TY - JOUR

T1 - On junction problem with damage parameter for Timoshenko and rigid inclusions inside elastic body

AU - Khludnev, A. M.

AU - Popova, T. S.

N1 - Publisher Copyright: © 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/8/1

Y1 - 2020/8/1

N2 - The paper is concerned with an equilibrium problem for 2D elastic body with a thin elastic Timoshenko inclusion and a thin rigid inclusion. The elastic inclusion is assumed to be delaminated from the elastic body thus forming an interfacial crack with the matrix. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration. A connection between two inclusions at a given point is characterized by a positive damage parameter. Existence of solutions of the problem considered is proved, and different equivalent formulations of the problem are analyzed; junction conditions at the connection point are found. A convergence of solutions as the damage parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is analyzed. An analysis of the limit models is performed. A solution existence of an inverse problem for finding the damage and rigidity parameters is proved provided that an additional information concerning the derivative of the energy functional with respect to the delamination length is given.

AB - The paper is concerned with an equilibrium problem for 2D elastic body with a thin elastic Timoshenko inclusion and a thin rigid inclusion. The elastic inclusion is assumed to be delaminated from the elastic body thus forming an interfacial crack with the matrix. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration. A connection between two inclusions at a given point is characterized by a positive damage parameter. Existence of solutions of the problem considered is proved, and different equivalent formulations of the problem are analyzed; junction conditions at the connection point are found. A convergence of solutions as the damage parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is analyzed. An analysis of the limit models is performed. A solution existence of an inverse problem for finding the damage and rigidity parameters is proved provided that an additional information concerning the derivative of the energy functional with respect to the delamination length is given.

KW - crack

KW - damage parameter

KW - elastic body

KW - inverse problem

KW - junction conditions

KW - rigidity parameter

KW - thin inclusion

KW - variational inequality

KW - SEMIRIGID INCLUSIONS

KW - MECHANICAL INTERPLAY

KW - CRACK

KW - ASYMPTOTIC-BEHAVIOR

KW - BODIES

KW - PLATE

UR - http://www.scopus.com/inward/record.url?scp=85085942137&partnerID=8YFLogxK

U2 - 10.1002/zamm.202000063

DO - 10.1002/zamm.202000063

M3 - Article

AN - SCOPUS:85085942137

VL - 100

JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

SN - 0044-2267

IS - 8

M1 - e202000063

ER -