Optimal design of a three-phase elliptical inclusion with an orthotropic interphase layer

We study the internal stress field inside an elliptical inclusion bonded to an infinite matrix through an interphase layer when the matrix is subjected to remote uniform in-plane stresses. Both the inclusion and the matrix are isotropic, whilst the interphase layer is occupied by a mathematically degenerate orthotropic material. The resulting inner and outer elliptical interfaces, which are generally non-confocal, have a common center at the origin and their principal axes are along the two coordinate axes. We show that the internal stress field can be uniform when 1) the anisotropic and thickness parameters of the interphase layer are chosen for given principal axes of the two interfaces; and 2) a condition is satisfied relating the remote stresses to the anisotropic, geometric and material parameters of the overall composite.