Elasticity of granular packings close to Jamming. Elasticit\'e des empilements granulaires proche de la transition de blocage

TL;DR

This study experimentally examines how a 2D granular packing responds mechanically to shear near the jamming transition, revealing nonlinear stress behaviors and the influence of the transition on constitutive laws.

Contribution

It introduces a novel experimental setup with tracking and photoelastic techniques to analyze stress and strain at the grain scale near jamming.

Findings

Shear strain induces both shear and normal stresses.

Stresses behave nonlinearly with shear strain.

Constitutive laws are governed by the jamming transition.

Abstract

We investigate experimentally the mechanical response to shear of a 2D packing of grains across the jamming transition. First, we develop a dedicated experimental setup, together with tracking and photoelastic techniques in order to prepare the packing in a controlled fashion and to quantify the stress and strain tensors at the grain scale. Second, we install a inflating probe (a 2D "balloon"), which shears the packing with a cylindrical symmetry. We probe experimentally stresses and strains for strain amplitudes as low as $10^{-3}$ and for a range of packing fractions within $2\%$ variation around the jamming transition. We observe not only that shear strain induces shear stresses, but also normal stresses. Moreover, we show that both shear and normal stresses behave nonlinearly with the shear strain. Finally, we show by scaling analysis that the constitutive laws are controlled by the Jamming transition.