M. Arnold and . Microscopie-optique, Techniques de l'Ingénieur, traité Analyse et Caractérisation, pp.1-22, 1993.

]. S. Degallaix and B. Ilschner, « Caractérisation expérimentale des matériaux I », 1 ère ed, Presses Polytechniques et universitaires romandes, 2007.

C. Perrot, R. Panneton, and X. Olny, Periodic unit cell reconstruction of porous media: Application to open-cell aluminum foams, Journal of Applied Physics, vol.101, issue.11, pp.1-11, 2007.
DOI : 10.1063/1.2745095
URL : https://hal.archives-ouvertes.fr/hal-00731850

H. C. Brinkman, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Flow, Turbulence and Combustion, vol.15, issue.1, pp.27-34, 1949.
DOI : 10.1002/andp.19063240204

R. Hill, 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

]. E. Kröner, J. Gittus, and J. Zarka, Statistical Modelling, 1987.
DOI : 10.1007/978-94-009-4181-6_8

J. B. Keller, « Effective behaviour of heterogeneous media », Statistical mechanics and statistical methods in theory and application, E. U. Landman, pp.631-664, 1997.

M. A. Biot, Theory of Propagation of Elastic Waves in a Fluid???Saturated Porous Solid. I. Low???Frequency Range, The Journal of the Acoustical Society of America, vol.28, issue.2, pp.168-178, 1956.
DOI : 10.1121/1.1908239
URL : https://hal.archives-ouvertes.fr/hal-01368668

M. A. Biot, Theory of Propagation of Elastic Waves in a Fluid???Saturated Porous Solid. II. Higher Frequency Range, The Journal of the Acoustical Society of America, vol.28, issue.2, pp.179-191, 1956.
DOI : 10.1121/1.1908241
URL : https://hal.archives-ouvertes.fr/hal-01368668

T. Lévy, Propagation of waves in a fluid-saturated porous elastic solid, International Journal of Engineering Science, vol.17, issue.9, pp.1005-1014, 1979.
DOI : 10.1016/0020-7225(79)90022-3

M. Avellaneda and S. Torquato, Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media, Physics of Fluids A: Fluid Dynamics, vol.3, issue.11, pp.2529-2540, 1991.
DOI : 10.1063/1.858194

J. Rubinstein and S. Torquato, Diffusion???controlled reactions: Mathematical formulation, variational principles, and rigorous bounds, The Journal of Chemical Physics, vol.88, issue.10, pp.6372-6380, 1988.
DOI : 10.1063/1.454474

M. E. Delany and E. N. Bazley, Acoustical properties of fibrous absorbent materials, Applied Acoustics, vol.3, issue.2, pp.105-116, 1970.
DOI : 10.1016/0003-682X(70)90031-9

I. P. Dunn and W. A. , Calculation of acoustic impedance of multi-layer absorbers, Applied Acoustics, vol.19, issue.5, pp.321-334, 1986.
DOI : 10.1016/0003-682X(86)90044-7

W. Qunli and «. , Empirical relations between acoustical properties and flow resistivity of porous plastic open-cell foam, Applied Acoustics, vol.25, issue.3, pp.141-148, 1988.
DOI : 10.1016/0003-682X(88)90090-4

]. A. Cummings and S. P. Beadle, Acoustic Properties Of Reticulated Plastic Foams, Journal of Sound and Vibration, vol.175, issue.1, pp.115-133, 1994.
DOI : 10.1006/jsvi.1994.1315

R. T. Muehleisen, C. W. Beamer, and B. D. , Measurements and empirical model of the acoustic properties of reticulated vitreous carbon, The Journal of the Acoustical Society of America, vol.117, issue.2, pp.536-544, 2005.
DOI : 10.1121/1.1850343

C. Zwikker and C. W. Kosten, Attenborough, « Acoustical characteristics of rigid fibrous absorbants and granular materials, Sound absorbing materials, pp.785-799, 1949.

J. F. Allard, R. Bourdier, and P. Depollier, Biot waves in layered media, Biot waves in layered media, pp.1926-1929, 1986.
DOI : 10.1063/1.337244

D. L. Johnson, J. Koplik, and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, Journal of Fluid Mechanics, vol.24, issue.-1, pp.379-402, 1987.
DOI : 10.1121/1.388036

Y. Champoux and J. F. Allard, Dynamic tortuosity and bulk modulus in air???saturated porous media, Journal of Applied Physics, vol.70, issue.4, pp.1975-1979, 1991.
DOI : 10.1063/1.349482

D. Lafarge and «. , Propagation du son dans les matériaux poreux à structure rigide saturés par un fluide visco-thermique, Thèse de doctorat de l'université du Maine, pp.1-296, 1993.

