Inclusions with constant eigenstress

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