12. Wave Propagation in Auxetic Solids

This chapter on wave propagation forms the second part of the elastodynamics of auxetic solids. Special emphasis is placed on the effect of negative Poisson’s ratio towards the velocity of longitudinal waves in prismatic bars c ₀, the velocity of plane waves of dilatation c ₁, the velocities of plane waves of distortion and torsional waves c ₂ and Rayleigh waves c ₃. A set of dimensionless wave velocities is introduced to facilitate the plotting of non-dimensional wave velocity in both the auxetic and conventional regions. As an alternative way of non-dimensionalization, all wave velocities can be normalized against the wave velocity for plane wave of dilatation. It is herein shown that some of the velocities of different types of waves are equal at non-positive Poisson’s ratio, i.e. c ₀ = c ₁ at v = 0, c ₀ = c ₂ at v = −0.5 and c ₀ = c ₃ at v = −0.733. In the case of solitary waves in plates, Kołat et al. (J Non-Cryst Solids 356:2001–2009, 2010) showed that the amplitudes and velocities are approximately related to the magnitude of the Poisson’s ratio, while the width of the initial pulse is related to the number of propagating solitary pulses.