Geodesic
On the derivation methods of the equations describing the effective models of layered media
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 27, Tome 250 (1998), pp. 219-243

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The derivation methods of the equations describing the effective models of layered periodic media are represented. Elastic and fluid media and porous Biot media can be as such ones. At first the effective models are derived by the strict approach and then some operations of the derivation are changed for more simple operations giving right results. As result the comparatively simple and justified method of derivation of the effective model equations is established. In particular, this method allows rather to simplify and to justify the derivation of the effective model in the case of media containing the Biot layers and to establish the equations of the effective model of the porous layered medium intersected by fractures on which there is slide contact. 
@article{ZNSL_1998_250_a14,
     author = {L. A. Molotkov},
     title = {On the derivation methods of the equations describing the effective models of layered media},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {219--243},
     publisher = {mathdoc},
     volume = {250},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_250_a14/}
}
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L. A. Molotkov. On the derivation methods of the equations describing the effective models of layered media. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 27, Tome 250 (1998), pp. 219-243. http://geodesic.mathdoc.fr/item/ZNSL_1998_250_a14/