Three-phase elliptical inclusions with internal uniform hydrostatic stress resultants in isotropic laminated plates

• Design a three-phase elliptical inclusion with internal uniform hydrostatic stress resultants.
• Find two conditions for internal uniform hydrostatic stress resultants within the inclusion.
• Find constant hoop stress resultants along the interphase/inclusion interface.

Within the framework of the Kirchhoff-Love isotropic and laminated plate theory, we study the internal stress resultants of a three-phase elliptical inclusion which is bonded to an infinite matrix through an interphase layer. The interfaces of the three-phase inclusion are two confocal ellipses. Two conditions are found to ensure that the internal stress resultants within the elliptical inclusion are uniform and hydrostatic. For given material and geometric parameters of the composite system, the two conditions can be interpreted as restrictions on the remote uniform membrane stress resultants and bending moments. When these two conditions are met, the hoop membrane stress resultant and hoop bending moment in the interphase layer are found to be uniform along the entire interphase/inclusion interface.