Complex variable method for equivalence of the elliptical inhomogeneity to Eshelby’s elliptical inclusion under remote loading

Two boundary value problems are formulated in this paper. Among them, one is for elliptical inhomogeneity embedded in an infinite matrix and other is for Eshelby’s elliptical eigenstrain inclusion in an infinite matrix. In both problems, the same remote loading is applied. Both problems are solved b...

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Veröffentlicht in:Zeitschrift für angewandte Mathematik und Physik Jg. 70; H. 6; S. 1 - 16
1. Verfasser: Chen, Y. Z.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2019
Springer Nature B.V
Schlagworte:
Boundary value problems
Complex variables
Constants
Elastic properties
Engineering
Equivalence
Inhomogeneity
Mathematical Methods in Physics
Stresses
Theoretical and Applied Mechanics
74A60
Numerical analysis
74B05
Eshelby’s inclusion
Closed-form solution
Inhomogeneity
74B10
74A20
Complex variable method
74A40
ISSN:0044-2275, 1420-9039
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Abstract Two boundary value problems are formulated in this paper. Among them, one is for elliptical inhomogeneity embedded in an infinite matrix and other is for Eshelby’s elliptical eigenstrain inclusion in an infinite matrix. In both problems, the same remote loading is applied. Both problems are solved by using the complex variable method. In the first problem, the solution for stresses in the inhomogeneity depends on the elastic constants on two phases and the remote loading. In addition, the solution for stresses in the Eshelby’s elliptical eigenstrain inclusion depends on the elastic constants for the matrix or the inclusion and the remote loading. It is known that the stress components in the inclusion are uniform for two problems. Letting the stress components in the inclusion for two problems be the same, the equivalent eigenstrains are evaluated, which has a linear relation with respect to the remote loading.
AbstractList Two boundary value problems are formulated in this paper. Among them, one is for elliptical inhomogeneity embedded in an infinite matrix and other is for Eshelby’s elliptical eigenstrain inclusion in an infinite matrix. In both problems, the same remote loading is applied. Both problems are solved by using the complex variable method. In the first problem, the solution for stresses in the inhomogeneity depends on the elastic constants on two phases and the remote loading. In addition, the solution for stresses in the Eshelby’s elliptical eigenstrain inclusion depends on the elastic constants for the matrix or the inclusion and the remote loading. It is known that the stress components in the inclusion are uniform for two problems. Letting the stress components in the inclusion for two problems be the same, the equivalent eigenstrains are evaluated, which has a linear relation with respect to the remote loading.
ArticleNumber 170
Author Chen, Y. Z.
Author_xml – sequence: 1
  givenname: Y. Z.
  surname: Chen
  fullname: Chen, Y. Z.
  email: chens@ujs.edu.cn
  organization: Division of Engineering Mechanics, Jiangsu University
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Cites_doi 10.1098/rspa.1993.0157
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10.1016/j.mechmat.2013.01.005
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Issue 6
Keywords 74A60
Numerical analysis
74B05
Eshelby’s inclusion
Closed-form solution
Inhomogeneity
74B10
74A20
Complex variable method
74A40
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Snippet Two boundary value problems are formulated in this paper. Among them, one is for elliptical inhomogeneity embedded in an infinite matrix and other is for...
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SubjectTerms Boundary value problems
Complex variables
Constants
Elastic properties
Engineering
Equivalence
Inhomogeneity
Mathematical Methods in Physics
Stresses
Theoretical and Applied Mechanics
Title Complex variable method for equivalence of the elliptical inhomogeneity to Eshelby’s elliptical inclusion under remote loading
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