Two-dimensional problems of the anisotropic elastic solid with an elliptic inclusion

Chyanbin Hwu, T. C.T. Ting

Research output: Contribution to journalArticle

79 Citations (Scopus)

Abstract

The two-dimensional elliptic inclusion problems have been widely studied and many important results have been obtained. Nevertheless, explicit real-form solutions for the stress inside the inclusion and in the matrix around the inclusion are available only for special anisotropic elastic materials. Solutions for which the inclusion as well as the matrix are of general anisotropic elastic materials are presented in this paper using the Stroh formalism. New identities which relate Stroh's complex eigenvalues and eigenvectors to real quantities obtainable directly from the elastic constants are derived, through which several solutions are expressed in real form. Among the real-form solutions obtained are the stress inside the inclusion, the hoop stress in the matrix around the interface boundary and the rotation of the inclusion. The special cases in which the inclusion is rigid or a void are also studied. For the elliptic hole subject to a uniform tensile stress perpendicular to the major axis of the elliptic hole, the stress-concentration factor at the end points of the major axis of the hole has a simple expression resembling the well-known classical result 1+ 2(a/b) for isotropic materials where 2a, 2b are, respectively, the major and minor axes of the elliptic hole. The hoop stress at the end points of the minor axis is independent of the shape of the elliptic hole.

Original languageEnglish
Pages (from-to)553-572
Number of pages20
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume42
Issue number4
DOIs
Publication statusPublished - 1989 Nov 1

Fingerprint

Inclusion
inclusions
hoops
Anisotropic Material
Elastic Material
End point
Minor
matrices
Stroh Formalism
Stress Concentration Factor
stress concentration
Elastic Constants
Eigenvalues and Eigenvectors
Elastic constants
Voids
tensile stress
Eigenvalues and eigenfunctions
Tensile stress
Perpendicular
Stress concentration

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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Two-dimensional problems of the anisotropic elastic solid with an elliptic inclusion. / Hwu, Chyanbin; Ting, T. C.T.

In: Quarterly Journal of Mechanics and Applied Mathematics, Vol. 42, No. 4, 01.11.1989, p. 553-572.

Research output: Contribution to journalArticle

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