Homogenization of Viscoelastic Heterogeneous Media with Allowance for Collective Influence of Boundaries

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Homogenization of Viscoelastic Heterogeneous Media with Allowance for Collective Influence of Boundaries. / Mishin, A. V.

In: Journal of Applied and Industrial Mathematics, Vol. 17, No. 1, 2023, p. 131-137.

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

BibTeX

@article{65387084291748e5b2d8193b48638bd2,

title = "Homogenization of Viscoelastic Heterogeneous Media with Allowance for Collective Influence of Boundaries",

abstract = "We obtain effective viscoelasticity coefficients for a heterogeneous medium based on ageneralized derivative formalism that reflects internal boundaries in the heterogeneous medium. Asolution is sought for the homogenized Green{\textquoteright}s function of the resulting modified operator takinginto account the homogenization and subsequent analysis of the operator. Based on the obtainedsolution of the many-body problem in a heterogeneous medium, the effective viscoelasticitycoefficients integrally take into account the microstructure of the system (physical properties andcharacteristic phase sizes) in explicit form.",

keywords = "Green{\textquoteright}s function, generalized derivative, heterogeneous medium, homogenization, microstructure, transition layer, viscoelasticity",

author = "Mishin, {A. V.}",

note = "This work was supported by the Russian Science Foundation, project no. 21-19-00733. Публикация для корректировки.",

year = "2023",

doi = "10.1134/S1990478923010143",

language = "English",

volume = "17",

pages = "131--137",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Homogenization of Viscoelastic Heterogeneous Media with Allowance for Collective Influence of Boundaries

AU - Mishin, A. V.

N1 - This work was supported by the Russian Science Foundation, project no. 21-19-00733. Публикация для корректировки.

PY - 2023

Y1 - 2023

N2 - We obtain effective viscoelasticity coefficients for a heterogeneous medium based on ageneralized derivative formalism that reflects internal boundaries in the heterogeneous medium. Asolution is sought for the homogenized Green’s function of the resulting modified operator takinginto account the homogenization and subsequent analysis of the operator. Based on the obtainedsolution of the many-body problem in a heterogeneous medium, the effective viscoelasticitycoefficients integrally take into account the microstructure of the system (physical properties andcharacteristic phase sizes) in explicit form.

AB - We obtain effective viscoelasticity coefficients for a heterogeneous medium based on ageneralized derivative formalism that reflects internal boundaries in the heterogeneous medium. Asolution is sought for the homogenized Green’s function of the resulting modified operator takinginto account the homogenization and subsequent analysis of the operator. Based on the obtainedsolution of the many-body problem in a heterogeneous medium, the effective viscoelasticitycoefficients integrally take into account the microstructure of the system (physical properties andcharacteristic phase sizes) in explicit form.

KW - Green’s function

KW - generalized derivative

KW - heterogeneous medium

KW - homogenization

KW - microstructure

KW - transition layer

KW - viscoelasticity

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85159273549&origin=inward&txGid=b0a163118af6a2bab1f6019ca99d0194

UR - https://www.mendeley.com/catalogue/332dbbc1-dce6-3bad-a557-da4576ce73a3/

U2 - 10.1134/S1990478923010143

DO - 10.1134/S1990478923010143

M3 - Article

VL - 17

SP - 131

EP - 137

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -

ID: 59244691