Effective anti-plane moduli of couple stress composites containing elliptic multi-coated nano-fibers with interfacial damage and variational bounds

Prediction of the anti-plane moduli of solids consisting of a given distribution of unidirectionally aligned elliptic multi-coated fibers with interfacial damage is the focus of this paper. The fibers and their coating layers may be in the order of nano or micro scales. All the constituent phases of the composite are supposed to be described in terms of couple stress elasticity. Accordingly, the bounds for the overall shear moduli of the aforementioned composites are provided by employing the principles of minimum potential and complementary energies. Certain subtleties associated with the elliptic multi-coated fibers for three cases of pure sliding (completely damaged), imperfect (partially damaged), and perfect (undamaged) interface conditions will be discussed. The inherent anisotropy introduced due to the ellipse geometry of the fibers' cross-sections is addressed. The effects of the ellipse aspect ratio as well as its size, interfacial damage, and rigidity on the effective anti-plane moduli of such composites will be examined.