Model reduction by mean-field homogenization in viscoelastic composites. II. Application to rigidly reinforced solids

The mean-field homogenization scheme proposed by Lahellec & Suquet (2007 Int. J. Solids Struct. 44, 507-529 (doi:10.1016/j.ijsolstr.2006.04.038)) and revisited in a companion paper (Idiart et al. 2020 Proc. R. Soc. A 20200407 (doi:10.1098/rspa.2020.0407)) is applied to random mixtures of a viscoelastic solid phase and a rigid phase. Two classes of mixtures with different microstructural arrangements are considered. In the first class the rigid phase is dispersed within the continuous viscoelastic phase in such a way that the elastic moduli of the mixture are given exactly by the Hashin-Shtrikman formalism. In the second class, both phases are intertwined in such a way that the elastic moduli of the mixture are given exactly by the Self-Consistent formalism. Results are reported for specimens subject to various complex deformation programmes. The scheme is found to improve on earlier approximations of common use and even recover exact results under several circumstances. However, it can also generate highly inaccurate predictions as a result of the loss of convexity of the free-energy density. An auspicious procedure to partially circumvent this issue is advanced.