TY - JOUR

T1 - Homogenization of the static anti-plane shear model for the reinforced composite

AU - Leonova, Evelina Ivanovna

PY - 2024/1/1

Y1 - 2024/1/1

N2 - The static problem of anti-plane shear of a thermoelastic composite, stitched with reinforcing threads, is considered. The original formulation contains a small positive parameter ε, which characterizes the distance between neighboring threads. It is also assumed that the thermomechanical characteristics of the composite body depend on ε. The asymptotic behavior of solutions as the parameter ε tends to zero is investigated. The limiting transition as ε → 0+ is mathematically rigorously justified and represents a homogenization procedure. This transition is based on the application of the standard Allaire-Nguetseng two-scale convergence method and its version by G. Allaire, A. Damlamian, U. Hornung for homogenization on thin inclusions. The result consists of the construction of a limit averaged model of anti-plane shear of the composite material. Using the newly obtained model, numerical experiments are performed, which show consistency of the theoretical conclusions.

AB - The static problem of anti-plane shear of a thermoelastic composite, stitched with reinforcing threads, is considered. The original formulation contains a small positive parameter ε, which characterizes the distance between neighboring threads. It is also assumed that the thermomechanical characteristics of the composite body depend on ε. The asymptotic behavior of solutions as the parameter ε tends to zero is investigated. The limiting transition as ε → 0+ is mathematically rigorously justified and represents a homogenization procedure. This transition is based on the application of the standard Allaire-Nguetseng two-scale convergence method and its version by G. Allaire, A. Damlamian, U. Hornung for homogenization on thin inclusions. The result consists of the construction of a limit averaged model of anti-plane shear of the composite material. Using the newly obtained model, numerical experiments are performed, which show consistency of the theoretical conclusions.

KW - anti-plane shear

KW - composite material

KW - homogenization

KW - numerical experiment

KW - thin inclusion

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85212340149&origin=inward&txGid=7877af6acdb65c94a07b7dc827d14258

UR - https://www.mendeley.com/catalogue/924074c7-0a35-3eff-8f4e-45d02716ea80/

U2 - 10.33048/semi.2024.21.069

DO - 10.33048/semi.2024.21.069

M3 - Article

VL - 21

SP - 1042

EP - 1063

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -