Continuum model of a one-dimensional lattice of metamaterials

Abstract

The continuum model of a one-dimensional crystal lattice of a metamaterial is studied in this paper. First, the dispersive relation of a lattice wave in a one-dimensional crystal lattice of metamaterial is established and compared with that of the classic material. Then, the continuous medium modeling of the metamaterial is studied. It leads to the classical continuum model, the strain gradient continuum model, and the nonlocal gradient continuum model based on different assumptions. The disadvantages of the classic continuum model and the gradient continuum model are discussed. The nonlocal gradient continuum model is derived based on the nonlocal assumption of a continuous displacement field. The stability of dispersive curves is guaranteed, and the conceptions of negative mass and infinite mass are also avoided. The dispersive curves which correspond to the three kinds of models are compared with those of a discrete crystal lattice of metamaterial. The disadvantages of the classic continuum model and the gradient continuum model and the appropriate selection of a nonlocal parameter in the nonlocal gradient continuum model are discussed based on the numerical results.