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

S. A. Sazhenkov, I. V. Fankina, A. I. Furtsev, P. V. Gilev, A. G. Gorynin, O. G. Gorynina, V. M. Karnaev, E. I. Leonova

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)282-318
Number of pages37
JournalSiberian Electronic Mathematical Reports
Volume18
DOIs
Publication statusPublished - 2021

Keywords

  • composite material
  • generalized solution
  • homogenization
  • linear thermoelasticity
  • numerical experiment
  • thin inclusion
  • two-scale convergence

OECD FOS+WOS

  • 1.01 MATHEMATICS

Fingerprint

Dive into the research topics of 'Multiscale analysis of a model problem of a thermoelastic body with thin inclusions'. Together they form a unique fingerprint.

Cite this