Geodesic
Carrying out homogenization in viscoelastic heterogeneous media taking into account the collective influence of boundaries
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 1, pp. 98-107

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The effective coefficients of viscoelasticity of a heterogeneous medium are obtained on the basis of the generalized derivative formalism, which reflects the internal boundaries of a heterogeneous medium. A solution is sought for the averaged Green's function for the found modified operator, taking into account the averaging and subsequent analysis of the operator. The effective viscoelasticity coefficients integrally take into account the microstructure of the system (physical properties and characteristic phase sizes) in an explicit form, that is a consequence of the solution obtained, which expresses the solution of the many-body problem in a heterogeneous medium.
Keywords: heterogeneous medium, transition layer, generalized derivative, Green's function, averaging, viscoelasticity. .
Mots-clés : microstructure 
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     author = {A. V. Mishin},
     title = {Carrying out homogenization in viscoelastic heterogeneous media taking into account the collective influence of boundaries},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {98--107},
     publisher = {mathdoc},
     volume = {26},
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     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_1_a8/}
}
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A. V. Mishin. Carrying out homogenization in viscoelastic heterogeneous media taking into account the collective influence of boundaries. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 1, pp. 98-107. http://geodesic.mathdoc.fr/item/SJIM_2023_26_1_a8/