Elastic unidirectional cylindrically-symmetric-fiber composites with general radially-variable anisotropic coatings

Differential substitution/coating schemes have been developed to construct various explicit expressions or determining initial-valued ordinary differential equations for the effective elastic cylindrically-symmetric fiber composite problems, which include those with general radially-variable anisotropic coatings. The schemes are stated from Hashin–Rosen-type multi-coated cylinder assemblage micro-geometry and Hill substitution formulae, with differential constructions for generalizations. When the volume proportion of the outermost cylindrical shell increases toward 1, one obtains the respective dilute solutions for the compound inhomogeneities suspended in a major matrix phase. Illustrating numerical comparisons of the predictions from the model and those of finite element simulations for the geometrically-close hexagonal arrays of anisotropic-coating cylinders, with the material data taken from the literature, are presented. •Elastic cylindrically-symmetric fibre composites are considered.•The fibres have general radially-variable anisotropic coatings.•Differential substitution/coating schemes are developed for the effective moduli.•The schemes are stated from multi-coated cylinder assemblage micro-geometry.•Hill substitution formulae with differential constructions for generalizations.•Illustrating numerical comparisons of the model and some finite element simulations.