Recursive multiscale homogenization of multiphysics behavior of fuzzy fiber composites reinforced by hollow carbon nanotubes

Abstract

Fuzzy fibers are fibers enhanced in terms of multiphysics properties with radially oriented carbon nanotubes grown on their surface through the chemical deposition process. For the first time, this paper attempts to present two generalized zeroth-order asymptotic homogenization schemes aimed at identifying the homogenized and local response of fuzzy fiber-reinforced composites, accounting for both multiphysics piezoelectric effect and cylindrically orthotropic material behavior. The unit cell problems are solved using the multiphysics finite-volume and the multiphysics finite-element techniques, respectively. While the former approach is based on the strong form solution of the equilibrium and conservation equations in an averaged sense in the discretized domain, the latter is based on the minimization of the total potential energy over the entire unit cell. A recursive multiscale analysis algorithm is developed wherein homogenized moduli (or local fields) obtained from the homogenization (or localization) analysis at one scale are utilized in the calculation of homogenized moduli (or local fields) at the next scale. Numerical examples indicate that good agreement of the homogenized properties and local field distributions generated by the two approaches is observed hence confirming the accuracy of the new homogenization methods for fuzzy fiber composites with multiphysics behaviors.