Abstract Using conformal mapping techniques and the theory of Cauchy singular integral equations, we prove that the internal stresses inside a non-elliptical inhomogeneity can remain uniform despite the presence of… Click to show full abstract
Abstract Using conformal mapping techniques and the theory of Cauchy singular integral equations, we prove that the internal stresses inside a non-elliptical inhomogeneity can remain uniform despite the presence of a nearby finite mode III Dugdale crack in the surrounding matrix which is subjected to a uniform remote loading. Our numerical results indicate that: (i) the existence of the two plastic zones in the vicinity of the “crack tips” significantly influences the non-elliptical shape of the inhomogeneity; (ii) the changes in the two plastic zone length ratios are quite different as the remote loading increases; (iii) at a critical remote loading, one plastic zone vanishes while the other plastic zone occupies practically the entire crack length.
               
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