Effective elastic properties of nanofiber-reinforced composites with Steigmann-Ogden interface effect

Abstract

Closed-form bound and exact solutions to the five independent effective elastic constants of nanofiber-reinforced composites with Steigmann-Ogden interface effect are obtained in this work. Four effective elastic constants (ke, ne, le, and pe) have identical bounds and depend only on the stretching stiffness of the interface, while the fifth effective elastic constant (me) has distinct bounds and depends on both the stretching and bending stiffness of the interface. Compared with Maxwell-type approximation formula in the semi-analytical form of Fourier series in the literature, the exact solution to the fifth effective elastic constant (me) is obtained in closed-form by generalized self-consistent method in this work. Both exact solutions are validated to fall inside the bound solutions. Moreover, limit analysis discloses that the bounds of the four effective elastic constants (ke, ne, le, and pe) of pure nanofibers coincide and deviate from the bulk elastic constants of the fiber in the classical case, but the bounds of the fifth effective elastic constant (me) of pure nanofibers are unexpected to be distinct in contrast to the four effective elastic constants (ke, ne, le, and pe) of pure nanofibers or all the effective elastic constants of conventional composites.