Longitudinal shear of a composite with elliptic nanofibers: Local stresses and effective stiffness

The paper addresses calculation of the local elastic fields and effective longitudinal shear stiffness of elliptic nano fiber composite with Gurtin-Murdoch interface. The series solutions are obtained for three most widely used model geometries of fibrous composite, namely, single inclusion, finite cluster of inclusions and a representative unit cell. Both the periodic and random microstructures are considered. The developed analytical method combines the superposition principle, multipole expansion and the technique of complex potentials. For the effective stiffness evaluation, both the Maxwell's and Rayleigh's approaches have been implemented. In the latter case, the exact formulas for the effective elastic moduli have been derived by analytical averaging the local strain and stress fields. The results show substantial effect of the inclusion shape and interface elasticity on the local stress concentration and effective elastic behavior of fibrous nano composite.