Complex variable method for equivalence of the elliptical inhomogeneity to Eshelby’s elliptical inclusion under remote loading
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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.
KeywordsInhomogeneity Eshelby’s inclusion Complex variable method Closed-form solution Numerical analysis
Mathematics Subject Classification74A20 74A40 74A60 74B05 74B10