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Nonstandard dynamics of elastic composites
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 threedimensional massspring networks and discrete Korn's inequality, Journal of the Mechanics and Physics of Solids, 54 (2006), 635669. 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, Analysis, Geometry, 3 (2007), 135156. 
[3] 
M. Berezhnyi, L. Berlyand and E. Khruslov, The homogenized model of small oscillations of complex fluids, Networks and Heterogeneous Media, 3 (2008), 835869. 
[4] 
M. Berezhnyi, "Homogenized Models of Complex Fluids," PhD Thesis, ILTPE, 2009 (in ukrainian), 159 p. URL: http://www.dlib.com.ua/userednenimodelistrukturovanykhridyn.html. 
[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), 317320 (in Russian). 
[6] 
L. Berlyand and E. Khruslov, Homogenized nonNewtonian viscoelastic rheology of a suspension of interacting particles in a viscous Newtonian fluid, SIAM, Journal of Applied Mathematics, 64 (2004), 10021034. doi: i:10.1137/S0036139902403913. 
[7] 
E. Cosserat et F. Cosserat, "Théorie des Corps Deformables," Hermann, Paris, 1909. 
[8] 
V. A. Ditkin and A. P. Prudnikov, "Integral Transforms and Operational Calculus," Oxford; New York: Pergamon, 1965, 529p. 
[9] 
G. Grioli, Ellasticá asymmetrica, Annali di matematica pura ed applicata, 4 (1960), 389418. doi: 10.1007/BF02414525. 
[10] 
T. Kato, "Perturbation Theory for Linear Operators," Springer, 1995, 652 p. 
[11] 
L. D. Landau and E. M. Lifshitz, "Course of Theoretical Physics. Quantum Mechanics. Nonrelativistic Theory," London: Pergamon, 1958, 515 p. 
[12] 
A. I. Leonov, Algebraic theory of linear viscoelastic nematodynamics, Mathematical Physics, Analysis and Geometry, 11 (2008), 87116. doi: 10.1007/s110400089041z. 
[13] 
V. Marchenko and E. Khruslov, "Homogenization of Partial Differential Equations," Birkhäuser, Boston, 2006, 401 p. 
[14] 
A. I. Marcushevich, "Theory of Analytic Functions: Brief Course," Mir, Moscow, 1983. 
[15] 
R. D. Mindlin and H. F. Tiersten, Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11 (1962), 415448. doi: 10.1007/BF00253946. 
[16] 
O. A. Oleinic, A. S. Shamaev and G. A. Iosif'yan, "Mathematical Problems in Elasticity and Homogenization," in "Studies in Mathematics and its Applications," 26, NorthHolland Publishing Co., Amsterdam, 1992, 398 p. 
[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), 133142. doi: 10.1016/S09270256(00)001488. 
[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), 38333851. doi: 10.1016/j.ijsolstr.2004.12.005. 
show all references
References:
[1] 
M. A. Berezhnyy and L. V. Berlyand, Continuum limit for threedimensional massspring networks and discrete Korn's inequality, Journal of the Mechanics and Physics of Solids, 54 (2006), 635669. 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, Analysis, Geometry, 3 (2007), 135156. 
[3] 
M. Berezhnyi, L. Berlyand and E. Khruslov, The homogenized model of small oscillations of complex fluids, Networks and Heterogeneous Media, 3 (2008), 835869. 
[4] 
M. Berezhnyi, "Homogenized Models of Complex Fluids," PhD Thesis, ILTPE, 2009 (in ukrainian), 159 p. URL: http://www.dlib.com.ua/userednenimodelistrukturovanykhridyn.html. 
[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), 317320 (in Russian). 
[6] 
L. Berlyand and E. Khruslov, Homogenized nonNewtonian viscoelastic rheology of a suspension of interacting particles in a viscous Newtonian fluid, SIAM, Journal of Applied Mathematics, 64 (2004), 10021034. doi: i:10.1137/S0036139902403913. 
[7] 
E. Cosserat et F. Cosserat, "Théorie des Corps Deformables," Hermann, Paris, 1909. 
[8] 
V. A. Ditkin and A. P. Prudnikov, "Integral Transforms and Operational Calculus," Oxford; New York: Pergamon, 1965, 529p. 
[9] 
G. Grioli, Ellasticá asymmetrica, Annali di matematica pura ed applicata, 4 (1960), 389418. doi: 10.1007/BF02414525. 
[10] 
T. Kato, "Perturbation Theory for Linear Operators," Springer, 1995, 652 p. 
[11] 
L. D. Landau and E. M. Lifshitz, "Course of Theoretical Physics. Quantum Mechanics. Nonrelativistic Theory," London: Pergamon, 1958, 515 p. 
[12] 
A. I. Leonov, Algebraic theory of linear viscoelastic nematodynamics, Mathematical Physics, Analysis and Geometry, 11 (2008), 87116. doi: 10.1007/s110400089041z. 
[13] 
V. Marchenko and E. Khruslov, "Homogenization of Partial Differential Equations," Birkhäuser, Boston, 2006, 401 p. 
[14] 
A. I. Marcushevich, "Theory of Analytic Functions: Brief Course," Mir, Moscow, 1983. 
[15] 
R. D. Mindlin and H. F. Tiersten, Effects of couplestresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11 (1962), 415448. doi: 10.1007/BF00253946. 
[16] 
O. A. Oleinic, A. S. Shamaev and G. A. Iosif'yan, "Mathematical Problems in Elasticity and Homogenization," in "Studies in Mathematics and its Applications," 26, NorthHolland Publishing Co., Amsterdam, 1992, 398 p. 
[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), 133142. doi: 10.1016/S09270256(00)001488. 
[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), 38333851. doi: 10.1016/j.ijsolstr.2004.12.005. 
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