Experimental Measures of Affine and Non-affine Deformation in Granular Shear

TL;DR

This study investigates how granular materials deform under shear, distinguishing between smooth affine and irreversible non-affine displacements, and introduces a granular temperature concept linked to non-affine diffusion.

Contribution

It provides experimental evidence connecting non-affine displacements with diffusion and granular temperature, and proposes a model for shear band formation based on diffusive fluxes.

Findings

Non-affine displacements follow a stretched exponential distribution.

Non-affine motion is associated with diffusion and granular temperature.

Shear band formation is explained by a balance of diffusive fluxes.

Abstract

Through 2D granular Couette flow experiments, we probe failure and deformation of disordered solids under shear. Shear produces smooth affine deformations in such a solid and also irresversible so-called non-affine particle displacements. We examine both processes. We show that the non-affine part is associated with diffusion, and also can be used to define a granular temperature. Distributions for single particle non-affine displacements, $\dri$, satisfy $P_1(\dri) \propto \exp [-|\dri/\Delta r|^{\alpha}]$ ($\alpha \stackrel{<}{\sim} 2$). We suggest that the shear band forms due to a radially outward diffusive flux/non-affine motion which is balanced in the steady state by inward diffusion due to density gradients.