Inclusions of uniform eigenstrains and constant or other stress dependence

It is shown that the Eshelby inclusions, that is inclusions of uniform eige nstrains and constant eigenstress, form in three dimensions a connected nin e-dimensional manifold, and, as a consequence, the only perturbations of an ellipsoid that preserve the Eshelby property are into another ellipsoid. T he method is illustrated in both two and three dimensions, and can be also used to treat similar questions of other than constant dependence of the st ress.