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.

Accepted:

Published online:

Xu Wang ^{1};
Peter Schiavone ^{2}

@article{CRMECA_2018__346_9_868_0, 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}, publisher = {Elsevier}, volume = {346}, number = {9}, year = {2018}, doi = {10.1016/j.crme.2018.07.009}, language = {en}, }

TY - JOUR AU - Xu Wang AU - Peter Schiavone TI - Two non-elliptical inhomogeneities with internal uniform stresses interacting with a mode-III crack JO - Comptes Rendus. Mécanique PY - 2018 SP - 868 EP - 876 VL - 346 IS - 9 PB - Elsevier DO - 10.1016/j.crme.2018.07.009 LA - en ID - CRMECA_2018__346_9_868_0 ER -

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/

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