Effective behaviour of viscoelastic polycrystals and associated local fields inferred from homogenization: Incremental collocation approach

We present the development of an incremental homogenization method to estimate the effective behaviour of linear viscoelastic anisotropic heterogeneous media. This procedure is based on the equivalence between the collocation method and an internal variables approach, shown by Mandel (1966) and Ricaud and Masson (2009) for the case of two-phase isotropic material. The new formulation is then illustrated for polycristalline materials. The derived estimates are in good concordance with reference ones obtained by numerical full-field computations (FFT) on representative microstructure.