J. Akerman and M. Höjer, How much transport can the climate stand????Sweden on a sustainable path in 2050, Energy Policy, vol.34, issue.14, pp.1944-1957, 2006.
DOI : 10.1016/j.enpol.2005.02.009

J. Allard, Propagation of sound in porous media: modelling sound absorbing materials, 1993.

J. Allard and Y. Champoux, New empirical equations for sound propagation in rigid frame fibrous materials, The Journal of the Acoustical Society of America, vol.91, issue.6, pp.3346-3353, 1992.
DOI : 10.1121/1.402824

N. Atalla, M. A. Hamdi, and R. Panneton, Enhanced weak integral formulation for the mixed (u_,p_) poroelastic equations, The Journal of the Acoustical Society of America, vol.109, issue.6, pp.3065-3068, 2001.
DOI : 10.1121/1.1365423

N. Atalla, R. Panneton, and P. Debergue, A mixed displacement-pressure formulation for poroelastic materials, The Journal of the Acoustical Society of America, vol.104, issue.3, pp.1444-1452, 1998.
DOI : 10.1121/1.424355

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.168-1781, 1956.
DOI : 10.1121/1.1908239

URL : https://hal.archives-ouvertes.fr/hal-01368668

M. A. Biot, Theory of Deformation of a Porous Viscoelastic Anisotropic Solid, Journal of Applied Physics, vol.27, issue.5, pp.459-4673, 1956.
DOI : 10.1063/1.1722402

URL : https://hal.archives-ouvertes.fr/hal-01368672

M. A. Biot, Mechanics of Deformation and Acoustic Propagation in Porous Media, Journal of Applied Physics, vol.33, issue.4, pp.1482-1498, 1962.
DOI : 10.1063/1.1728759

URL : https://hal.archives-ouvertes.fr/hal-01368725

M. A. Biot and D. G. Willis, The elastic coefficients of the theory of consolidation, J. Appl. Mech, vol.24, pp.594-601, 1957.
URL : https://hal.archives-ouvertes.fr/hal-01368677

Y. Champoux and J. 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

J. Comiti and M. Renaud, A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles, Chemical Engineering Science, vol.44, issue.7, pp.1539-1545, 1989.
DOI : 10.1016/0009-2509(89)80031-4

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, 2011.
DOI : 10.1063/1.3631021

K. Dovstam, Augmented Hooke's law in frequency domain. A three dimensional, material damping formulation, International Journal of Solids and Structures, vol.32, issue.19, pp.2835-2852, 1995.
DOI : 10.1016/0020-7683(94)00269-3

A. Geslain, O. Dazel, J. Groby, S. Sahraoui, and W. Lauriks, Influence of static compression on mechanical parameters of acoustic foams, The Journal of the Acoustical Society of America, vol.130, issue.2, pp.818-825, 2011.
DOI : 10.1121/1.3605535

L. J. Gibson and M. F. Ashby, Cellular solids ? Structure and properties, 1988.

P. Göransson, Acoustic and vibrational damping in porous solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.55, issue.1838, pp.89-108, 2006.
DOI : 10.1098/rsta.2005.1688

P. Göransson, R. Guastavino, 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, pp.3-5354, 2009.
DOI : 10.1016/j.jsv.2009.06.028

R. Guastavino and P. Göransson, A 3D displacement measurement methodology for anisotropic porous cellular foam materials, Polymer Testing, vol.26, issue.6, pp.711-719, 2007.
DOI : 10.1016/j.polymertesting.2007.02.008

N. Hörlin, 3D hierarchical -FEM applied to elasto-acoustic modelling of layered porous media, Journal of Sound and Vibration, vol.285, issue.1-2, pp.341-363, 2005.
DOI : 10.1016/j.jsv.2004.08.032

N. Hörlin and P. Göransson, Weak, anisotropic symmetric formulations of Biot's equations for vibro-acoustic modelling of porous elastic materials, International Journal for Numerical Methods in Engineering, vol.96, issue.2, pp.1519-1540, 2010.
DOI : 10.1002/nme.2955

N. Hörlin, M. Nordström, and P. Göransson, A 3-D hierarchical FE formulation of Biot's eguations for elasto-acoustic modelling of porous media, J. Sound Vib, vol.254, issue.4, pp.633-652, 2001.

