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Finite element simulations on fibrous composites with nonlinear viscoelastic response of the matrix phase are performed to explain why so called two-point averaging schemes may fail to deliver a realistic macroscopic response. Nevertheless, the potential of two-point averaging schemes (the overall response estimated in terms of localized averages of a two-phase composite medium) has been put forward in number of studies either in its original format or modified to overcome the inherited stiffness of classical ”elastic” localization rules. However, when the material model and geometry of the microstructure promote the formation of shear bands, none of the existing two-point averaging schemes will provide an adequate macroscopic response, since they all fail to capture the above phenomenon. Several examples are presented here to support this statement.

On Adequacy of Two-point Averaging Schemes for Composites with Nonlinear Viscoelastic Phases