Transmission and reflection of strongly nonlinear solitary waves at granular interfaces

TL;DR

This paper investigates how strongly nonlinear solitary waves interact with granular interfaces, developing a discrete model to predict transmitted wave amplitudes and refraction angles, validated by simulations, revealing an analogue of Snell's law in granular media.

Contribution

The authors introduce a novel discrete model treating solitary waves as quasiparticles to predict wave behavior at granular interfaces, extending it to oblique angles and revealing a Snell's law analogue.

Findings

Model accurately predicts transmitted wave amplitudes.

Refraction and reflection follow an analogue of Snell's law.

Validated findings with numerical simulations.

Abstract

The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-cohesive granular lattices displays rich behaviour, characterized by the breakdown of continuum equations of motion in the vicinity of the interface. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy and linear momentum conserving) discrete model to predict the amplitudes of the transmitted solitary waves generated when an incident solitary wave front, parallel to the interface, moves from a denser to a lighter granular hexagonal lattice. Our findings are corroborated with simulations. We then successfully extend this model to oblique interfaces, where we find that the angle of refraction and reflection of a solitary wave follows, below a critical value, an analogue of Snell's law in which the solitary wave speed replaces the speed of sound, which is zero in the sonic vacuum.