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Asymptotic evaluation of effective complex moduli of fibre‐reinforced viscoelastic composite materials
Author(s) -
Andrianov I.,
Danishevs'kyy V.,
Weichert D.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310062
Subject(s) - moduli , asymptotic homogenization , homogenization (climate) , viscoelasticity , asymptotic expansion , boundary value problem , mathematical analysis , mathematics , composite number , materials science , composite material , physics , algorithm , biodiversity , ecology , quantum mechanics , biology
We propose an asymptotic approach for the evaluation of effective complex moduli of viscoelastic fibre‐reinforced composite materials. Our method is based on the homogenization technique. We start with a non‐trivial expansion of the input plane‐strain boundary value problem by ratios of visco‐elastic constants. This allows to simplify the governing equations to forms analogous to the complex transport problem. Then we apply the asymptotic homogenization method, coming from the original problem on multi‐connected domain to the cell problem, defined on a unit cell of the periodic structure. For the analytical solution of the cell problem we apply the boundary perturbation technique, the asymptotic expansion by a distance between two neighbouring fibres and the method of two‐point Padé approximants. As results we derive uniform analytical representations for effective complex moduli, valid for all values of the components volume fractions and properties.