Anisotropic elastic theory of preloaded granular media

Europhysics Letters

Volumn 68, Issue 1, 2004, Pages 51-57

  Gay, C ^a   Da Silveira, R A ^b  

^a CENTRE DE RECHERCHE PAUL PASCAL   (France)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 5644244641     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2004-10162-1     Document Type: Article

References (46)

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2. For recent reviews, see NEDDERMAN R. M., Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge) 1992; SAVAGE S. B., in Physics of Dry Granular Media, edited by HERRMANN H. J., HOVI J.-P. and LUDING S. (Kluwer Academic Publishers, Dordrecht) 1998; BOUCHAUD J.-P., Les Houches LXXVII Lecture Notes, 2002 (cond-mat/0211196).
3. For recent reviews, see NEDDERMAN R. M., Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge) 1992; SAVAGE S. B., in Physics of Dry Granular Media, edited by HERRMANN H. J., HOVI J.-P. and LUDING S. (Kluwer Academic Publishers, Dordrecht) 1998; BOUCHAUD J.-P., Les Houches LXXVII Lecture Notes, 2002 (cond-mat/0211196).
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31. According to the classification of Chang and Gao [23], our theory describes a "micro-polar continuum", however, importantly, in our case the continuum is anisotropic. Because our grains are spherical and we neglect torques transmitted by inter-grain contacts, the medium further reduces to an anisotropic "quasi-micro-polar continuum". When our description is applied to a statistically isotropic medium, with vanishing grain reorientation according to eq. (9), it coincides with the first order of Chang and Gao's isotropic "non-polar theory" [23]. In similar approaches but that now include anisotropy, EMERIAULT F. and CHANG C. S. (J. Eng. Mech. ASCE, 123 (1997) 1289) treat non-linear responses, and EMERIAULT F. and CLAQUIN C. (Granular Matter, 2 (2000) 201) focus on (linear) viscoelastic responses. In neither case, however, is grain reorientation involved in relating microscopic displacements to macroscopic strains.
32. According to the classification of Chang and Gao [23], our theory describes a "micro-polar continuum", however, importantly, in our case the continuum is anisotropic. Because our grains are spherical and we neglect torques transmitted by inter-grain contacts, the medium further reduces to an anisotropic "quasi-micro-polar continuum". When our description is applied to a statistically isotropic medium, with vanishing grain reorientation according to eq. (9), it coincides with the first order of Chang and Gao's isotropic "non-polar theory" [23]. In similar approaches but that now include anisotropy, EMERIAULT F. and CHANG C. S. (J. Eng. Mech. ASCE, 123 (1997) 1289) treat non-linear responses, and EMERIAULT F. and CLAQUIN C. (Granular Matter, 2 (2000) 201) focus on (linear) viscoelastic responses. In neither case, however, is grain reorientation involved in relating microscopic displacements to macroscopic strains.
33. In experiments without external preloading, the medium is still preloaded by its own weight, albeit in a non-uniform fashion. Since our description is local (i.e., fabric tensors may vary in space), this non-uniformity does not present a difficulty.
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35. ⊥ do not vary to first order.
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