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The mechanical behaviour of αFe-Cu composites is numerically investigated for large plastic deformations under simple tension and compression by three-dimensional (3D) finite element (FE) simulations, where an elasto-viscoplastic material model is applied. Seven types of the aforementioned polycrystals are systematically studied in order to reveal the effects of local events on the global behaviour, in particular, the role of the bcc-fcc-grain interaction. Compared to the axisymmetric 3D model taking the real microstructure as the cross-section in Schneider et al. (2010), the current work uses periodic boundary conditions (PBCs) and a Poisson-Voronoi microstructure to simulate the flow behaviour, the stress in each phase, the crystallographic texture, and the local strain distribution of the Fe-Cu polycrystals. In particular, the crystallographic texture evolution and its dependence upon the phase distribution have been investigated. A quantitative study is performed for the mean value of the local strain in both phases, where a good agreement with the experimental result is shown for the Fe17-Cu83 composite under tension. Furthermore, a comparison is performed between the numerical results presented here and those in Schneider et al. (2010) which uses the same material model for two types of the above mentioned seven polycrystals.