A morphing strategy to couple non-local to local continuum mechanics

Gilles Lubineau; Yan Azdoud; Fei Han; Christian C. Rey; Abe H. Askari

doi:10.1016/j.jmps.2012.02.009

A morphing strategy to couple non-local to local continuum mechanics

Gilles Lubineau, Yan Azdoud, Fei Han, Christian C. Rey, Abe H. Askari

Research output: Contribution to journal › Article › peer-review

182 Scopus citations

Abstract

A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. © 2012 Elsevier Ltd.

Original language	English (US)
Pages (from-to)	1088-1102
Number of pages	15
Journal	Journal of the Mechanics and Physics of Solids
Volume	60
Issue number	6
DOIs	https://doi.org/10.1016/j.jmps.2012.02.009
State	Published - Jun 2012

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Funding for this research was provided by KAUST baseline funding and by the BOEING company (agreement "Analysis methods for multifunctional composite materials in the presence of electromagnetic effect"). The authors are grateful to KAUST and the BOEING company for their financial support.

ASJC Scopus subject areas

Mechanics of Materials
Mechanical Engineering
Condensed Matter Physics

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10.1016/j.jmps.2012.02.009

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title = "A morphing strategy to couple non-local to local continuum mechanics",

abstract = "A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. {\textcopyright} 2012 Elsevier Ltd.",

author = "Gilles Lubineau and Yan Azdoud and Fei Han and Rey, {Christian C.} and Askari, {Abe H.}",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Funding for this research was provided by KAUST baseline funding and by the BOEING company (agreement {"}Analysis methods for multifunctional composite materials in the presence of electromagnetic effect{"}). The authors are grateful to KAUST and the BOEING company for their financial support.",

year = "2012",

month = jun,

doi = "10.1016/j.jmps.2012.02.009",

language = "English (US)",

volume = "60",

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AU - Lubineau, Gilles

AU - Azdoud, Yan

AU - Han, Fei

AU - Rey, Christian C.

AU - Askari, Abe H.

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: Funding for this research was provided by KAUST baseline funding and by the BOEING company (agreement "Analysis methods for multifunctional composite materials in the presence of electromagnetic effect"). The authors are grateful to KAUST and the BOEING company for their financial support.

PY - 2012/6

Y1 - 2012/6

N2 - A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. © 2012 Elsevier Ltd.

AB - A method for coupling non-local continuum models with long-range central forces to local continuum models is proposed. First, a single unified model that encompasses both local and non-local continuum representations is introduced. This model can be purely non-local, purely local or a hybrid depending on the constitutive parameters. Then, the coupling between the non-local and local descriptions is performed through a transition (morphing) affecting only the constitutive parameters. An important feature is the definition of the morphing functions, which relies on energy equivalence. This approach is useful in large-scale modeling of materials that exhibit strong non-local effects. The computational cost can be reduced while maintaining a reasonable level of accuracy. Efficiency, robustness and basic properties of the approach are discussed using one- and two-dimensional examples. © 2012 Elsevier Ltd.

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DO - 10.1016/j.jmps.2012.02.009

M3 - Article

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JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

IS - 6

ER -

A morphing strategy to couple non-local to local continuum mechanics

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