Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in anti-plane shear

Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby... We use conformal mapping techniques to examine the uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in an elastic matrix subjected to remote uniform stresses in anti-plane shear. We show that for a prescribed set of two real loading and two complex geometric parameters, it is possible to determine the single unknown complex coefficient in the mapping function and the (unique) shape of the corresponding inhomogeneity enclosing internal uniform stresses. Our results indicate that the shape of the inhomogeneity depends on the circular Eshelby inclusion whereas the uniform stress field inside the inhomogeneity does not. Finally, we note that the influence of the circular Eshelby inclusion in the vicinity of the inhomogeneity allows for the possibility of a sharp corner on the boundary of the inhomogeneity. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive of Applied Mechanics Springer Journals

Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in anti-plane shear

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Engineering; Theoretical and Applied Mechanics; Classical Mechanics
ISSN
0939-1533
eISSN
1432-0681
D.O.I.
10.1007/s00419-018-1401-y
Publisher site
See Article on Publisher Site

Abstract

We use conformal mapping techniques to examine the uniformity of stresses inside a non-elliptical inhomogeneity interacting with a circular Eshelby inclusion in an elastic matrix subjected to remote uniform stresses in anti-plane shear. We show that for a prescribed set of two real loading and two complex geometric parameters, it is possible to determine the single unknown complex coefficient in the mapping function and the (unique) shape of the corresponding inhomogeneity enclosing internal uniform stresses. Our results indicate that the shape of the inhomogeneity depends on the circular Eshelby inclusion whereas the uniform stress field inside the inhomogeneity does not. Finally, we note that the influence of the circular Eshelby inclusion in the vicinity of the inhomogeneity allows for the possibility of a sharp corner on the boundary of the inhomogeneity.

Journal

Archive of Applied MechanicsSpringer Journals

Published: May 31, 2018

References

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