Displacements representations for the problems with spherical and circular material surfaces

Sofia G. Mogilevskaya; Volodymyr I. Kushch; Anna Y. Zemlyanova

doi:10.1093/qjmam/hbz013

Displacements representations for the problems with spherical and circular material surfaces

Sofia G. Mogilevskaya, Volodymyr I. Kushch, Anna Y. Zemlyanova

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

26 Scopus citations

Abstract

The displacements representations of the type used by Christensen and Lo (J. Mech. Phys. Solids 27, 1979) are modified to allow for analytical treatment of problems involving spherical and circular material surfaces that possess constant surface tension. The modified representations are used to derive closed-form expressions for the local elastic fields and effective moduli of macroscopically isotropic composite materials containing spherical and circular inhomogeneities with the interfaces described by the complete Gurtin-Murdoch and Steigmann-Ogden models.

Original language	English (US)
Pages (from-to)	449-471
Number of pages	23
Journal	Quarterly Journal of Mechanics and Applied Mathematics
Volume	72
Issue number	4
DOIs	https://doi.org/10.1093/qjmam/hbz013
State	Published - Nov 1 2019
Externally published	Yes

Bibliographical note

Funding Information:
The first author (S.M.) gratefully acknowledges the support provided by the Theodore W. Bennett Chair, University of Minnesota. The second author (V.K.) acknowledges the support from Science and Technology Center in Ukraine (STCU), award #6247. The third author (A.Z.) gratefully acknowledges the support from Simons Collaboration grant, award # 319217.

Publisher Copyright:
© The Author(s), 2019. Published by Oxford University Press; all rights reserved.

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abstract = "The displacements representations of the type used by Christensen and Lo (J. Mech. Phys. Solids 27, 1979) are modified to allow for analytical treatment of problems involving spherical and circular material surfaces that possess constant surface tension. The modified representations are used to derive closed-form expressions for the local elastic fields and effective moduli of macroscopically isotropic composite materials containing spherical and circular inhomogeneities with the interfaces described by the complete Gurtin-Murdoch and Steigmann-Ogden models.",

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AU - Mogilevskaya, Sofia G.

AU - Kushch, Volodymyr I.

AU - Zemlyanova, Anna Y.

N1 - Funding Information: The first author (S.M.) gratefully acknowledges the support provided by the Theodore W. Bennett Chair, University of Minnesota. The second author (V.K.) acknowledges the support from Science and Technology Center in Ukraine (STCU), award #6247. The third author (A.Z.) gratefully acknowledges the support from Simons Collaboration grant, award # 319217. Publisher Copyright: © The Author(s), 2019. Published by Oxford University Press; all rights reserved.

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N2 - The displacements representations of the type used by Christensen and Lo (J. Mech. Phys. Solids 27, 1979) are modified to allow for analytical treatment of problems involving spherical and circular material surfaces that possess constant surface tension. The modified representations are used to derive closed-form expressions for the local elastic fields and effective moduli of macroscopically isotropic composite materials containing spherical and circular inhomogeneities with the interfaces described by the complete Gurtin-Murdoch and Steigmann-Ogden models.

AB - The displacements representations of the type used by Christensen and Lo (J. Mech. Phys. Solids 27, 1979) are modified to allow for analytical treatment of problems involving spherical and circular material surfaces that possess constant surface tension. The modified representations are used to derive closed-form expressions for the local elastic fields and effective moduli of macroscopically isotropic composite materials containing spherical and circular inhomogeneities with the interfaces described by the complete Gurtin-Murdoch and Steigmann-Ogden models.

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Displacements representations for the problems with spherical and circular material surfaces

Abstract

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