A coated rigid elliptical inclusion loaded by a couple in the presence of uniform interfacial and hoop stresses

We consider a confocally coated rigid elliptical inclusion, loaded by a couple and introduced into a remote uniform stress field. We show that uniform interfacial and hoop stresses along the inclusion-coating interface can be achieved when the two remote normal stresses and the remote shear stress each satisfy certain conditions. Our analysis indicates that: (i) the uniform interfacial tangential stress depends only on the area of the inclusion and the moment of the couple; (ii) the rigid-body rotation of the rigid inclusion depends only on the area of the inclusion, the coating thickness, the shear moduli of the composite and the moment of the couple; (iii) for given remote normal stresses and material parameters, the coating thickness and the aspect ratio of the inclusion are required to satisfy a particular relationship; (iv) for prescribed remote shear stress, moment and given material parameters, the coating thickness, the size and aspect ratio of the inclusion are also related. Finally, a harmonic rigid inclusion emerges as a special case if the coating and the matrix have identical elastic properties.