Auxeticity from nonlinear vibrational modes

It is demonstrated that the large-amplitude, short-wavelength vibrational modes excited in the lattice can change its elastic properties due to physical and/or geometric nonlinearity of the lattice bonds. Depending on the symmetry of the vibrational mode the symmetry of the elastic properties of the lattice can also change. Using as an example the two-dimensional honeycomb structure with beta-FPU pairwise interparticle interactions, we demonstrate that the excitation of a large-amplitude vibrational mode in combination with equiaxial tensile strain can change the sign of the Poisson's ratio from positive to negative, thus leading to the auxetic property of the lattice. It is shown that the considered lattice supports discrete breathers, i.e., spatially localized nonlinear vibrational modes. The excitation of the discrete breathers as a result of the modulational instability of the extended short-wavelength modes is analyzed. Our results contribute to the understanding of the relation between the elastic properties and nonlinear dynamics of the lattices of interacting particles. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim