Stress-stress Correlations Reveal Force Chains in Gels

TL;DR

This study uses numerical simulations to analyze microscopic stress correlations in gels, revealing long-range, anisotropic force chains similar to granular solids, and demonstrates how these correlations indicate network rigidity and structural changes during solidification.

Contribution

It applies a theoretical framework to soft particulate gels, showing that stress correlations reveal force chains and differentiate between floppy and rigid network states.

Findings

Stress correlations exhibit long-range anisotropic patterns.

Force chains are identified through stress-stress correlations.

Patterns reflect changes in shear modulus and network topology.

Abstract

We investigate the spatial correlations of microscopic stresses in soft particulate gels, using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations in amorphous assemblies of athermal grains that acquire rigidity under an external load. These correlations exhibit a pinch-point singularity in Fourier space leading to long-range correlations and strong anisotropy in real space, which are at the origin of force-chains in granular solids. Our analysis for the model particulate gels at low particle volume fractions demonstrates that stress-stress correlations in these soft materials have characteristics very similar to those in granular solids and can be used to identify force chains. We show that the stress-stress correlations can distinguish floppy from rigid gel networks and the intensity patterns reflect changes in shear moduli and network topology, due to the emergence of rigid structures during solidification.