Splitting of Strain Solitons upon Their Interaction in the Auxetic Rod

Abstract

The problem of longitudinal wave propagation in a rod made from an auxetic material is considered. It is shown that a negative Poisson's ratio leads to a qualitatively different (anomalous) dispersion behavior of linear waves. Accounting for geometric and physical elastic nonlinearities leads to the possibility of generating in a rod of stationary strain waves of a substantially non-sinusoidal profile---solitons and their periodic analogues. By means of numerical simulation it is shown that qualitatively different scenarios of interaction of solitons depend on the relative collision velocity.