madeo, and . Neff, A panorama of dispersion curves for the weighted isotropic relaxed micromorphic model, Zeitschrift für Angewandte Mathematik und Mechanik, 2017.

F. Dell-'isola, U. Andreaus, and L. Placidi, At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola, Mathematics and Mechanics of Solids, vol.20, issue.8, pp.887-928, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00869677

F. Dell-'isola, A. D. Corte, and I. Giorgio, Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives, Mathematics and Mechanics of Solids, vol.22, issue.4, pp.852-872, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01256929

A. Pierre and . Deymier, Acoustic metamaterials and phononic crystals, Springer series in solid-state sciences, pp.378-2013

Y. Fan, M. Collet, M. Ichchou, L. Li, O. Bareille et al., Energy flow prediction in built-up structures through a hybrid finite element/wave and finite element approach, Mechanical Systems and Signal Processing, pp.66-67137, 2016.
DOI : 10.1016/j.ymssp.2015.05.014

I. Ghiba, P. Neff, A. Madeo, L. Placidi, and G. Rosi, The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics, Mathematics and Mechanics of Solids, vol.67, issue.4, pp.1171-1197, 2015.
DOI : 10.1007/BF01170371

URL : https://hal.archives-ouvertes.fr/hal-01167932

Z. Liu, X. Zhang, Y. Mao, 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. Lucklum, M. Ke, and M. Zubtsov, Two-dimensional phononic crystal sensor based on a cavity mode, Sensors and Actuators B: Chemical, vol.171, issue.172, pp.171-172271, 2012.
DOI : 10.1016/j.snb.2012.03.063

A. Madeo, G. Barbagallo, M. Valerio-d-'agostino, L. Placidi, and P. Neff, First evidence of nonlocality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, p.47220160169, 2016.

A. Madeo, M. Collet, M. Miniaci, K. Billon, M. Ouisse et al., Modeling Phononic Crystals via the Weighted Relaxed Micromorphic Model with Free and Gradient Micro-Inertia, Journal of Elasticity, vol.25, issue.7, 2017.
DOI : 10.1143/JJAP.38.1282

A. Madeo, P. Neff, E. C. Aifantis, G. Barbagallo, and M. Valerio-d-'agostino, On the role of microinertia in enriched continuum mechanics, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, p.47320160722, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01720513

A. Madeo, P. Neff, G. Barbagallo, M. Valerio-d-'agostino, and I. Ghiba, A Review on Wave Propagation Modeling in Band-Gap Metamaterials via Enriched Continuum Models, Mathematical Modelling in Solid Mechanics, Advanced Structured Materials, pp.89-105, 2017.
DOI : 10.1177/1081286512474016

A. Madeo, P. Neff, M. Valerio-d-'agostino, and G. Barbagallo, Complete band gaps including non-local effects occur only in the relaxed micromorphic model, Comptes Rendus M??canique, vol.344, issue.11-12, pp.11-12784, 2016.
DOI : 10.1016/j.crme.2016.07.002

URL : https://hal.archives-ouvertes.fr/hal-01719611

A. Madeo, P. Neff, L. Ghiba, G. Placidi, and . Rosi, Band gaps in the relaxed linear micromorphic continuum, Zeitschrift für Angewandte Mathematik und Mechanik, pp.880-887, 2014.
DOI : 10.1016/S0997-7538(01)01144-5

URL : https://hal.archives-ouvertes.fr/hal-01082378

A. Madeo, P. Neff, L. Ghiba, G. Placidi, and . Rosi, Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps, Continuum Mechanics and Thermodynamics, vol.49, issue.3, pp.4-5551, 2015.
DOI : 10.1016/j.ijengsci.2011.04.005

URL : http://arxiv.org/pdf/1309.1722

A. Madeo, P. Neff, G. Ghiba, and . Rosi, Reflection and transmission of elastic waves in non-local band-gap metamaterials: A comprehensive study via the relaxed micromorphic model, Journal of the Mechanics and Physics of Solids, vol.95, pp.441-479, 2016.
DOI : 10.1016/j.jmps.2016.05.003

URL : https://hal.archives-ouvertes.fr/hal-01343543

P. Neff, M. Ghiba, A. Lazar, and . Madeo, The relaxed linear micromorphic continuum: well-posedness of the static problem and relations to the gauge theory of dislocations, The Quarterly Journal of Mechanics and Applied Mathematics, vol.68, issue.1, pp.53-84, 2015.
DOI : 10.1093/qjmam/hbu027

P. Neff, A. Ghiba, L. Madeo, G. Placidi, and . Rosi, A unifying perspective: the relaxed linear micromorphic continuum, Continuum Mechanics and Thermodynamics, vol.44, issue.1, pp.639-681, 2014.
DOI : 10.1016/j.ijengsci.2006.08.002

URL : https://hal.archives-ouvertes.fr/hal-01167202

P. Neff, A. Madeo, G. Barbagallo, M. Valerio-d-'agostino, R. Abreu et al., Real wave propagation in the isotropic-relaxed micromorphic model, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, vol.59, issue.2197, p.47320160790, 2017.
DOI : 10.1016/j.euromechsol.2016.02.009

URL : https://hal.archives-ouvertes.fr/hal-01720523

P. Neff, D. Pauly, and K. Witsch, A canonical extension of Korn??s first inequality to motivated by gradient plasticity with plastic spin, Comptes Rendus Mathematique, vol.349, issue.23-24, pp.1251-1254, 2011.
DOI : 10.1016/j.crma.2011.10.003

P. Neff, D. Pauly, and K. Witsch, Maxwell meets Korn: A new coercive inequality for tensor fields in RN??N with square-integrable exterior derivative, Mathematical Methods in the Applied Sciences, vol.14, issue.1, pp.65-71, 2012.
DOI : 10.1051/cocv:2007050

P. Neff, D. Pauly, and K. Witsch, Poincar?? meets Korn via Maxwell: Extending Korn's first inequality to incompatible tensor fields, Journal of Differential Equations, vol.258, issue.4, pp.1267-1302, 2015.
DOI : 10.1016/j.jde.2014.10.019

URL : http://arxiv.org/pdf/1203.2744

K. Pham, V. G. Kouznetsova, and M. G. Geers, Transient computational homogenization for heterogeneous materials under dynamic excitation, Journal of the Mechanics and Physics of Solids, vol.61, issue.11, pp.612125-2146, 2013.
DOI : 10.1016/j.jmps.2013.07.005

L. Placidi, U. Andreaus, and I. Giorgio, Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model, Journal of Engineering Mathematics, vol.97, issue.1, pp.1-21, 2017.
DOI : 10.1016/j.ijengsci.2015.10.003

A. Spadoni, M. Ruzzene, S. Gonella, and F. Scarpa, Phononic properties of hexagonal chiral lattices, Wave Motion, vol.46, issue.7, pp.435-450, 2009.
DOI : 10.1016/j.wavemoti.2009.04.002

URL : https://infoscience.epfl.ch/record/165484/files/Paper7_ChiralWaves.pdf

A. Sridhar, V. G. Kouznetsova, and M. G. Geers, Homogenization of locally resonant acoustic metamaterials towards an emergent enriched continuum, Computational Mechanics, vol.35, issue.1, pp.423-435, 2016.
DOI : 10.1007/s11044-014-9447-2

K. Yi, M. Collet, M. Ichchou, and L. Li, Flexural waves focusing through shunted piezoelectric patches, Smart Materials and Structures, vol.25, issue.7, p.75007, 2016.
DOI : 10.1088/0964-1726/25/7/075007