TY - JOUR

T1 - Modeling of bonded elastic structures by a variational method: Theoretical analysis and numerical simulation

AU - Furtsev, Alexey

AU - Itou, Hiromichi

AU - Rudoy, Evgeny

N1 - Funding Information: This work was supported by the Russian Foundation for Basic Research , Russia (Grant No. 19-51-50004 ) and Japan Society for the Promotion of Science (Grant No. J19-721 ) under the Japan-Russia Research Cooperative Program. Publisher Copyright: © 2019 Elsevier Ltd Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - The paper deals with an equilibrium problem of two bodies adhesively bonded to each other along the part of interface between them. There is a crack on the rest part of the interface. The bonding between the bodies is described by “spring type” condition modeling a soft and thin material layer. We also impose non-penetration conditions and Tresca's friction conditions on the interface including both the adhesive layer and the crack. The non-penetration condition excludes mutual penetration of bodies. A formula for the derivative of the energy functional with respect to the crack length is obtained. It is shown that the derivative can be represented as a path-independent integral (J-integral). Moreover, a non-overlapping domain decomposition method for the bonded structure is proposed and its convergence is studied theoretically and numerically. The numerical study shows the efficiency of the proposed method and the importance of the non-penetration condition.

AB - The paper deals with an equilibrium problem of two bodies adhesively bonded to each other along the part of interface between them. There is a crack on the rest part of the interface. The bonding between the bodies is described by “spring type” condition modeling a soft and thin material layer. We also impose non-penetration conditions and Tresca's friction conditions on the interface including both the adhesive layer and the crack. The non-penetration condition excludes mutual penetration of bodies. A formula for the derivative of the energy functional with respect to the crack length is obtained. It is shown that the derivative can be represented as a path-independent integral (J-integral). Moreover, a non-overlapping domain decomposition method for the bonded structure is proposed and its convergence is studied theoretically and numerically. The numerical study shows the efficiency of the proposed method and the importance of the non-penetration condition.

KW - Adhesive contact

KW - Bonded structure

KW - Delamination crack

KW - Domain decomposition method

KW - Nonpenetration condition

KW - Path-independent integral

KW - Tresca's friction

KW - UNILATERAL CONDITIONS

KW - ENERGY

KW - INEQUALITIES

KW - CRACK PROBLEMS

KW - SOFT

KW - DOMAIN DECOMPOSITION METHOD

KW - INTERFACE

KW - EQUILIBRIUM

KW - CONVERGENCE

KW - INCLUSION

UR - http://www.scopus.com/inward/record.url?scp=85070214531&partnerID=8YFLogxK

U2 - 10.1016/j.ijsolstr.2019.08.006

DO - 10.1016/j.ijsolstr.2019.08.006

M3 - Article

AN - SCOPUS:85070214531

VL - 182-183

SP - 100

EP - 111

JO - International Journal of Solids and Structures

JF - International Journal of Solids and Structures

SN - 0020-7683

ER -