Geodesic
On the new approach of obtaining of average effective model equations of periodic media
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 21, Tome 195 (1991), pp. 82-102 
L. A. Molotcov. On the new approach of obtaining of average effective model equations of periodic media. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 21, Tome 195 (1991), pp. 82-102. http://geodesic.mathdoc.fr/item/ZNSL_1991_195_a9/
@article{ZNSL_1991_195_a9,
     author = {L. A. Molotcov},
     title = {On the new approach of obtaining of average effective model equations of~periodic media},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--102},
     year = {1991},
     volume = {195},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1991_195_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

For layered and periodic media the fields of displacements and tensions are determined by matrix method. In the case of little length of periods and large number of periods the expression of these fields become simpler rather and satisfy new equations. If the original medium consists of elastic and liquid layers the obtained equations describe the simplificated model of media with many cracks, filled with liqued.