Elastic Energy, Fluctuations and Temperature for Granular Materials

TL;DR

This paper investigates the energy distribution and fluctuations in sheared granular materials, proposing a generalized granular temperature that smoothly transitions between kinetic and elastic energy regimes, aligning with equilibrium statistical mechanics.

Contribution

It introduces a generalized granular temperature incorporating elastic and kinetic energies, providing a unified description of energy fluctuations in granular materials.

Findings

Elastic energy dominates at high pressure ratios.

Energy fluctuations are primarily elastic in certain regimes.

The generalized temperature aligns with equilibrium statistical mechanics.

Abstract

We probe, using a model system, elastic and kinetic energies for sheared granular materials. For large enough $P/E_y$ (pressure/Young's modulus) and $P/\rho v^2$ ($P/$kinetic energy density) elastic dominates kinetic energy, and energy fluctuations become primarily elastic in nature. This regime has likely been reached in recent experiments. We consider a generalization of the granular temperature, $T_g$, with both kinetic and elastic terms and that changes smoothly from one regime to the other. This $T_g$ is roughly consistent with a temperature adapted from equilibrium statistical mechanics.