W. Jang, A. M. Kraynik, and S. Kyriakides, On the microstructure of open-cell foams and its effect on elastic properties, International Journal of Solids and Structures, vol.45, issue.7-8, pp.1845-1875, 2008.
DOI : 10.1016/j.ijsolstr.2007.10.008

W. Jang, S. Kyriakides, and A. M. 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, pp.472872-2883, 2010.
DOI : 10.1016/j.ijsolstr.2010.06.014

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

P. Khurana, L. Boeckx, W. Lauriks, P. Leclaire, O. Dazel et al., A description of transversely isotropic sound absorbing porous materials by transfer matrices, The Journal of the Acoustical Society of America, vol.125, issue.2, pp.915-921, 2009.
DOI : 10.1121/1.3035840

D. Lafarge, P. Lemarnier, J. 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

G. A. Lesieutre, Finite elements for dynamic modelling of uniaxial rods with frequency-dependent material properties, Int. J. Solids Structures, vol.28, pp.1567-1579, 1992.

M. Melon, E. Mariez, C. Ayrault, and S. Sahraoui, Acoustical and mechanical characterization of anisotropic open-cell foams, The Journal of the Acoustical Society of America, vol.104, issue.5, pp.2622-2627, 1998.
DOI : 10.1121/1.423897

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.2012
DOI : 10.1063/1.3673523

URL : https://hal.archives-ouvertes.fr/hal-00731446

C. Perrot, R. Panneton, and X. Olny, From microstructure to acoustic behaviour of porous materials, Canadian Acoustics -Acoustique Canadienne, vol.32, issue.3, pp.18-19, 2004.

S. Sahraoui, E. Mariez, and M. Etchessahar, Linear elastic properties of anisotropic open-cell foams, The Journal of the Acoustical Society of America, vol.110, issue.1, pp.635-637, 2001.
DOI : 10.1121/1.1378351

K. Svanberg, The method of moving asymptotes???a new method for structural optimization, International Journal for Numerical Methods in Engineering, vol.20, issue.2, pp.359-373, 1987.
DOI : 10.1002/nme.1620240207

K. Svanberg, A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations, SIAM Journal on Optimization, vol.12, issue.2, pp.555-573, 2002.
DOI : 10.1137/S1052623499362822

C. Zwikker and C. Kosten, Sound absorbing materials., chapter II and III, 1949.

J. Akerman and M. Höjer, How much transport can the climate stand????Sweden on a sustainable path in 2050, Energy Policy, vol.34, issue.14, pp.1944-1957, 2006.
DOI : 10.1016/j.enpol.2005.02.009

J. Allard, Propagation of sound in porous media: modelling sound absorbing materials, 1993.

J. Allard and Y. Champoux, New empirical equations for sound propagation in rigid frame fibrous materials, The Journal of the Acoustical Society of America, vol.91, issue.6, pp.3346-3353, 1992.
DOI : 10.1121/1.402824

N. Atalla, M. A. Hamdi, and R. Panneton, Enhanced weak integral formulation for the mixed (u_,p_) poroelastic equations, The Journal of the Acoustical Society of America, vol.109, issue.6, pp.3065-3068, 2001.
DOI : 10.1121/1.1365423

N. Atalla, R. Panneton, and P. Debergue, A mixed displacement-pressure formulation for poroelastic materials, The Journal of the Acoustical Society of America, vol.104, issue.3, pp.1444-1452, 1998.
DOI : 10.1121/1.424355

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.168-1781, 1956.
DOI : 10.1121/1.1908239

URL : https://hal.archives-ouvertes.fr/hal-01368668

M. A. Biot, Theory of Deformation of a Porous Viscoelastic Anisotropic Solid, Journal of Applied Physics, vol.27, issue.5, pp.459-4673, 1956.
DOI : 10.1063/1.1722402

URL : https://hal.archives-ouvertes.fr/hal-01368672

M. A. Biot, Mechanics of Deformation and Acoustic Propagation in Porous Media, Journal of Applied Physics, vol.33, issue.4, pp.1482-1498, 1962.
DOI : 10.1063/1.1728759

URL : https://hal.archives-ouvertes.fr/hal-01368725

M. A. Biot and D. G. Willis, The elastic coefficients of the theory of consolidation, J. Appl. Mech, vol.24, pp.594-601, 1957.
URL : https://hal.archives-ouvertes.fr/hal-01368677

