On the absence of the Eshelby property for slender non-ellipsoidal inhomogeneities

he method of matched asymptotic expansions is applied to construct an asymptotic model for the Eshelby inhomogeneity problem in the case of a slender sufficiently rigid inhomogeneity. On the basis of the obtained asymptotic model, it is shown that the only infinitesimal perturbations of the elongated ellipsoid that preserve constancy of stresses inside the inhomogeneity are those into another elongated ellipsoid.