Auxetic behavior of crystals from rotational degrees of freedom

We review the results obtained for the 2D microscopic model of crystal having finite size particles proposed by Ishibashi and Iwata and later generalized in order to take into account deformability of particles. We focus on the elastic properties of the discrete model and also discuss various continuum analogues to the model, including the multifield continuum approximation. Several new results are reported, e.g., we describe the conditions of thermodynamic stability of the model and study the variation of Poisson ratio of the model as the function of model parameters in single-crystal and poly-crystal states. The role of the rotational degrees of freedom pertaining to the finite size particles is highlighted. Particularly we demonstrate that the microscopic rotations are responsible for auxetic behavior (i.e., exhibiting negative Poisson ratio) of the macroscopically isotropic poly-crystal.