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In the second part of the paper, under the assumption that periodically distributed cracks in the internal layer can open or close according to Signorini's conditions, the homogenization procedure is carried out. With the help of two types of scaling, three effective models of the laminate with smeared-out cracks are proposed: a model of moderately thick laminates with cracks of high density, a model for thin laminates with cracks of arbitrary density, and for thin laminates with densely distributed cracks. The models derived show nonlinear and hyperelastic features, the relevant hyperelastic potentials being convex or strictly convex. The homogenized constitutive relations assume Kachanov's form in which the damage moduli tensor is uniquely determined.