A circular Eshelby inclusion interacting with a coated non-elliptical inhomogeneity with internal uniform stresses in anti-plane shear

Abstract

We consider a coated non-elliptical inhomogeneity interacting with a nearby circular Eshelby inclusion inside an infinite elastic matrix subjected to anti-plane shear deformations and uniform remote stresses. Using conformal mapping techniques, we prove that despite the presence of the Eshelby inclusion, it is possible to design the system to achieve a uniform stress distribution inside the inhomogeneity. The conformal mapping function used in the analysis is constructed to give rise to an infinite number of first-order poles inside the unit circle in the image plane in order to satisfy all of the conditions required by the complex potential in the matrix. Our analysis indicates that the inhomogeneity's internal uniform stress field is unaffected by the Eshelby inclusion whereas the non-elliptical shape of the coated inhomogeneity is attributed solely to the nearby Eshelby inclusion.