Geodesic
Equivalent body forces for jumps of stresses and displacements in Biot model of anisotropic porous medium
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 33-44

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The aim of this paper is to establish formulas for body forces equivalent to jumps of stresses and displacements in anisotropic Biot model. Scheme used follows the scheme typical for elastic medium. We derive Betti identity, reciprocity relations and representation integrals for porous medium. Applying representation integrals to a volume containing discontinuity surfaces we obtain equivalent body forces. Finally, physical consequences and equivalent forces for isotropic Biot model are presented. 
@article{ZNSL_1997_239_a2,
     author = {A. V. Bakulin},
     title = {Equivalent body forces for jumps of stresses and displacements in {Biot} model of anisotropic porous medium},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--44},
     publisher = {mathdoc},
     volume = {239},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a2/}
}
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A. V. Bakulin. Equivalent body forces for jumps of stresses and displacements in Biot model of anisotropic porous medium. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 26, Tome 239 (1997), pp. 33-44. http://geodesic.mathdoc.fr/item/ZNSL_1997_239_a2/