TY - JOUR

T1 - Junction problem for thin elastic and volume rigid inclusions in elastic body

AU - Khludnev, A. M.

N1 - Publisher Copyright: © 2022 The Author(s).

PY - 2022/11/14

Y1 - 2022/11/14

N2 - The article concerns a junction problem for two-dimensional elastic body with a thin elastic inclusion and a volume rigid inclusion. It is assumed that the inclusions have a common point. A delamination of the thin inclusion from the surrounding elastic body is assumed thus forming an interfacial crack. Constraint-type boundary conditions are imposed at the crack faces to prevent interpenetration between the faces. Moreover, a connection between the crack faces is characterized by a positive damage parameter. Limit transitions are justified as the damage parameter tends to infinity and to zero. In addition to this, a transition to limit is analysed as a rigidity parameter of the thin inclusion tends to infinity. Limit models are investigated. In particular, junction conditions at the common point are found for all cases considered. This article is part of the theme issue 'Non-smooth variational problems and applications'.

AB - The article concerns a junction problem for two-dimensional elastic body with a thin elastic inclusion and a volume rigid inclusion. It is assumed that the inclusions have a common point. A delamination of the thin inclusion from the surrounding elastic body is assumed thus forming an interfacial crack. Constraint-type boundary conditions are imposed at the crack faces to prevent interpenetration between the faces. Moreover, a connection between the crack faces is characterized by a positive damage parameter. Limit transitions are justified as the damage parameter tends to infinity and to zero. In addition to this, a transition to limit is analysed as a rigidity parameter of the thin inclusion tends to infinity. Limit models are investigated. In particular, junction conditions at the common point are found for all cases considered. This article is part of the theme issue 'Non-smooth variational problems and applications'.

KW - crack

KW - damage parameter

KW - junction conditions

KW - rigid inclusion

KW - thin elastic inclusion

KW - variational inequality

UR - http://www.scopus.com/inward/record.url?scp=85138548115&partnerID=8YFLogxK

U2 - 10.1098/rsta.2021.0360

DO - 10.1098/rsta.2021.0360

M3 - Article

C2 - 36154469

AN - SCOPUS:85138548115

VL - 380

SP - 20210360

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8428

IS - 2236

M1 - 20210360

ER -