Two non-elliptical inhomogeneities with internal uniform stresses interacting with a mode-III crack

Xu Wang; Peter Schiavone

doi:10.1016/j.crme.2018.07.009

Two non-elliptical inhomogeneities with internal uniform stresses interacting with a mode-III crack

Xu Wang ¹; Peter Schiavone ²

¹ School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China
² Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, Alberta T6G 1H9, Canada

Comptes Rendus. Mécanique, Volume 346 (2018) no. 9, pp. 868-876.

Abstract

We use the method of Green's functions to analyze an inverse problem in which we aim to identify the shapes of two non-elliptical elastic inhomogeneities, embedded in an infinite matrix subjected to uniform remote stress, which enclose uniform stress distributions despite their interaction with a finite mode-III crack. The problem is reduced to an equivalent Cauchy singular integral equation, which is solved numerically using the Gauss–Chebyshev integration formula. The shapes of the two inhomogeneities and the corresponding location of the crack can then be determined by identifying a conformal mapping composed in part of a real density function obtained from the solution of the aforementioned singular integral equation. Several examples are given to demonstrate the solution.

Received: 2018-05-22
Accepted: 2018-07-11
Published online: 2018-07-24

DOI: 10.1016/j.crme.2018.07.009

Keywords: Two non-elliptical inhomogeneities, Mode-III crack, Conformal mapping, Cauchy singular integral equation

Author's affiliations:

Xu Wang ¹; Peter Schiavone ²

¹ School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China
² Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, Alberta T6G 1H9, Canada

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     author = {Xu Wang and Peter Schiavone},
     title = {Two non-elliptical inhomogeneities with internal uniform stresses interacting with a {mode-III} crack},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {868--876},
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     language = {en},
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Xu Wang; Peter Schiavone. Two non-elliptical inhomogeneities with internal uniform stresses interacting with a mode-III crack. Comptes Rendus. Mécanique, Volume 346 (2018) no. 9, pp. 868-876. doi : 10.1016/j.crme.2018.07.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.07.009/

References
Cited by

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