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

Alexey Furtsev, Hiromichi Itou, Evgeny Rudoy

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)100-111
Number of pages12
JournalInternational Journal of Solids and Structures
Volume182-183
DOIs
Publication statusPublished - 1 Jan 2020

Fingerprint

Variational Methods
Theoretical Analysis
Cracks
Numerical Simulation
Computer simulation
Crack
Modeling
cracks
Derivatives
Domain decomposition methods
simulation
J integral
Adhesives
Nonoverlapping Domain Decomposition
J-integral
Derivative
Friction
Domain Decomposition Method
Equilibrium Problem
Energy Functional

Keywords

  • Adhesive contact
  • Bonded structure
  • Delamination crack
  • Domain decomposition method
  • Nonpenetration condition
  • Path-independent integral
  • Tresca's friction

Cite this

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Modeling of bonded elastic structures by a variational method : Theoretical analysis and numerical simulation. / Furtsev, Alexey; Itou, Hiromichi; Rudoy, Evgeny.

In: International Journal of Solids and Structures, Vol. 182-183, 01.01.2020, p. 100-111.

Research output: Contribution to journalArticle

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T2 - Theoretical analysis and numerical simulation

AU - Furtsev, Alexey

AU - Itou, Hiromichi

AU - Rudoy, Evgeny

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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.

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