Dissipative Solitary Waves in Granular Crystals

TL;DR

This paper quantitatively characterizes dissipative effects in one-dimensional granular crystals using solitary wave propagation, developing an optimized model that captures dissipation with material-dependent parameters.

Contribution

It introduces a new extended Hertzian model incorporating dissipation via a discrete Laplacian of velocities, validated through experiments and computations.

Findings

Dissipation exponent is consistent across materials

Material-dependent prefactors are identified

Extended model accurately predicts dissipative behavior

Abstract

We provide a quantitative characterization of dissipative effects in one-dimensional granular crystals. We use the propagation of highly nonlinear solitary waves as a diagnostic tool and develop optimization schemes that allow one to compute the relevant exponents and prefactors of the dissipative terms in the equations of motion. We thereby propose a quantitatively-accurate extension of the Hertzian model that encompasses dissipative effects via a discrete Laplacian of the velocities. Experiments and computations with steel, brass, and polytetrafluoroethylene reveal a {\em common} dissipation exponent with a material-dependent prefactor.