Homogenized Stiffnesses of Periodic Fibre-Reinforced Composites
A two-phase fibre-reinforced composite is studied here, whose constituents are isotropic elastic arranged in a hexagonal array. The asymptotic homogenization method, applied to get the overall properties of this composite, yields exact closed-form solutions, which are amenable to a relatively easy computation. Limiting cases of rigid and empty fibres are considered. Hill’s universal relations follow from the formulae. The exact formulae explicitly display Avellaneda and Swart’s micro-structural parameters, which have a physical meaning, and provide formulae for them. A comparison between the hexagonal and square geometries is given.
KeywordsFibre-reinforced composite effective properties homogenization
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