Nonlocal approach to square lattice dynamics

Abstract

The algorithm is developed to model two-dimensional dynamic processes in a nonlocal square lattice on the basis of the shift operators. The governing discrete equations are obtained for local and nonlocal models. Their dispersion analysis reveals important differences in the dispersion curve and in the sign of the group velocity caused by nonlocality. The continuum limit allows to examine possible auxetic behavior of the material described by the nonlocal discrete model.