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Research Papers

On Spherical Inhomogeneity With Steigmann–Ogden Interface

[+] Author and Article Information
Anna Y. Zemlyanova

Department of Mathematics,
Kansas State University,
138 Cardwell Hall,
Manhattan, KS 66506
e-mail: azem@ksu.edu

Sofia G. Mogilevskaya

Department of Civil, Environmental,
and Geo-Engineering,
University of Minnesota,
500 Pillsbury Drive S.E.,
Minneapolis, MN 55455
e-mail: mogil003@umn.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 25, 2018; final manuscript received September 13, 2018; published online October 1, 2018. Assoc. Editor: Shengping Shen.

J. Appl. Mech 85(12), 121009 (Oct 01, 2018) (10 pages) Paper No: JAM-18-1444; doi: 10.1115/1.4041499 History: Received July 25, 2018; Revised September 13, 2018

The problem of an infinite isotropic elastic space subjected to uniform far-field load and containing an isotropic elastic spherical inhomogeneity with Steigmann–Ogden interface is considered. The interface is treated as a shell of vanishing thickness possessing surface tension as well as membrane and bending stiffnesses. The constitutive and equilibrium equations of the Steigmann–Ogden theory for a spherical surface are written in explicit forms. Closed-form analytical solutions are derived for two cases of loading conditions—the hydrostatic loading and deviatoric loading with vanishing surface tension. The single inhomogeneity-based estimates of the effective properties of macroscopically isotropic materials containing spherical inhomogeneities with Steigmann–Ogden interfaces are presented. It is demonstrated that, in the case of vanishing surface tension, the Steigmann–Ogden model describes a special case of thin and stiff uniform interphase layer.

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Figures

Grahic Jump Location
Fig. 2

A spherical inhomogeneity with Steigmann–Ogden interface in an infinite matrix

Grahic Jump Location
Fig. 1

Notations related to a spherical material surface

Grahic Jump Location
Fig. 3

Normalized jumps (a) △σrr/μ and (b) △σ/μ for φ = 0

Grahic Jump Location
Fig. 4

Normalized jumps (a) △σrr/μ and (b) △σ/μ for φ = 90

Grahic Jump Location
Fig. 5

Normalized jumps (a) △σrr/μ and (b) △σ/μ as for θ = 90

Grahic Jump Location
Fig. 6

Normalized effective shear modulus for the composite material with overall isotropy

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