Exterior elastic fields of non-elliptical inclusions characterized by Laurent polynomials

In this paper, a new method to analytically carry out the exterior elastic fields of a class of non-elliptical inclusions, i.e., those characterized by Laurent polynomials, is developed. Two complex variable fields, which exactly characterize the Eshelby’s tensor, are explicitly achieved for the hyp...

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Bibliographic Details
Published in:European journal of mechanics, A, Solids A, Solids, 2016-11, Vol.60, p.112-121
Main Authors: Lee, Y.-G., Zou, W.-N.
Format: Article
Language:English
Subjects:
Eshelby’s tensor
Exterior fields
Non-elliptical inclusion
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Summary:In this paper, a new method to analytically carry out the exterior elastic fields of a class of non-elliptical inclusions, i.e., those characterized by Laurent polynomials, is developed. Two complex variable fields, which exactly characterize the Eshelby’s tensor, are explicitly achieved for the hypocycloidal and the quasi-parallelogram inclusions. Numerical examples show that the exterior fields near the inclusion are dominated by the boundary shape, but the fields far away from the inclusion tend to be convergent and can be well approximated by those of its equivalent circular/elliptical inclusion. These solutions are firstly reported, and largely make up for the deficiency in the list of the analytical results of non-elliptical inclusions in 2D isotropic elasticity. •The non-elliptical inclusions characterized by Laurent polynomials are studied.•An analytical method is developed to derive the exterior fields of the inclusions.•The influence ranges of the exterior fields are quantitatively analyzed.
ISSN:0997-7538
1873-7285
DOI:10.1016/j.euromechsol.2016.06.010