D. Lafarge, P. Lemarinier, J. F. Allard, and V. Tarnow, Dynamic compressibility of air in porous structures at audible frequencies, The Journal of the Acoustical Society of America, vol.102, issue.4, pp.1995-2006, 1997.
DOI : 10.1121/1.419690

S. R. Pride, F. D. Morgan, and A. F. Gangi, Drag forces of porous-medium acoustics, Drag forces of porous media acoustics, pp.4964-4975, 1993.
DOI : 10.1103/PhysRevB.47.4964

]. S. Gasser, F. Paun, and Y. Bréchet, Absorptive properties of rigid porous media: Application to face centered cubic sphere packing, The Journal of the Acoustical Society of America, vol.117, issue.4, pp.2090-2099, 2005.
DOI : 10.1121/1.1863052

C. Perrot, F. Chevillotte, and R. Panneton, Dynamic viscous permeability of an open-cell aluminum foam: Computations versus experiments, Journal of Applied Physics, vol.103, issue.2, pp.1-8, 2008.
DOI : 10.1063/1.2829774
URL : https://hal.archives-ouvertes.fr/hal-00414900

C. Perrot, F. Chevillotte, M. T. Hoang, G. Bonnet, F. Bécot et al., Microstructure, transport, and acoustic properties of open-cell foam samples: Experiments and three-dimensional numerical simulations, Journal of Applied Physics, vol.111, issue.1, p.14911, 2012.
DOI : 10.1063/1.3673523
URL : https://hal.archives-ouvertes.fr/hal-00731446

M. T. Hoang and C. Perrot, Solid films and transports in cellular foams, Journal of Applied Physics, vol.112, issue.5, p.54911, 2012.
DOI : 10.1063/1.4751345
URL : https://hal.archives-ouvertes.fr/hal-00731906

F. Han, G. Seiffert, Y. Zhao, and B. Gibbs, Acoustic absorption behaviour of an open-celled aluminium foam, Journal of Physics D: Applied Physics, vol.36, issue.3, pp.294-302, 2003.
DOI : 10.1088/0022-3727/36/3/312

Z. Xie, T. Ikeda, Y. Okuda, and H. Nakajima, Sound absorption characteristics of lotus-type porous copper fabricated by unidirectional solidification, Materials Science and Engineering A, vol.386, issue.1-2, pp.390-395, 2004.
DOI : 10.1016/S0921-5093(04)00966-9

M. Hakamada, T. Kuromura, Y. Chen, H. Kusuda, and M. Mabuchi, Sound absorption characteristics of porous aluminum fabricated by spacer method, Journal of Applied Physics, vol.100, issue.11, p.114908, 2006.
DOI : 10.1063/1.2390543

M. Hakamada, T. Kuromura, Y. Chen, H. Kusuda, and M. Mabuchi, High sound absorption of porous aluminum fabricated by spacer method, Applied Physics Letters, vol.88, issue.25, p.254106, 2006.
DOI : 10.1063/1.2216104

W. Pannert, R. Winkler, and M. Merkel, On the acoustical properties of metallic hollow sphere structures (MHSS), Materials Letters, vol.63, issue.13-14, pp.1121-1124, 2009.
DOI : 10.1016/j.matlet.2008.10.063

D. L. Johnson, J. Koplik, and R. Dashen, Theory of dynamic permeability and tortuosity in fluid-saturated porous media, Journal of Fluid Mechanics, vol.24, issue.-1, p.379, 1987.
DOI : 10.1121/1.388036

C. Boutin and J. Auriault, Dynamic behaviour of porous media saturated by a viscoelastic fluid. Application to bituminous concretes, International Journal of Engineering Science, vol.28, issue.11, pp.1157-1181, 1990.
DOI : 10.1016/0020-7225(90)90115-Y
URL : https://hal.archives-ouvertes.fr/hal-00936259

Y. Champoux and J. F. Allard, Dynamic tortuosity and bulk modulus in air???saturated porous media, Journal of Applied Physics, vol.70, issue.4, p.1975, 1991.
DOI : 10.1063/1.349482

