2013/03/09 by Michel Destrade, Giuseppe Saccomandi · 1 citation
Physics and Astronomy · #cond-mat.soft #nlin.PS
paper · pdf · doi:10.1016/j.wavemoti.2007.07.002
published as Wave Motion, 45 (2008) 325-336
arxiv created 2013/03/09 · arxiv updated 2013/03/12
We present a phenomenological approach to dispersion in nonlinear elasticity. A simple, thermomechanically sound, constitutive model is proposed to describe the (non-dissipative) properties of a hyperelastic dispersive solid, without recourse to a microstructure or a special geometry. As a result, nonlinear and dispersive waves can travel in the bulk of such solids, and special waves emerge, some classic (periodic waves or pulse solitary waves of infinite extend), some exotic (kink or pulse waves of compact support). We show that for incompressible dispersive power-law solids and forth-order elasticity solids, solitary waves can however only exist in the case of linear transverse polarization. We also study the influence of pre-stretch and hardening. We provide links with other (quasi-continuum, asymptotic) theories; in particular, an appropriate asymptotic multiscale expansion specializes our exact equations of motion to the vectorial MKdV equation, for any hyperelastic material.