Homogenization of viscoelastic composites with fibres of diamond-shaped cross-section

The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic composite materials with fibres of diamond-shaped cross-section. The Correspondence principle allows transforming the governing boundary value problems to quasistatic ones. Then, we apply the homogenization approach. For solving the cell problem for small volume fractions, the boundary shape perturbation procedure and the composite cylinder assemblage model are used. For a volume fraction equal to 1/2, we use the Dykhne–Keller–Mendelson formula. Matching of limit solutions by two-point Padé approximants gives a formula for the effective properties valid for any volume fraction from the interval [0, 0.5].