Computation of the size-dependent elastic moduli of nano-fibrous and nano-porous composites by FFT

The present work is concerned with nanocomposites consisting of a matrix containing unidirectional nanofibers or nanopores. In such a nanocomposite, due to the exceptionally high surface-to-volume ratio of a nanofiber or nanopore, the fiber-matrix interface or pore surface stresses, which are usually neglected in determining the effective properties of classical fibrous and porous composites, have a non-negligible effect on the effective properties at the macroscopic scale. The purpose of this work is first to compute the effective elastic moduli of unidirectional nano-fibrous and nano-porous composites accounting for interface/surface stresses and second to study the dependencies of these effective moduli on the size, shape and distribution of nanofibers and nanopores in the matrix. To achieve this twofold objective, a coherent interface/surface model is adopted for the nanofiber-matrix interface and pore surface, and a numerical method based on the fast Fourier transform (FFT) is elaborated. The numerical results obtained for the effective elastic moduli of fibrous and porous nanocomposites are compared with the analytical estimates obtained from the generalized self-consistent model (GSCM), with some relevant bounds and with the corresponding numerical results provided by the extended finite element method (XFEM)/level-set approach.