Mechanisms for impulsive energy dissipation and small scale effects in micro-granular media

TL;DR

This paper investigates impulse response and energy dissipation mechanisms in micro-granular chains, revealing complex dynamics driven by surface forces that differ significantly from macro-scale behavior.

Contribution

It introduces a detailed analytical model for micro-granular interactions including hysteresis and adhesive effects, uncovering novel scale-dependent dynamical phenomena.

Findings

Enhanced energy dissipation linked to cluster formation rate

Robustness of phenomena across feasible conditions

Universal relation between re-clustering rate and damping

Abstract

We study impulse response in 1-D homogeneous micro-granular chains on a linear elastic substrate. Micro-granular interactions are analytically described by the Schwarz contact model which includes nonlinear compressive as well as snap-to/from-contact adhesive effects forming a hysteretic loop in the force deformation relationship. We observe complex transient dynamics, including disintegration of solitary pulses, local clustering and low- to high-frequency energy transfers resulting in enhanced energy dissipation. We study in detail the underlying dynamics of cluster formation in the impulsively loaded medium, and relate enhanced energy dissipation to the rate of cluster formation. These unusual and interesting dynamical phenomena are shown to be robust over a range of physically feasible conditions, and are solely scale effects, since they are attributed to surface forces, which have no effect at the macro-scale. We establish a universal relation between the re-clustering rate and the effective damping in these systems. Our findings demonstrate that scale effects generating new nonlinear features can drastically affect the dynamics and acoustics of micro-granular materials.