Microscopic strain correlations in sheared amorphous solids

TL;DR

This paper studies how strain fluctuations in sheared amorphous solids are spatially correlated, revealing a quadrupolar symmetry with an algebraic decay that varies during deformation, and models this behavior using interacting Eshelby inclusions.

Contribution

It introduces a model based on interacting Eshelby inclusions to explain the observed strain correlation decay in sheared amorphous solids.

Findings

Correlation decay exponent close to 1 in steady state

Transient stages show exponent between 3 and 1

Enhanced inclusion density correlates with plastic flow

Abstract

We investigate spatial correlations of strain fluctuations in sheared colloidal glasses and simulations of sheared amorphous solids. The correlations reveal a quadrupolar symmetry reminiscent of the strain field due to an Eshelby's inclusion. However, they display an algebraic decay $1/r^{\alpha}$, where the exponent $\alpha$ is close to $1$ in the steady state, unlike the Eshelby field, for which $\alpha=3$ . The exponent takes values between $3$ to $1$ in the transient stages of deformation. We explain these observations using a simple model based on interacting Eshelby inclusions. As the system is sheared beyond the linear response to plastic flow, the density correlations of inclusions are enhanced and it emerges as key to understanding the elastoplastic response of the system to applied shear.