Why Do Granular Materials Stiffen with Shear Rate? A Test of Novel Stress-Based Statistics

TL;DR

This paper investigates why granular materials stiffen with shear rate, testing a stress-based statistical ensemble against traditional energy-based models, and finds the stress-based approach aligns better with experimental observations.

Contribution

The study introduces and tests a stress-based statistical ensemble model for granular shear, showing it explains rate-dependent stress growth more accurately than energy-based models.

Findings

Stress grows linearly with the logarithm of shear rate in experiments.

Stress-based statistical ensemble predictions match experimental data.

Energy-based models predict a different, less accurate rate dependence.

Abstract

Recent experiments exhibit a rate-dependence for granular shear such that the stress grows linearly in the logarithm of the shear rate, \dot{\gamma}. Assuming a generalized activated process mechanism, we show that these observations are consistent with a recent proposal for a stress-based statistical ensemble. By contrast, predictions for rate-dependence using conventional energy-based statistical mechanics to describe activated processes, predicts a rate dependence that of (\ln (\dot{\gamma}))^{1/2}.