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1. | Institute for Low Temperature Physics and Engineering, Ukrainian Academy of Sciences, Lenin Ave 47, Kharkiv 61164, Ukraine |
References:
[1] |
M. A. Berezhnyy and L. V. Berlyand, Continuum limit for three-dimensional mass-spring networks and discrete Korn's inequality,, Journal of the Mechanics and Physics of Solids, 54 (2006), 635.
doi: 10.1016/j.jmps.2005.09.006. |
[2] |
M. A. Berezhnyi, The asymptotic bahavior of viscous incompressible fluid small oscillations with solid interacting particles,, Journal of Mathematical Physics, 3 (2007), 135.
|
[3] |
M. Berezhnyi, L. Berlyand and E. Khruslov, The homogenized model of small oscillations of complex fluids,, Networks and Heterogeneous Media, 3 (2008), 835.
|
[4] |
M. Berezhnyi, "Homogenized Models of Complex Fluids,", PhD Thesis, (2009). Google Scholar |
[5] |
L. V. Berlyand and A. D. Okhotsimskii, Averaged description of an elastic medium with a large number of small absolutely rigid inclusions,, Dokl. Akad. Nauk SSSR, 268 (1983), 317.
|
[6] |
L. Berlyand and E. Khruslov, Homogenized non-Newtonian viscoelastic rheology of a suspension of interacting particles in a viscous Newtonian fluid,, SIAM, 64 (2004), 1002.
doi: i:10.1137/S0036139902403913. |
[7] |
E. Cosserat et F. Cosserat, "Théorie des Corps Deformables,", Hermann, (1909). Google Scholar |
[8] |
V. A. Ditkin and A. P. Prudnikov, "Integral Transforms and Operational Calculus,", Oxford; New York: Pergamon, (1965).
|
[9] |
G. Grioli, Ellasticá asymmetrica,, Annali di matematica pura ed applicata, 4 (1960), 389.
doi: 10.1007/BF02414525. |
[10] |
T. Kato, "Perturbation Theory for Linear Operators,", Springer, (1995).
|
[11] |
L. D. Landau and E. M. Lifshitz, "Course of Theoretical Physics. Quantum Mechanics. Non-relativistic Theory,", London: Pergamon, (1958).
|
[12] |
A. I. Leonov, Algebraic theory of linear viscoelastic nematodynamics,, Mathematical Physics, 11 (2008), 87.
doi: 10.1007/s11040-008-9041-z. |
[13] |
V. Marchenko and E. Khruslov, "Homogenization of Partial Differential Equations,", Birkh\, (2006).
|
[14] |
A. I. Marcushevich, "Theory of Analytic Functions: Brief Course,", Mir, (1983).
|
[15] |
R. D. Mindlin and H. F. Tiersten, Effects of couple-stresses in linear elasticity,, Archive for Rational Mechanics and Analysis, 11 (1962), 415.
doi: 10.1007/BF00253946. |
[16] |
O. A. Oleinic, A. S. Shamaev and G. A. Iosif'yan, "Mathematical Problems in Elasticity and Homogenization,", in, 26 (1992).
|
[17] |
I. Y. Smolin, P. V. Makarov, D. V. Shmick and I. V. Savlevich, A micropolar model of plastic deformation of polycrystals at the mesolevel,, Computational Materials Science, 19 (2000), 133.
doi: 10.1016/S0927-0256(00)00148-8. |
[18] |
X. Zhang and P. Sharma, Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems,, International Journal of Solids and Structures, 42 (2005), 3833.
doi: 10.1016/j.ijsolstr.2004.12.005. |
show all references
References:
[1] |
M. A. Berezhnyy and L. V. Berlyand, Continuum limit for three-dimensional mass-spring networks and discrete Korn's inequality,, Journal of the Mechanics and Physics of Solids, 54 (2006), 635.
doi: 10.1016/j.jmps.2005.09.006. |
[2] |
M. A. Berezhnyi, The asymptotic bahavior of viscous incompressible fluid small oscillations with solid interacting particles,, Journal of Mathematical Physics, 3 (2007), 135.
|
[3] |
M. Berezhnyi, L. Berlyand and E. Khruslov, The homogenized model of small oscillations of complex fluids,, Networks and Heterogeneous Media, 3 (2008), 835.
|
[4] |
M. Berezhnyi, "Homogenized Models of Complex Fluids,", PhD Thesis, (2009). Google Scholar |
[5] |
L. V. Berlyand and A. D. Okhotsimskii, Averaged description of an elastic medium with a large number of small absolutely rigid inclusions,, Dokl. Akad. Nauk SSSR, 268 (1983), 317.
|
[6] |
L. Berlyand and E. Khruslov, Homogenized non-Newtonian viscoelastic rheology of a suspension of interacting particles in a viscous Newtonian fluid,, SIAM, 64 (2004), 1002.
doi: i:10.1137/S0036139902403913. |
[7] |
E. Cosserat et F. Cosserat, "Théorie des Corps Deformables,", Hermann, (1909). Google Scholar |
[8] |
V. A. Ditkin and A. P. Prudnikov, "Integral Transforms and Operational Calculus,", Oxford; New York: Pergamon, (1965).
|
[9] |
G. Grioli, Ellasticá asymmetrica,, Annali di matematica pura ed applicata, 4 (1960), 389.
doi: 10.1007/BF02414525. |
[10] |
T. Kato, "Perturbation Theory for Linear Operators,", Springer, (1995).
|
[11] |
L. D. Landau and E. M. Lifshitz, "Course of Theoretical Physics. Quantum Mechanics. Non-relativistic Theory,", London: Pergamon, (1958).
|
[12] |
A. I. Leonov, Algebraic theory of linear viscoelastic nematodynamics,, Mathematical Physics, 11 (2008), 87.
doi: 10.1007/s11040-008-9041-z. |
[13] |
V. Marchenko and E. Khruslov, "Homogenization of Partial Differential Equations,", Birkh\, (2006).
|
[14] |
A. I. Marcushevich, "Theory of Analytic Functions: Brief Course,", Mir, (1983).
|
[15] |
R. D. Mindlin and H. F. Tiersten, Effects of couple-stresses in linear elasticity,, Archive for Rational Mechanics and Analysis, 11 (1962), 415.
doi: 10.1007/BF00253946. |
[16] |
O. A. Oleinic, A. S. Shamaev and G. A. Iosif'yan, "Mathematical Problems in Elasticity and Homogenization,", in, 26 (1992).
|
[17] |
I. Y. Smolin, P. V. Makarov, D. V. Shmick and I. V. Savlevich, A micropolar model of plastic deformation of polycrystals at the mesolevel,, Computational Materials Science, 19 (2000), 133.
doi: 10.1016/S0927-0256(00)00148-8. |
[18] |
X. Zhang and P. Sharma, Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems,, International Journal of Solids and Structures, 42 (2005), 3833.
doi: 10.1016/j.ijsolstr.2004.12.005. |
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