S. R. Pride, F. D. Morgan, and A. F. Gangi, Drag forces of porous-medium acoustics, Drag forces of porous media acoustics, p.4964, 1993.
DOI : 10.1103/PhysRevB.47.4964

D. K. Wilson, Relaxation???matched modeling of propagation through porous media, including fractal pore structure, The Journal of the Acoustical Society of America, vol.94, issue.2, pp.1136-1145, 1993.
DOI : 10.1121/1.406961

D. Lafarge, P. Lemarinier, J. F. Allard, and V. Tarnow, Dynamic compressibility of air in porous structures at audible frequencies, Dynamic compressibility of air in porous structures at audible frequencies, p.1995, 1997.
DOI : 10.1121/1.419690

C. Boutin and C. , Periodic homogenization and consistent estimates of transport parameters through sphere and polyhedron packings in the whole porosity range, Physical Review E, vol.82, issue.3, p.36313, 2010.
DOI : 10.1103/PhysRevE.82.036313
URL : https://hal.archives-ouvertes.fr/hal-00943731

]. A. Craggs and J. G. , Effective densities and resistivities for acoustic propagation in narrow tubes, Journal of Sound and Vibration, vol.92, issue.3, pp.321-331, 1984.
DOI : 10.1016/0022-460X(84)90382-1

M. Y. Zhou and P. Sheng, First-principles calculations of dynamic permeability in porous media, Physical Review B, vol.39, issue.16, p.12027, 1989.
DOI : 10.1103/PhysRevB.39.12027

A. M. Chapman and J. J. Higdon, Oscillatory Stokes flow in periodic porous media, Oscillatory Stokes flow in periodic porous media, pp.2099-2116, 1992.
DOI : 10.1063/1.858507

M. Firdaouss, J. Guermond, and D. Lafarge, Some remarks on the acoustic parameters of sharp-edged porous media, International Journal of Engineering Science, vol.36, issue.9, pp.1035-1081, 1998.
DOI : 10.1016/S0020-7225(98)00002-0

A. Cortis and D. M. , On the viscous length scale of wedge-shaped porous media, International Journal of Engineering Science, vol.39, issue.8, pp.951-962, 2001.
DOI : 10.1016/S0020-7225(00)00073-2

]. A. Cortis, D. M. Smeulders, J. Guermond, and D. Lafarge, Influence of pore roughness on high-frequency permeability, Influence of pore roughness on high-frequency permeability, pp.1766-75, 2003.
DOI : 10.1063/1.1571545

]. S. Gasser, F. Paun, and Y. Brechet, Absorptive properties of rigid porous media: Application to face centered cubic sphere packing, The Journal of the Acoustical Society of America, vol.117, issue.4, pp.2090-2099, 2005.
DOI : 10.1121/1.1863052

C. Perrot, F. Chevillotte, and R. Panneton, Dynamic viscous permeability of an open-cell aluminum foam: Computations versus experiments, Journal of Applied Physics, vol.103, issue.2, p.24909, 2008.
DOI : 10.1063/1.2829774
URL : https://hal.archives-ouvertes.fr/hal-00414900

K. Schladitz, S. Peters, D. Reinel-bitzer, A. Wiegmann, and J. Ohser, Design of acoustic trim based on geometric modeling and flow simulation for non-woven, Computational Materials Science, vol.38, issue.1, pp.56-66, 2006.
DOI : 10.1016/j.commatsci.2006.01.018

]. C. Perrot, F. Chevillotte, and R. Panneton, Bottom-up approach for microstructure optimization of sound absorbing materials, The Journal of the Acoustical Society of America, vol.124, issue.2, p.940, 2008.
DOI : 10.1121/1.2945115
URL : https://hal.archives-ouvertes.fr/hal-00732089

]. F. Chevillotte, C. Perrot, and R. Panneton, Microstructure based model for sound absorption predictions of perforated closed-cell metallic foams, The Journal of the Acoustical Society of America, vol.128, issue.4, pp.1766-1776, 2010.
DOI : 10.1121/1.3473696
URL : https://hal.archives-ouvertes.fr/hal-00692860

M. J. Lee, J. H. Leamy, and . Nadler, Acoustic absorption calculation in irreducible porous media: A unified computational approach, The Journal of the Acoustical Society of America, vol.126, issue.4, p.1862, 2009.
DOI : 10.1121/1.3205399

