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According to the point of view that static dense granular matter is a nonlinear elastic body, we derive an analytic sound speed expression given by its elastic potential, for the case of samples with cylindrical symmetry and sound waves propagating in the directions along and perpendicular to the symmetry axis. By a detailed comparison of the expressions with experiments reported in the literature, we conclude that the acoustic method can determine all material parameters appearing in the elastic potential accurately, which provides us with an important way of studying detailed nonlinear elasticity behaviors of granular materials, if stresses, density, and their uniformity of samples are thoroughly controlled and measured.
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Keywords:
- sound velocity /
- granular matter /
- nonlinear elasticity
[1] de Gennes P G 1999 Rev. Mod. Phys. 71 S374
[2] Lu K Q, Liu J X 2004 Physics 33 629 (in Chinese) [陆坤权, 刘寄星 2004 物理 33 629]
[3] Sun Q C, Hou M Y, Jin F 2011 Physics and Mechanics of Granular Materials (Beijing: Sciencs Press) (in Chinese) [孙其诚, 厚美瑛, 金峰 2011 颗粒物质物理与力学 (北京: 科学出版社)]
[4] Gudehus G 2010 Physical Soil Mechanics (Berlin: Springer)
[5] Jia X, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[6] Khidas Y, Jia X P 2010 Phys. Rev. E 81 021303
[7] Jia X P, Laurent J, Khidas Y, Langlois V 2009 Chin. Sci. Bull. 54 4327
[8] Bonneau L, Andreotti B, Clement E 2007 Phys. Rev. E 75 016602
[9] Bonneau L, Andreotti B, Clement E 2008 Phys. Rev. Lett. 101 118001
[10] Andreotti B, Bonneau L 2009 Phys. Rev. Lett. 103 238001
[11] Zhang Q, Hou M, Jiang Y M, Liu M 2012 Phys. Rev. E 85 031306
[12] Zhang Q, Li Y C, Liu R, Jiang Y M, Hou M Y 2012 Acta Phys. Sin. 61 234501 (in Chinese) [张琪, 李寅阊, 刘锐, 蒋亦民, 厚美瑛 2012 物理学报 61 234501]
[13] Domenico S N 1977 Geophysics 42 1339
[14] Makse H A, Gland N, Johnson D L, Schwartz L 2004 Phys. Rev. E 70 061302
[15] Martin P C, Parodi O, Pershan P S 1972 Phys. Rev. A 6 2401
[16] Mayer M, Liu M 2010 Phys. Rev. E 82 042301
[17] Jiang Y M, Liu M 2003 Phys. Rev. Lett. 91 144301
[18] Humrickhouse P W 2009 in: Nakagawa M, Luding S ed. Powders and Grains (Melville New York: American Institute of Physics) pp1104-1107
[19] Jiang Y M, Zheng H P, Peng Z, Fu L P, Song S X, Sun Q C, Mayer M, Liu M 2012 Phys. Rev. E 85 051304
[20] Landau L D, Lifshitz E M 1986 Theory of Elasticity (Oxford: Pergamon Press)
[21] Velicky B, Caroli C 2002 Phys. Rev. E 65 021307
[22] Goddard 1990 Proc. R. Soc. London A 430 105
[23] Coste C, Gilles B 1999 Eur. Phys. J. B 7 155
[24] Gilles B, Coste C 2003 Phys. Rev. Lett. 90 174302
[25] Rothenburg L, Kru N P 2004 Int. J. Solids. Struct. 41 5763
[26] Song C, Wang P, Makse H A 2008 Nature 453 629
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[1] de Gennes P G 1999 Rev. Mod. Phys. 71 S374
[2] Lu K Q, Liu J X 2004 Physics 33 629 (in Chinese) [陆坤权, 刘寄星 2004 物理 33 629]
[3] Sun Q C, Hou M Y, Jin F 2011 Physics and Mechanics of Granular Materials (Beijing: Sciencs Press) (in Chinese) [孙其诚, 厚美瑛, 金峰 2011 颗粒物质物理与力学 (北京: 科学出版社)]
[4] Gudehus G 2010 Physical Soil Mechanics (Berlin: Springer)
[5] Jia X, Caroli C, Velicky B 1999 Phys. Rev. Lett. 82 1863
[6] Khidas Y, Jia X P 2010 Phys. Rev. E 81 021303
[7] Jia X P, Laurent J, Khidas Y, Langlois V 2009 Chin. Sci. Bull. 54 4327
[8] Bonneau L, Andreotti B, Clement E 2007 Phys. Rev. E 75 016602
[9] Bonneau L, Andreotti B, Clement E 2008 Phys. Rev. Lett. 101 118001
[10] Andreotti B, Bonneau L 2009 Phys. Rev. Lett. 103 238001
[11] Zhang Q, Hou M, Jiang Y M, Liu M 2012 Phys. Rev. E 85 031306
[12] Zhang Q, Li Y C, Liu R, Jiang Y M, Hou M Y 2012 Acta Phys. Sin. 61 234501 (in Chinese) [张琪, 李寅阊, 刘锐, 蒋亦民, 厚美瑛 2012 物理学报 61 234501]
[13] Domenico S N 1977 Geophysics 42 1339
[14] Makse H A, Gland N, Johnson D L, Schwartz L 2004 Phys. Rev. E 70 061302
[15] Martin P C, Parodi O, Pershan P S 1972 Phys. Rev. A 6 2401
[16] Mayer M, Liu M 2010 Phys. Rev. E 82 042301
[17] Jiang Y M, Liu M 2003 Phys. Rev. Lett. 91 144301
[18] Humrickhouse P W 2009 in: Nakagawa M, Luding S ed. Powders and Grains (Melville New York: American Institute of Physics) pp1104-1107
[19] Jiang Y M, Zheng H P, Peng Z, Fu L P, Song S X, Sun Q C, Mayer M, Liu M 2012 Phys. Rev. E 85 051304
[20] Landau L D, Lifshitz E M 1986 Theory of Elasticity (Oxford: Pergamon Press)
[21] Velicky B, Caroli C 2002 Phys. Rev. E 65 021307
[22] Goddard 1990 Proc. R. Soc. London A 430 105
[23] Coste C, Gilles B 1999 Eur. Phys. J. B 7 155
[24] Gilles B, Coste C 2003 Phys. Rev. Lett. 90 174302
[25] Rothenburg L, Kru N P 2004 Int. J. Solids. Struct. 41 5763
[26] Song C, Wang P, Makse H A 2008 Nature 453 629
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