Solvability of the equivalent inclusion problem for an ellipsoidal inhomogeneity

Alexander B. Freidin, Vladislav A. Kucher

Research output

5 Citations (Scopus)

Abstract

The problem of an elastic ellipsoidal inhomogeneity in an infinite matrix is considered for the case of arbitrary anisotropy. Using the Fourier representation of Hill’s tensor, which we derive directly from the classical Eshelby solution for an ellipsoidal inclusion, and assuming certain conditions on the elasticity tensors, we prove the solvability of the Eshelby equivalent inclusion problem. This justifies a formula for the anisotropic polarization tensor for an ellipsoid
Original languageEnglish
Pages (from-to)255-262
JournalMathematics and Mechanics of Solids
Volume21
Issue number2
DOIs
Publication statusPublished - 2016

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Inhomogeneity
Tensors
Solvability
Tensor
Inclusion
Infinite Matrices
Ellipsoid
Classical Solution
Justify
Anisotropy
Elasticity
Polarization
Arbitrary

Cite this

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abstract = "The problem of an elastic ellipsoidal inhomogeneity in an infinite matrix is considered for the case of arbitrary anisotropy. Using the Fourier representation of Hill’s tensor, which we derive directly from the classical Eshelby solution for an ellipsoidal inclusion, and assuming certain conditions on the elasticity tensors, we prove the solvability of the Eshelby equivalent inclusion problem. This justifies a formula for the anisotropic polarization tensor for an ellipsoid",
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AU - Kucher, Vladislav A.

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AB - The problem of an elastic ellipsoidal inhomogeneity in an infinite matrix is considered for the case of arbitrary anisotropy. Using the Fourier representation of Hill’s tensor, which we derive directly from the classical Eshelby solution for an ellipsoidal inclusion, and assuming certain conditions on the elasticity tensors, we prove the solvability of the Eshelby equivalent inclusion problem. This justifies a formula for the anisotropic polarization tensor for an ellipsoid

U2 - 10.1177/1081286515588636

DO - 10.1177/1081286515588636

M3 - Article

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SP - 255

EP - 262

JO - Mathematics and Mechanics of Solids

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SN - 1081-2865

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