M. J. Lee, J. H. Leamy, and . Nadler, Frequency band structure and absorption predictions for multi-periodic acoustic composites, Journal of Sound and Vibration, vol.329, issue.10, pp.1809-1822, 2010.
DOI : 10.1016/j.jsv.2009.11.030

C. Perrot, R. Panneton, and X. Olny, Periodic unit cell reconstruction of porous media: Application to open-cell aluminum foams, Journal of Applied Physics, vol.101, issue.11, p.113538, 2007.
DOI : 10.1063/1.2745095
URL : https://hal.archives-ouvertes.fr/hal-00731850

C. Perrot, R. Panneton, and X. Olny, Computation of the dynamic thermal dissipation properties of porous media by Brownian motion simulation: Application to an open-cell aluminum foam, Journal of Applied Physics, vol.102, issue.7, p.74917, 2007.
DOI : 10.1063/1.2786899
URL : https://hal.archives-ouvertes.fr/hal-00731846

X. Wang and T. J. Lu, Optimized acoustic properties of cellular solids, The Journal of the Acoustical Society of America, vol.106, issue.2, pp.756-765, 1999.
DOI : 10.1121/1.427094

]. I. Malinouskaya, V. V. Mourzenko, J. Thovert, and P. M. Adler, Wave propagation through saturated porous media, Wave propagation through saturated porous media, p.66302, 2008.
DOI : 10.1103/PhysRevE.77.066302
URL : https://hal.archives-ouvertes.fr/hal-00414177

]. T. Miyoshi, M. Itoh, S. Akiyama, and A. Kitahara, ALPORAS Aluminum Foam: Production Process, Properties, and Applications, Advanced Engineering Materials, vol.2, issue.4, pp.179-183, 2000.
DOI : 10.1002/(SICI)1527-2648(200004)2:4<179::AID-ADEM179>3.0.CO;2-G

T. J. Lu, F. Chen, and D. , Sound absorption of cellular metals with semiopen cells, The Journal of the Acoustical Society of America, vol.108, issue.4, pp.1697-1709, 2000.
DOI : 10.1121/1.1286812

T. J. Lu, A. Hess, and M. F. Ashby, Sound absorption in metallic foams, Journal of Applied Physics, vol.85, issue.11, pp.7528-7539, 1999.
DOI : 10.1063/1.370550

E. Lind-nordgren and P. Göransson, Optimising open porous foam for acoustical and vibrational performance, Journal of Sound and Vibration, vol.329, issue.7, pp.753-767, 2010.
DOI : 10.1016/j.jsv.2009.10.009

J. Banhart, Manufacturing routes for metallic foams, JOM, vol.45, issue.222, 2000.
DOI : 10.1007/s11837-000-0062-8

M. Henry, P. Lemarinier, J. Allard, J. Bonardet, and A. Gedeon, Evaluation of the characteristic dimensions for porous sound???absorbing materials, Journal of Applied Physics, vol.77, issue.1, pp.17-20, 1995.
DOI : 10.1063/1.359366

D. Lafarge and . Comments-on, Comments on ??????Rigorous link between fluid permeability, electrical conductivity, and relaxation times for transport in porous media??????, Physics of Fluids A: Fluid Dynamics, vol.5, issue.2, p.500, 1993.
DOI : 10.1063/1.858873

R. J. Brown, « Connection between formation factor for electrical-resistivity and fluidsolid coupling factor in Biot equations for acoustic waves in fluid-filled porous media, pp.45-1269, 1980.

D. Lafarge, 1993); translation in English : «Sound propagation in rigid porous media saturated by a viscothermal fluid Seybert, « Transfer function method for measuring characteristic impedance and propagation constant of porous materials, Propagation du son dans les matériaux poreux à structure rigide saturés par un fluide viscothermique, p.637, 1989.

]. R. Panneton and X. Olny, Acoustical determination of the parameters governing viscous dissipation in porous media, The Journal of the Acoustical Society of America, vol.119, issue.4, p.2027, 2006.
DOI : 10.1121/1.2169923

]. X. Olny and R. Panneton, Acoustical determination of the parameters governing thermal dissipation in porous media, The Journal of the Acoustical Society of America, vol.123, issue.2, p.814, 2008.
DOI : 10.1121/1.2828066

M. R. Stinson and G. A. Daigle, Electronic system for the measurement of flow resistance, The Journal of the Acoustical Society of America, vol.83, issue.6, p.2422, 1988.
DOI : 10.1121/1.396321

