On the effective properties of composites made of viscoelastic constituents

We show that the effective behavior of composites made of viscoelastic rheological constituents can be modeled by a rheology of which the internal properties can be quasi-analytically determined from the volume fractions and rheological properties of the phases. A three-chain generalized Maxwell rheology can be used to model the behavior of a matrix-inclusion system of which both matrix and inclusions are described by the Zener rheology. Validations against exact results of the inverse Laplace–Carson are realized for a large range of the contrast between the phases. The developed solutions cover the existent solutions of the case of Maxwellian constituents.