Micromechanical schemes based on the discrete homogenization method are developed to predict the effective mechanical properties of 3D dry textiles, including the bending moduli, and accounting for internal scale effects by the consideration of additional rotational degrees of freedom at the mesoscopic level. The unit of repeat identified for a given interlock is represented as a set of structural beam like elements that defines the representative volume element (RVE), with periodicity boundary conditions. The complex interactions between yarns within the RVE lead to a non affine motion of the yarns responsible for internal scale effects, which are accounted for by a micropolar anisotropic continuum obtained by the discrete homogenization method. The Cosserat moduli are identified together with the associated internal bending lengths versus the microstructural geometrical and mechanical parameters that characterize the internal organization of yarns within each preform. A satisfactory agreement is obtained between the effective classical and nonclassical moduli predicted by homogenization and those computed by finite element simulations.