L. L. Beranek, Acoustic Impedance of Porous Materials, The Journal of the Acoustical Society of America, vol.13, issue.3, p.248, 1942.
DOI : 10.1121/1.1916172

]. P. Leclaire, O. Umnova, K. Horoshenkov, and L. Maillet, Porosity measurement by comparison of air volumes, Review of Scientific Instruments, vol.74, issue.3, pp.1366-1370, 2003.
DOI : 10.1063/1.1542666
URL : https://hal.archives-ouvertes.fr/hal-01326049

R. Panneton and E. Gros, « A missing mass method to measure the open porosity of porous solids, Acta Acustica United With Acustica, vol.91, issue.2, pp.342-350, 2005.

B. Allard, M. Castagnède, W. Henri, and . Lauriks, Evaluation of tortuosity in acoustic porous materials saturated by air, Review of Scientific Instruments, vol.65, issue.3, pp.754-755, 1994.
DOI : 10.1063/1.1145097

D. L. Johnson, T. J. Plona, C. Scala, F. Pasierb, and H. Kojima, Tortuosity and Acoustic Slow Waves, Tortuosity and acoustic slow waves, pp.1840-1844, 1982.
DOI : 10.1103/PhysRevLett.49.1840

]. P. Leclaire, L. Kelders, W. Lauriks, M. Melon, N. Brown et al., Determination of the viscous and thermal characteristic lengths of plastic foams by ultrasonic measurements in helium and air, Journal of Applied Physics, vol.80, issue.4, pp.2009-2012, 1996.
DOI : 10.1063/1.363817
URL : https://hal.archives-ouvertes.fr/hal-01326774

J. Groby, E. Ogam, L. De-ryck, N. Sebaa, and W. Lauriks, Analytical method for the ultrasonic characterization of homogeneous rigid porous materials from transmitted and reflected coefficients, The Journal of the Acoustical Society of America, vol.127, issue.2, pp.764-772, 2010.
DOI : 10.1121/1.3283043
URL : https://hal.archives-ouvertes.fr/hal-00440830

A. Cortis and J. G. Berryman, Frequency-dependent viscous flow in channels with fractal rough surfaces, Physics of Fluids, vol.22, issue.5, p.53603, 2010.
DOI : 10.1063/1.3407659

T. Lévy, Propagation of waves in a fluid-saturated porous elastic solid, International Journal of Engineering Science, vol.17, issue.9, p.1005, 1979.
DOI : 10.1016/0020-7225(79)90022-3

J. L. Auriault, L. Borne, and R. Chambon, Dynamics of porous saturated media, checking of the generalized law of Darcy, The Journal of the Acoustical Society of America, vol.77, issue.5, p.1641, 1985.
DOI : 10.1121/1.391962

R. Burridge and J. B. Keller, Poroelasticity equations derived from microstructure, The Journal of the Acoustical Society of America, vol.70, issue.4, p.1140, 1981.
DOI : 10.1121/1.386945

M. R. Stinson, The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross???sectional shape, The Journal of the Acoustical Society of America, vol.89, issue.2, p.550, 1991.
DOI : 10.1121/1.400379

E. B. Matzke, The Three-Dimensional Shape of Bubbles in Foam-An Analysis of the Role of Surface Forces in Three-Dimensional Cell Shape Determination, American Journal of Botany, vol.33, issue.1, p.33, 1946.
DOI : 10.2307/2437492

A. M. Kraynik, D. A. Reinelt, and F. Van-swol, Structure of Random Foam, Structure of Random Foam, p.208301, 2004.
DOI : 10.1103/PhysRevLett.93.208301

]. S. Brunauer, P. H. Emmett, and E. Teller, Adsorption of Gases in Multimolecular Layers, Adsorption of Gases in Multimolecular Layers, p.309, 1938.
DOI : 10.1021/ja01269a023

]. P. Göransson, R. Gustavino, and N. Hörlin, Measurement and inverse estimation of 3D anisotropic flow resistivity for porous materials, Journal of Sound and Vibration, vol.327, issue.3-5, p.354, 2009.
DOI : 10.1016/j.jsv.2009.06.028

]. N. Martys and E. J. Garboczi, Length scales relating the fluid permeability and electrical conductivity in random two-dimensional model porous media, Physical Review B, vol.46, issue.10, p.6080, 1992.
DOI : 10.1103/PhysRevB.46.6080

