We discuss a phenomenological model in 2d for elastic materials with stiff heterogeneities arranged into a periodic checkerboard-type pattern. The main task is to determine the effective deformation behavior by characterizing the weak Sobolev limits of deformation maps whose gradients are locally close to rotations on the stiff components. We rigorously show that such composites exhibit an auxetic deformation behavior and can thus be considered mechanical metamaterials with a negative Poisson ratio. The proof requires, in particular, a new quantitative rigidity result for non-connected domains. Finally, we present a full homogenization result via Gamma-convergence under the assumption of physical growth conditions. This is joint work with Wolf-Patrick Düll (Universität Stuttgart) and Dominik Engl (KU Eichstätt-Ingolstadt).