Computation of the relaxation effective moduli for fibrous viscoelastic composites using the asymptotic homogenization method

A two-phase parallel fibre-reinforced periodic viscoelastic composite is considered wherein the constituents are isotropy. Simple closed-form formulae are obtained for the effective properties of composites with square and hexagonal cells by means of the two-scale asymptotic homogenization method. The computation of the effective properties of non-ageing linear viscoelastic composites with periodic structure containing long cylindrical fibres of circular cross-section is performed. The local problems and overall viscoelastic properties are obtained in explicit form using the elastic-viscoelastic correspondence principle and assuming perfect contact conditions at the interface between constituents. Comparison with different viscoelastic models allowing explicit inverse Laplace transforms such as, traditional Maxwell and Kelvin models and Rabotnov-Scott Blair fractional exponential model are shown. The analytical results are verified by comparison with computational ones.