We attempt to formulate the elasto-plastic constitutive equations which reflect the basic features of the microscopic mechanism of plastic deformation and at the same time remains sufficiently simple to be applicable in FEM solution of the practical problems. The constitutive equations are based on a simplified verison of polycrystal plasticity. In modeling of the properties of single crystal grains of the polycrystal attention is paid to active and latent hardenings, and especially to the Bauschinger effect. The stress response along three sets of typical examples of complex deformation histories are predicted and compared with precise data of tension-torsion tests. The predictions are in good agreement with the observed behavior.

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