TY - JOUR

T1 - Multiscale analysis of a model problem of a thermoelastic body with thin inclusions

AU - Sazhenkov, S. A.

AU - Fankina, I. V.

AU - Furtsev, A. I.

AU - Gilev, P. V.

AU - Gorynin, A. G.

AU - Gorynina, O. G.

AU - Karnaev, V. M.

AU - Leonova, E. I.

N1 - Funding Information: Sazhenkov, S.A., Fankina, I.V., Furtsev, A.I., Gilev, P.V., Gorynin, A.G., Goryn-ina, O.G., Karnaev, V.M., Leonova, E.I., Multiscale Analysis of a Model Problem of a Thermoelastic Body with Thin Inclusions. © 2021 Sazhenkov S.A., Fankina I.V., Furtsev A.I., Gilev P.V., Gorynin A.G., Gorynina O.G., Karnaev V.M., Leonova E.I. The work was carried out with the financial support from the Mathematical Center in Akadem-gorodok, Novosibirsk, Russia (Agreement with the Ministry of Science and Higher Education of the Russian Federation no. 075-15-2019-1613). Received February, 29, 2021, published March, 23, 2021. Publisher Copyright: © 2021 Sazhenkov S.A., Fankina I.V., Furtsev A.I., Gilev PA7., Gorynin A.G., Gorynina O.G., Karnaev A’.Μ., Leonova E.I. All Rights Reserved. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021

Y1 - 2021

N2 - A model statical problem for a thermoelastic body with thin inclusions is studied. This problem incorporates two small positive parameters δ and ε, which describe the thickness of an individual inclusion and the distance between two neighboring inclusions, respectively. Relying on the variational formulation of the problem, by means of the modern methods of asymptotic analysis, we investigate the behavior of solutions as δ and ε tend to zero. As the result, we construct two models corresponding to the limiting cases. At first, as δ→0, we derive a lim iting model in which inclusions are thin (of zero diameter). Then, from this limiting model, as ε→ 0, we derive a homogenized model, which describes effective behavior on the macroscopic scale, i.e., on the scale where there is no need to take into account each individual inclusion. The limiting passage as ε 0 is based on the use of homogenization theory. The final section of the article presents a series of numerical experiments for the established limiting models.

AB - A model statical problem for a thermoelastic body with thin inclusions is studied. This problem incorporates two small positive parameters δ and ε, which describe the thickness of an individual inclusion and the distance between two neighboring inclusions, respectively. Relying on the variational formulation of the problem, by means of the modern methods of asymptotic analysis, we investigate the behavior of solutions as δ and ε tend to zero. As the result, we construct two models corresponding to the limiting cases. At first, as δ→0, we derive a lim iting model in which inclusions are thin (of zero diameter). Then, from this limiting model, as ε→ 0, we derive a homogenized model, which describes effective behavior on the macroscopic scale, i.e., on the scale where there is no need to take into account each individual inclusion. The limiting passage as ε 0 is based on the use of homogenization theory. The final section of the article presents a series of numerical experiments for the established limiting models.

KW - composite material

KW - generalized solution

KW - homogenization

KW - linear thermoelasticity

KW - numerical experiment

KW - thin inclusion

KW - two-scale convergence

UR - http://www.scopus.com/inward/record.url?scp=85104753189&partnerID=8YFLogxK

U2 - 10.33048/semi.2021.18.020

DO - 10.33048/semi.2021.18.020

M3 - Article

AN - SCOPUS:85104753189

VL - 18

SP - 282

EP - 318

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -