TY - JOUR

T1 - Asymptotic Justification of the Models of Thin Inclusions in an Elastic Body in the Antiplane Shear Problem

AU - Rudoy, E. M.

AU - Itou, H.

AU - Lazarev, N. P.

N1 - Funding Information: The authors were supported by the Russian Foundation for Basic Research (projects nos. 18–41–140003 and 19–51–50004) and the Japan Society for the Promotion of Science (project no. J19–721). Publisher Copyright: © 2021, Pleiades Publishing, Ltd. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/2

Y1 - 2021/2

N2 - The equilibrium problem for an elastic body having an inhomogeneous inclusion withcurvilinear boundaries is considered within the framework of antiplane shear. We assume thatthere is a power-law dependence of the shear modulus of the inclusion on a small parametercharacterizing its width. We justify passage to the limit as the parameter vanishes and constructan asymptotic model of an elastic body containing a thin inclusion. We also show that, dependingon the exponent of the parameter, there are the five types of thin inclusions: crack, rigid inclusion,ideal contact, elastic inclusion, and a crack with adhesive interaction of the faces. The strongconvergence is established of the family of solutions of the original problem to the solution of thelimiting one.

AB - The equilibrium problem for an elastic body having an inhomogeneous inclusion withcurvilinear boundaries is considered within the framework of antiplane shear. We assume thatthere is a power-law dependence of the shear modulus of the inclusion on a small parametercharacterizing its width. We justify passage to the limit as the parameter vanishes and constructan asymptotic model of an elastic body containing a thin inclusion. We also show that, dependingon the exponent of the parameter, there are the five types of thin inclusions: crack, rigid inclusion,ideal contact, elastic inclusion, and a crack with adhesive interaction of the faces. The strongconvergence is established of the family of solutions of the original problem to the solution of thelimiting one.

KW - antiplane shear

KW - asymptotic analysis

KW - crack

KW - inhomogeneous elastic body

KW - thin elastic inclusion

KW - thin rigid inclusion

UR - http://www.scopus.com/inward/record.url?scp=85104742847&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=46091547

U2 - 10.1134/S1990478921010117

DO - 10.1134/S1990478921010117

M3 - Article

AN - SCOPUS:85104742847

VL - 15

SP - 129

EP - 140

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

M1 - 11

ER -