Y. Champoux and J. 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

J. Comiti and M. Renaud, A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles, Chemical Engineering Science, vol.44, issue.7, pp.1539-1545, 1989.
DOI : 10.1016/0009-2509(89)80031-4

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, 2011.
DOI : 10.1063/1.3631021

K. Dovstam, Augmented Hooke's law in frequency domain. A three dimensional, material damping formulation, International Journal of Solids and Structures, vol.32, issue.19, pp.2835-2852, 1995.
DOI : 10.1016/0020-7683(94)00269-3

A. Geslain, O. Dazel, J. Groby, S. Sahraoui, and W. Lauriks, Influence of static compression on mechanical parameters of acoustic foams, The Journal of the Acoustical Society of America, vol.130, issue.2, pp.818-825, 2011.
DOI : 10.1121/1.3605535

L. J. Gibson and M. F. Ashby, Cellular solids ? Structure and properties, 1988.

P. Göransson, Acoustic and vibrational damping in porous solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.55, issue.1838, pp.89-108, 2006.
DOI : 10.1098/rsta.2005.1688

P. Göransson, R. Guastavino, 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, pp.3-5354, 2009.
DOI : 10.1016/j.jsv.2009.06.028

R. Guastavino and P. Göransson, A 3D displacement measurement methodology for anisotropic porous cellular foam materials, Polymer Testing, vol.26, issue.6, pp.711-719, 2007.
DOI : 10.1016/j.polymertesting.2007.02.008

N. Hörlin, 3D hierarchical -FEM applied to elasto-acoustic modelling of layered porous media, Journal of Sound and Vibration, vol.285, issue.1-2, pp.341-363, 2005.
DOI : 10.1016/j.jsv.2004.08.032

N. Hörlin and P. Göransson, Weak, anisotropic symmetric formulations of Biot's equations for vibro-acoustic modelling of porous elastic materials, International Journal for Numerical Methods in Engineering, vol.96, issue.2, pp.1519-1540, 2010.
DOI : 10.1002/nme.2955

N. Hörlin, M. Nordström, and P. Göransson, A 3-D hierarchical FE formulation of Biot's eguations for elasto-acoustic modelling of porous media, J. Sound Vib, vol.254, issue.4, pp.633-652, 2001.

W. Jang, A. M. Kraynik, and S. Kyriakides, On the microstructure of open-cell foams and its effect on elastic properties, International Journal of Solids and Structures, vol.45, issue.7-8, pp.1845-1875, 2008.
DOI : 10.1016/j.ijsolstr.2007.10.008

W. Jang, S. Kyriakides, and A. M. 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, pp.472872-2883, 2010.
DOI : 10.1016/j.ijsolstr.2010.06.014

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

P. Khurana, L. Boeckx, W. Lauriks, P. Leclaire, O. Dazel et al., A description of transversely isotropic sound absorbing porous materials by transfer matrices, The Journal of the Acoustical Society of America, vol.125, issue.2, pp.915-921, 2009.
DOI : 10.1121/1.3035840

D. Lafarge, P. Lemarnier, J. 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

G. A. Lesieutre, Finite elements for dynamic modelling of uniaxial rods with frequency-dependent material properties, Int. J. Solids Structures, vol.28, pp.1567-1579, 1992.

M. Melon, E. Mariez, C. Ayrault, and S. Sahraoui, Acoustical and mechanical characterization of anisotropic open-cell foams, The Journal of the Acoustical Society of America, vol.104, issue.5, pp.2622-2627, 1998.
DOI : 10.1121/1.423897

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.2012
DOI : 10.1063/1.3673523

URL : https://hal.archives-ouvertes.fr/hal-00731446

C. Perrot, R. Panneton, and X. Olny, From microstructure to acoustic behaviour of porous materials, Canadian Acoustics -Acoustique Canadienne, vol.32, issue.3, pp.18-19, 2004.

S. Sahraoui, E. Mariez, and M. Etchessahar, Linear elastic properties of anisotropic open-cell foams, The Journal of the Acoustical Society of America, vol.110, issue.1, pp.635-637, 2001.
DOI : 10.1121/1.1378351

K. Svanberg, The method of moving asymptotes???a new method for structural optimization, International Journal for Numerical Methods in Engineering, vol.20, issue.2, pp.359-373, 1987.
DOI : 10.1002/nme.1620240207

K. Svanberg, A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations, SIAM Journal on Optimization, vol.12, issue.2, pp.555-573, 2002.
DOI : 10.1137/S1052623499362822

C. Zwikker and C. Kosten, Sound absorbing materials., chapter II and III, 1949.

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

M. A. Biot, Theory of Deformation of a Porous Viscoelastic Anisotropic Solid, Journal of Applied Physics, vol.27, issue.5, pp.459-467, 1956.
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J. S. Lee, E. I. Kim, Y. Y. Kim, J. S. Kim, and Y. J. Kang, Optimal poroelastic layer sequencing for sound transmission loss maximization by topology optimization method, The Journal of the Acoustical Society of America, vol.122, issue.4, pp.2097-2106, 2007.
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F. Franco, K. A. Cunefare, and M. Ruzzene, Structural-Acoustic Optimization of Sandwich Panels, Journal of Vibration and Acoustics, vol.129, issue.3, pp.330-340, 2007.
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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, pp.940-948, 2008.
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C. Perrot, F. Chevillotte, R. Panneton, and X. Olny, Bottom-up approach for microstructure optimization of sound absorbing materials, Invited Paper?Proceedings of the 19th International Congress on Acoustics, 2007.
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C. Perrot, R. Panneton, and X. Olny, From microstructure to acoustic behaviour of porous materials, Canadian Acoustics?Acoustique Canadienne, vol.32, issue.3, pp.18-19, 2004.

X. Olny, F. Sgard, C. Perrot, and R. Panneton, Microscopic and mesoscopic approaches for describing and building sound absorbing porous materials, Proceedings of the Second TUL-ENTPE Workshop, pp.187-206, 2004.
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C. Perrot, R. Panneton, X. Olny, and R. Bouchard, Mesostructural approach for characterising macroscopic parameters of open cell foams with computed microtomography, Proceedings of the Institute of Acoustics, pp.169-175, 2003.
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K. Dovstam, Augmented Hooke's law in frequency domain. A three dimensional, material damping formulation, International Journal of Solids and Structures, vol.32, issue.19, pp.2835-2852, 1995.
DOI : 10.1016/0020-7683(94)00269-3

J. F. Allard, Propagation of Sound in Porous Media: Modelling Sound Absorbing Materials, 1993.

D. Lafarge, P. Lemarnier, 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.
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W. E. Warren and A. M. Kraynik, The Linear Elastic Properties of Open-Cell Foams, Journal of Applied Mechanics, vol.55, issue.2, pp.341-346, 1988.
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W. E. Warren and A. M. Kraynik, Linear Elastic Behavior of a Low-Density Kelvin Foam With Open Cells, Journal of Applied Mechanics, vol.64, issue.4, pp.787-794, 1997.
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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

M. A. Biot, Theory of Deformation of a Porous Viscoelastic Anisotropic Solid, Journal of Applied Physics, vol.27, issue.5, pp.459-467, 1956.
DOI : 10.1063/1.1722402

URL : https://hal.archives-ouvertes.fr/hal-01368672

N. E. Hörlin, M. Nordström, and P. Göransson, A 3-D hierarchical FE formulation of Biot's eguations for elasto-acoustic modelling of porous media, J. Sound Vib, vol.254, issue.4, pp.633-652, 2001.

N. E. Hörlin, 3-D hierarchical hp-FEM applied to elasto-acoustic modelling of layered porous media, 2005.

W. E. Warren and A. M. Kraynik, The Linear Elastic Properties of Open-Cell Foams, Journal of Applied Mechanics, vol.55, issue.2, pp.341-346, 1988.
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W. E. Warren and A. M. Kraynik, Linear Elastic Behavior of a Low-Density Kelvin Foam With Open Cells, Journal of Applied Mechanics, vol.64, issue.4, pp.787-794, 1997.
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J. F. Allard, C. , and Y. , New empirical equations for sound propagation in rigid frame fibrous materials, The Journal of the Acoustical Society of America, vol.91, issue.6, pp.3346-3353, 1992.
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J. Comiti, R. , and M. , A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles, Chemical Engineering Science, vol.44, issue.7, pp.1539-1545, 1989.
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