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M.E. Eglit and T.A. Yakubenko, "On Effective Moduli of Inhomogeneous Media Characterized by Several Small Parameters," Mech. Solids. 46 (1), 80-88 (2011)
Year 2011 Volume 46 Number 1 Pages 80-88
DOI 10.3103/S0025654411010134
Title On Effective Moduli of Inhomogeneous Media Characterized by Several Small Parameters
Author(s) M.E. Eglit (Lomonosov Moscow State University, GSP-2, Leninskie Gory, Moscow, 119992 Russia, m.eglit@mail.ru)
T.A. Yakubenko (Institute of Mechanics, Lomonosov Moscow State University, Michurinskii pr-t 1, Moscow, 119192 Russia, yakubta@mail.ru)
Abstract Composites and porous media of elongated structure, as well as materials with pores or inclusions having the shape of parallelepipeds or channels of rectangular cross-section, are considered under certain conditions on the inclusion-to-matrix modulus ratio and the volume fraction of inclusions (pores). The effective moduli are calculated by the method of mathematical homogenization theory. Numerical results on the dependence of the effective moduli on the prolateness of the structure, the shape of the inclusions (pores), the inclusion-to-matrix modulus ratio, and the volume fraction of inclusions (pores) are given. The effective moduli computed according to the algorithm of mathematical homogenization theory are compared with those given by the explicit approximate formulas earlier developed by the authors.
Keywords composites, porous media, homogenization, effective moduli, explicit formulas, numerical computations
References
1.  N. S. Bakhvalov and G. P. Panasenko, Homogenization of Processes in Periodic Media (Nauka, Moscow, 1984) [in Russian].
2.  B. E. Pobedrya, Mechanics of Composite Materials (Izd-vo MGU, Moscow, 1984) [in Russian].
3.  N. S. Bakhvalov and M. E. Eglit, "Multiparametric Problems of Homogenenization Theory," in Ser. Adv. Math. Appl. Sci.. Vol. 50: Homogenenization, Ed. by V. Berdichevsky et al. (World Scientific, 1999), pp. 92-106.
4.  T. A. Yakubenko, "Averaging a Periodic Porous Medium with Periods of Different Orders in the Different Directions," Russ. J. Num. Anal. Math. Model. 13 (2), 149-157 (1998).
5.  T. A. Yakubenko, Homogenization of Periodic Structures with Nonsmooth Data, Preprint No. 2 (Izd-vo MGU, Mekh.-Mat. Dept., 1999) [in Russian].
6.  T. A. Yakubenko, "Effective Characteristics of a Three-Dimensional Porous Medium of Special Structure," Zh. Vychisl. Mat. Mat. Fiz. 42 (1), 89-100 (2002) [Comput. Math. Math. Phys. (Engl. Transl.) 42 (1), 85-96 (2002)].
7.  T. A. Yakubenko, "Effective Moduli of Periodic Composites of Elongated Structure ," Zh. Vychisl. Mat. Mat. Fiz. 44 (9), 1638-1653 (2004) [Comput. Math. Math. Phys. (Engl. Transl.) 44 (9), 1557-1572 (2004)].
8.  T. A. Yakubenko, "Calculation of Effective Moduli of Composite Materials," Zh. Vychisl. Mat. Mat. Fiz. 46 (6), 1128-1136 (2006) [Comput. Math. Math. Phys. (Engl. Transl.) 46 (6), 1073-1080 (2006)].
9.  N. S. Bakhvalov and M. E. Eglit, "Effective Moduli of Composites Reinforced by Systems of Plates and Bars," Zh. Vychisl. Mat. Mat. Fiz. 38 (5), 813-834 (1998) [Comput. Math. Math. Phys. (Engl. Transl.) 38 (5), 783-804 (1998)].
10.  N. S. Bakhvalov and M. E. Eglit, "On the Velocity of Perturbation Propagation in Microinhomogeneous Elastic Media with a Small Shear Elasticity," Dokl. Ross. Akad. Nauk 323 (1), 13-18 (1992) [Dokl. Phys. (Engl. Transl.)].
11.  N. S. Bakhvalov and M. E. Eglit, "On Propagation of Small Perturbations in a Weakly Heat Conducting and Weakly Viscous Microinhomogeneous Media," Dokl. Ross. Akad. Nauk 325 (1), 9-15 (1992) [Dokl. Phys. (Engl. Transl.)].
12.  N. S. Bakhvalov and M. E. Eglit, "Averaging of the Equations of the Dynamics of Composites of Slightly Compressible Elastic Components," Zh. Vychisl. Mat. Mat. Fiz. 33 (7), 1066-1082 (1993) [Comput. Math. Math. Phys. (Engl. Transl.) 33 (7), 939-952 (1993)].
13.  N. S. Bakhvalov, G. V. Sandrakov, and M. E. Eglit, "Mathematical Study of Sound Waves Propagation Progress in Mixtures," Vestnik Moskov. Univ. Ser. I. Mat. Mekh., No. 6, 19-21 (1996) [Moscow Univ. Math. Bull. (Engl. Transl.) 51 (6), 5-7 (1996)].
14.  N. S. Bakhvalov, K. Yu. Bogachev, and M. E. Eglit, "Numerical Calculation of Effective Elastic Moduli for Incompressible Porous Material," Mekh. Komp. Mater. 32 (5), 579-587 (1996) [Mech. Comp. Mater. (Engl. Transl.) 32 (5), 399-405 (1996)]
Received 15 June 2010
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