Lennard–Jones and Yeoh potentials: attenuation of oscillating acoustic waves

Abstract

A combined analytical and numerical study of oscillating elastic waves propagating in a 1D hyperelastic material modeled by the Lennard–Jones hyperelastic potential reveals that, due to different velocities of oscillating waves, the faster parts of the initially harmonic wave overtake the slower moving parts with formation and propagation of multiple shock wave fronts. These shock fronts cause the mechanical energy to decay with the release of heat. Thus, it is shown that in the considered purely mechanical system without viscous or dry friction, the mechanical energy can dissipate. The observed phenomenon opens up the possibility for creating a new type of vibration isolators without viscous or dry friction dampers. The use of the Lennard–Jones hyperelastic potential together with the Yeoh polynomial potential has recently been proposed for modeling different rubber-based cross-linked polymers.