General mean-field homogenization schemes for viscoelastic composites containing multiple phases of coated inclusions

We consider matrix materials reinforced with multiple phases of coated inclusions. All materials are linear viscoelastic. We present general schemes for the prediction of the effective properties based on mean-field homogenization. There are four contributions in this work. First, we present a two-step homogenization procedure in a general setting which besides the usual assumptions of Eshelby-based models, does not suffer any restriction in terms of material properties, aspect ratio or orientation. Second, for a matrix reinforced with coated inclusions, we propose two general homogenization schemes, a two-step method and a two-level recursive scheme. We develop and compare the mathematical expressions obtained by the two schemes and a generalized Mori–Tanaka (M–T) model. Third, for a two-phase composite, either standalone or stemming from two-step or two-level schemes, we use a double-inclusion model based on a closed-form but non-trivial interpolation between M–T and inverse M–T estimates. Fourth, we conduct an extensive validation of the proposed schemes as well as others against experimental data and unit cell finite element simulations for a variety of viscoelastic composite materials. Under severe conditions, the proposed schemes perform much better than other existing homogenization methods.