Chapter Fifteen - Elliptic fiber composite with an imperfect interface

Abstract

In this chapter, the local fields and effective transport properties and longitudinal shear stiffness of an elliptic fiber composite with imperfect interface are studied. The complete series solutions are obtained for three most widely used model geometries of a fibrous composite, namely, single inhomogeneity, finite cluster, and a representative unit cell containing multiple elliptic inhomogeneities. Both the periodic and random microstructures are considered. The spring-type and Gurtin–Murdoch imperfect interface are treated in a unified manner. The multipole expansion method combines the superposition principle, the technique of complex potentials, and new results in the theory of special functions. An appropriate choice of the potentials reduces the boundary-value problem to an infinite, well-posed system of linear algebraic equations. The exact formulas for the effective conductivity and longitudinal shear moduli have been derived in the framework of Maxwell and Rayleigh homogenization schemes. A parametric study of the model problem is performed. The obtained accurate, statistically meaningful results display a substantial effect of the inhomogeneity shape and interface elasticity on the local stress concentration and effective elastic behavior of the fibrous nanocomposite.