Hybrid hierarchical homogenization theory for unidirectional CNTs-coated fuzzy fiber composites undergoing inelastic deformations

Abstract A new hybrid homogenization approach is proposed for simulating the homogenized and local response of unidirectional fuzzy fiber nanocomposites undergoing inelastic deformations. Fuzzy fiber composites are hierarchical reinforcing structures where the fibers coated with radially aligned carbon nanotubes (CNTs) are embedded in the matrix. In this spirit, the fuzzy fiber composites are modeled as a three-scale medium. At the microscale, the CNTs-reinforced matrix is homogenized as nanocomposite interphase (NCP) attached to the main fiber via the asymptotic expansion homogenization (AEH). At the mesoscale, an intermediate equivalent fiber that substitutes for the NCP and the main fiber is constructed using the composite cylinder assemblage (CCA) and the transformation field analysis (TFA) techniques. At the macroscale, homogenization of the equivalent fiber and the surrounding matrix is handled by AEH which yields the effective response of the whole fuzzy fiber composites. The new technique facilitates accurate and efficient studies of the inelastic deformation mechanisms of periodic fuzzy fiber arrays with single or multiple inclusions under biaxial and triaxial loading conditions, eliminating exhausting interphase mesh discretizations encountered in the classical full-field homogenization. An added advantage is that the proposed theory captures the fiber-fiber interaction neglected in the classical CCA-TFA, an issue that leads to the exceptionally stiff post-yielding stress-strain response common in the mean-field micromechanics approaches.