R. M. Sullivan, L. J. Ghosn, and B. A. Lerch, A general tetrakaidecahedron model for open-celled foams, International Journal of Solids and Structures, vol.45, issue.6, p.1754, 2008.
DOI : 10.1016/j.ijsolstr.2007.10.028

]. V. Ambegaokar, B. I. Halperin, and J. S. Langer, Hopping Conductivity in Disordered Systems, Hopping conductivity in disordered systems, p.2612, 1971.
DOI : 10.1103/PhysRevB.4.2612

A. J. Katz and A. H. Thompson, Quantitative prediction of permeability in porous rock, Physical Review B, vol.34, issue.11, p.8179, 1986.
DOI : 10.1103/PhysRevB.34.8179

L. M. Schwartz, N. Martys, D. P. Bentz, E. J. Garboczi, and S. Torquato, Cross-property relations and permeability estimation in model porous media, Cross-property relations and permeability estimation in model porous media, p.4584, 1993.
DOI : 10.1103/PhysRevE.48.4584

]. A. Debray, J. Allard, W. Lauriks, and L. , Acoustical measurement of the trapping constant of porous materials, Review of Scientific Instruments, vol.68, issue.12, p.4462, 1997.
DOI : 10.1063/1.1148414

M. Sadouki, M. Fellah, Z. E. Fellah, E. Ogam, N. Sebaa et al., Measuring static thermal permeability and inertial factor of rigid porous materials (L), Measuring static thermal permeability and inertial factor of rigid porous materials, p.2627, 2011.
DOI : 10.1121/1.3641402

C. Boutin, Rayleigh scattering of acoustic waves in rigid porous media, The Journal of the Acoustical Society of America, vol.122, issue.4, p.1888, 2007.
DOI : 10.1121/1.2756755
URL : https://hal.archives-ouvertes.fr/hal-00943752

N. Kino, G. Nakano, and Y. Suzuki, Non-acoustical and acoustical properties of reticulated and partially reticulated polyurethane foams, Applied Acoustics, vol.73, issue.2, p.95, 2012.
DOI : 10.1016/j.apacoust.2011.06.009

O. Doutres, N. Atalla, and K. Dong, Effect of the microstructure closed pore content on the acoustic behavior of polyurethane foams, Journal of Applied Physics, vol.110, issue.6, p.64901, 2011.
DOI : 10.1063/1.3631021

O. Umnova, D. Tsiklauri, and R. Venegas, Effect of boundary slip on the acoustical properties of microfibrous materials, The Journal of the Acoustical Society of America, vol.126, issue.4, p.1850, 2009.
DOI : 10.1121/1.3204087

C. Lee and M. J. Leamy, Computation of acoustic absorption in media composed of packed microtubes exhibiting surface irregularity, J. Acoust. Soc. Am, vol.130, p.826, 2011.

D. Pilon, R. Panneton, and F. Sgard, Behavioral criterion quantifying the edge-constrained effects on foams in the standing wave tube, The Journal of the Acoustical Society of America, vol.114, issue.4, p.1980, 2003.
DOI : 10.1121/1.1598193

J. Wojtowicki and R. Panneton, « Improving the efficiency of sealing parts for hollow body network», in Noise & Vibration Conference and Exhibition, SAE Technical Paper No, 2005.

T. Dupont, P. Leclaire, O. Sicot, X. L. Gong, and R. Panneton, Acoustic properties of air-saturated porous materials containing dead-end porosity, Journal of Applied Physics, vol.110, issue.9, p.94903, 2011.
DOI : 10.1063/1.3646556
URL : https://hal.archives-ouvertes.fr/hal-00550953

Y. Li, X. Wang, X. Wang, Y. Ren, F. Han et al., Sound absorption characteristics of aluminum foam with spherical cells, Journal of Applied Physics, vol.110, issue.11, p.113525, 2011.
DOI : 10.1063/1.3665216

S. Mahasaranon, K. V. Horoshenkov, A. Khan, and H. Benkreira, The effect of continuous pore stratification on the acoustic absorption in open cell foams, Journal of Applied Physics, vol.111, issue.8, p.84901, 2012.
DOI : 10.1063/1.3701710

K. V. Horoshenkov, A. Khan, F. Bécot, L. Jaouen, F. Sgard et al., Reproducibility experiments on measuring acoustical properties of rigid-frame porous media (round-robin tests), The Journal of the Acoustical Society of America, vol.122, issue.1, p.345, 2007.
DOI : 10.1121/1.2739806

