Stress-stress Correlations in Soft Particulate Gels

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. This leads to long-range correlations and strong anisotropy in real space, which are at the origin of force-chains in granular solids. Our analysis of 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 intensity patterns reflect changes in shear moduli and network topology, due to the

emergence of rigid structures close to the rigidity transition. Using the angular dependence

of the stress-stress correlation functions obtained from simulations, the properties of the elastic tensor is extracted and then fed back to the theory to obtain the stress-stress correlation patterns. The analysis proposed here opens a promising route to gain novel insights into the emerging elasticity of soft particulate gels and its connection to stress localization.