Three-phase elliptical inclusions with internal uniform hydrostatic stresses

For an elastic inclusion embedded within an elastic matrix, it is the inter facial stresses that control mechanical integrity of the inclusion/matrix s ystem. To eliminate the stress peaks at the interface, the uniform hydrosta tic stress state within the inclusion is of particular interest because it achieves both uniform normal stress and vanishing tangential stress along t he entire interface. Motivated by practical significance of interphase laye r, the present paper studies the internal stress state of a three-phase ell iptic inclusion which is bonded to an infinite matrix through an intermedia te elastic layer. What is essential is that the interfaces of the three-pha se elliptic inclusion considered are two confocal ellipses. A simple condit ion is found that ensures that the internal stress state within the ellipti c inclusion is uniform and hydrostatic. For given remote stresses and mater ial parameters, this condition gives a simple relationship between the thic kness of the interphase layer and the aspect ratio of the elliptic inclusio n. The exact stress field is obtained in elementary form when this conditio n is met. In particular, the hoop stress in the interphase layer is found t o be uniform along the entire interphase/inclusion interface. It is believe d that the availability of this condition relies on the confocal character of the elliptic interfaces. (C) 1999 Elsevier Science Ltd. All rights reser ved.