A. Testouri, L. R. Arriaga, C. Honorez, M. Ranft, J. Rodrigues et al., Generation of porous solids with well-controlled morphologies by combining foaming and flow chemistry on a Lab-on-a-Chip, Colloids Surf. A: Physicochem. Eng, p.17, 2012.
DOI : 10.1016/j.colsurfa.2012.02.048

J. F. Allard and N. Atalla, Propagation of sound in porous media: Modelling sound absorbing materials, p.358, 2009.

M. A. Biot, Theory of Propagation of Elastic Waves in a Fluid???Saturated Porous Solid. I. Low???Frequency Range, The Journal of the Acoustical Society of America, vol.28, issue.2, pp.168-179, 1956.
DOI : 10.1121/1.1908239
URL : https://hal.archives-ouvertes.fr/hal-01368668

]. Y. Champoux and J. F. Allard, Dynamic tortuosity and bulk modulus in air???saturated porous media, Journal of Applied Physics, vol.70, issue.4, p.1975, 1991.
DOI : 10.1063/1.349482

P. Sheng and M. Y. Zhou, Dynamic Permeability in Porous Media, Dynamic permeability in porous media, p.1591, 1988.
DOI : 10.1103/PhysRevLett.61.1591

R. Burridge and J. B. Keller, Poroelasticity equations derived from microstructure, The Journal of the Acoustical Society of America, vol.70, issue.4, p.1140, 1981.
DOI : 10.1121/1.386945

]. D. Weaire and S. Hutzler, Foam Physics, Advanced Engineering Materials, vol.4, issue.10, p.260, 1999.
DOI : 10.1002/1527-2648(20021014)4:10<723::AID-ADEM723>3.0.CO;2-9

]. L. Gong, S. Kyriakides, and W. Jang, Compressive response of open-cell foams. Part I: Morphology and elastic properties, International Journal of Solids and Structures, vol.42, issue.5-6, p.1355, 2005.
DOI : 10.1016/j.ijsolstr.2004.07.023

R. M. Sullivan, L. J. Ghosn, B. A. Lerch, R. M. Sullivan, L. J. Ghosn et al., A general tetrakaidecahedron model for open-celled foams, Elongated Tetrakaidecahedron micromechanics model for space shuttle external tank foams, pp.1754-215137, 2008.
DOI : 10.1016/j.ijsolstr.2007.10.028

S. Jang, A. M. Kyriakides, and . Kraynik, On the compressive strength of open-cell metal foams with Kelvin and random cell structures, International Journal of Solids and Structures, vol.47, issue.21, p.2872, 2010.
DOI : 10.1016/j.ijsolstr.2010.06.014

P. Thiyagasundaram, B. V. Sankar, and N. K. , Elastic Properties of Open-Cell Foams with Tetrakaidecahedral Cells Using Finite Element Analysis, AIAA Journal, vol.48, issue.4, p.818, 2010.
DOI : 10.2514/1.J050022

]. L. Boeckx, M. Brennan, K. Verniers, and J. Vandenbroeck, A Numerical Scheme for Investigating the Influence of the Three Dimensional Geometrical Features of Porous Polymeric Foam on Its Sound Absorbing Behavior, Acta Acustica united with Acustica, vol.96, issue.2, p.239, 2010.
DOI : 10.3813/AAA.918273

L. L. Beranek, Acoustic Impedance of Porous Materials, The Journal of the Acoustical Society of America, vol.13, issue.3, p.248, 1942.
DOI : 10.1121/1.1916172

M. R. Stinson and G. A. Daigle, Electronic system for the measurement of flow resistance, The Journal of the Acoustical Society of America, vol.83, issue.6, p.2422, 1988.
DOI : 10.1121/1.396321

J. C. Michel, H. Moulinec, and P. Suquet, Effective properties of composite materials with periodic microstructure: a computational approach, Computer Methods in Applied Mechanics and Engineering, vol.172, issue.1-4, p.109, 1999.
DOI : 10.1016/S0045-7825(98)00227-8

J. F. Allard, B. Castagnede, M. Henry, and W. Lauriks, Evaluation of tortuosity in acoustic porous materials saturated by air, Review of Scientific Instruments, vol.65, issue.3, p.754, 1994.
DOI : 10.1063/1.1145097

R. D. Priester and R. B. Turner, « The morphology of flexible polyurethane matrix polymers); in Low density cellular plastics: physical basis of behavior, pp.78-103, 1994.

