Geodesic
Calculation of effective moduli of composite materials
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 1128-1136

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Effective properties of composite and porous materials are determined by using an approach based on two-scale asymptotic expansions. Explicit approximate formulas are derived for the effective moduli of composite and porous materials of elongated structures. A numerical method is proposed for finding solutions to cell problems, which are used to determine “exact” effective moduli. Examples are computed for a two-dimensional porous medium with variously shaped pores and various degrees of “elongation”. The effective moduli produced by the explicit approximate formulas prove to be similar to those found by numerically solving cell problems. 
@article{ZVMMF_2006_46_6_a12,
     author = {T. A. Yakubenko},
     title = {Calculation of effective moduli of composite materials},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1128--1136},
     publisher = {mathdoc},
     volume = {46},
     number = {6},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a12/}
}
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T. A. Yakubenko. Calculation of effective moduli of composite materials. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 6, pp. 1128-1136. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_6_a12/