Abstract
It is shown that the Eshelby inclusions, that is inclusions of uniform eigenstrains and constant eigenstress, form in three dimensions a connected nine-dimensional manifold, and, as a consequence, the only perturbations of an ellipsoid that preserve the Eshelby property are into another ellipsoid. The 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 stress.
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