]. E. Mariez, S. Sahraoui, and J. F. Allard, « Elastic constants of polyurethane foam's skeleton for Biot model, Proceedings of Internoise 96, pp.951-954, 1996.

C. Langlois, R. Panneton, and N. Atalla, Polynomial relations for quasi-static mechanical characterization of isotropic poroelastic materials, The Journal of the Acoustical Society of America, vol.110, issue.6, p.3032, 2001.
DOI : 10.1121/1.1419091

R. Panneton, Comments on the limp frame equivalent fluid model for porous media, The Journal of the Acoustical Society of America, vol.122, issue.6, p.217, 2008.
DOI : 10.1121/1.2800895

]. D. Pilon, R. Panneton, and F. Sgard, Behavioral criterion quantifying the edge-constrained effects on foams in the standing wave tube, Behavioral criterion quantifying the edgeconstrained effects on foams in the standing wave tube, p.1980, 2003.
DOI : 10.1121/1.1598193

P. Hörlin, P. Göransson, R. Göransson, N. Gustavino, and . Hörlin, Weak, anisotropic symmetric formulations of Biot's equations for vibro-acoustic modelling of porous elastic materials, Measurement and inverse estimation of 3D anisotropic flow resistivity for porous materials Cuenca and P. Göransson, « Inverse ertimation of the elastic and anelastic properties of the porous frame of anisotropic open-cell foams, pp.1519-621, 2009.
DOI : 10.1002/nme.2955

]. H. Utsuno, T. Tanaka, T. Fujikawa, and A. F. , Transfer function method for measuring characteristic impedance and propagation constant of porous materials, The Journal of the Acoustical Society of America, vol.86, issue.2, pp.637-643, 1989.
DOI : 10.1121/1.398241

]. A. Seybert and D. F. Ross, Experimental determination of acoustic properties using a two???microphone random???excitation technique, The Journal of the Acoustical Society of America, vol.61, issue.5, pp.1362-1370, 1977.
DOI : 10.1121/1.381403

]. B. Song and J. S. Bolton, A transfer-matrix approach for estimating the characteristic impedance and wave numbers of limp and rigid porous materials, The Journal of the Acoustical Society of America, vol.107, issue.3, pp.1131-1152, 2000.
DOI : 10.1121/1.428404

O. Doutres, Y. Salissou, N. Atalla, and R. Panneton, Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube, Applied Acoustics, vol.71, issue.6, pp.506-509, 2010.
DOI : 10.1016/j.apacoust.2010.01.007
URL : https://hal.archives-ouvertes.fr/hal-00508767

R. Panneton and X. Only, Acoustical determination of the parameters governing viscous dissipation in porous media, The Journal of the Acoustical Society of America, vol.119, issue.4, pp.2027-2040, 2006.
DOI : 10.1121/1.2169923

X. Only and R. Panneton, « Acoustical determination of the parameters governing thermal dissipation in porous media, J. Acoust. Soc. Am, vol.123, issue.2, pp.814-824, 2008.

B. Annexe, Modèles semi-phénoménologiques Minh Tan

K. Attenborough, (e.g. page 41) omit four relevant aspects: (i) the availability of 'exact' solutions for specific idealised pore microstructures (these include cylinders, slits, triangles and rectangles see for example Ch.3 of Predicting Outdoor Sound

M. Li, K. Horoshenkov, T. , F. Attenborough, and K. M. , (ii) reference to the cell model approach in general and 'exact' results for stacked spheres in particular (see O, 2006.

O. Li, K. Umnova, K. M. Attenborough, . K. Lid, K. V. Wilson et al., A cell model for the Acoustical properties of Packings of SpheresNote that these references offer a model for the acoustical properties of stacked spheres (this idealisation is mentioned specifically on page 42) requiring knowledge only of sphere radius and porosity without the need for any adjustable parameters] (iii) reference to the relaxation time approach Relaxationmatched modeling of propagation through porous media, including fractal pore structure and (iv) models based on pore size distributions (see for example Pade approximants for the acoustical properties of rigid frame porous media with pore size distribution Models for the acoustical properties of air-saturated granular media, J. Acoust. Soc. Am. Acustica combined with Acta Acustica J. Acoust. Soc. Am. J. Acoust. Soc. Am. Acta Acustica, vol.107, issue.1, pp.3113-3119, 1993.