Inclusions with constant eigenstress

The Eshelby conjecture, stating that the only inclusions of constant eigenstrain that may sustain constant eigenstress are ellipsoidal shaped, is being considered by a geometric approach. It is established that the class of shapes that may sustain constant eigenstresses form a 9-dimensional manifold embedded in the space of all possible shapes. In particular, it is shown that the only infinitesimal perturbations of an ellipsoidal inclusion that preserve the constancy of eigenstresses are those that perturb the ellipsoid into another ellipsoid. (C) 1998 Elsevier Science Ltd. All rights reserved.