Mechanical response of an inclined frictional granular layer approaching unjamming

TL;DR

This study investigates how the mechanical properties of inclined frictional granular layers change as they approach unjamming, revealing a decreasing shear modulus and the role of soft modes near the transition.

Contribution

It provides an orthotropic elastic analysis of granular layers under gravity, highlighting how shear modulus and vibration modes evolve with tilt angle approaching unjamming.

Findings

Shear modulus decreases with tilt angle.

Shear modulus remains finite at unjamming.

Soft modes increase near the transition.

Abstract

We present an orthotropic elastic analysis of frictional granular layers under gravity by studying their stress response to a localized overload at the layer surface for several substrate tilt angles. The distance to the unjamming transition is controlled by the tilt angle {\alpha} with respect to the critical angle \alpha_c. We find that the shear modulus of the system decreases with {\alpha}, but reaches a finite value as \alpha tends to \alpha_c. We also analyze the vibration modes of the system and show that the soft modes play an increasing, though not crucial, role approaching the transition.