A generalized self-consistent method for nano composites accounting for fiber section shape under antiplane shear

• We present a micromechanics model of nano composites with elliptical fiber.
• We obtain a closed-form solution of the effective antiplane shear modulus.
• We study the effect of fiber section aspect ratio on the elastic properties.

A three-phase confocal elliptical cylinder model with interface stress is proposed. Based on the model, a generalized self-consistent method for the nano composites accounting for fiber section shape under antiplane shear is obtained. By applying the theory of Gurtin–Murdoch surface/interface and the conformal mapping technique, a closed-form solution of the effective antiplane shear modulus is obtained. Several existing solutions can be regarded as the degenerated cases. The major results are: (a) the effective antiplane shear modulus is size dependent when the size of the elliptical section fiber is on the order of nanometer, whereas the interface effect can be neglected when the fiber with large characteristic dimensions; (b) the interface effect of the nano fiber increases with the increase of the fiber section aspect ratio γ from 0 to 1; (c) the higher the fiber volume fraction is, the greater the interface effect is; (d) when the modulus of the fiber is small, the effective modulus of the nano composites depends strongly on the fiber interface effect, whereas when the modulus of the fiber is large, the fiber interface effect has little influence on the effective antiplane shear modulus.