Three-phase anisotropic elliptical inclusions with internal uniform in-plane and anti-plane stresses

We study the stress field of a three-phase composite in which an internal elliptical inclusion is bonded to the surrounding matrix through an interphase layer. The linearly elastic materials occupying both the inclusion and the matrix are generally anisotropic, whereas the interphase layer is made of an isotropic elastic material. The two interfaces of the three-phase composite are confocal ellipses. Two conditions are found that ensure that the internal in-plane and anti-plane stress field is uniform. When these conditions are met, the mean stress within the isotropic interphase layer is also uniform. A real form expression of the internal uniform stress field inside the inclusion is derived. Several examples are presented to demonstrate and validate the obtained results.