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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 can distinguish floppy from rigid gel networks and that the intensity patterns reflect changes in shear moduli and network topology, due to the emergence of rigid structures during solidification. 

Prestress in amorphous solids bears the memory of their formation and plays a profound role in their mechanical properties. Here we develop a set of mathematical tools to investigate mechanical response of prestressed systems, using stress rather than strain as the fundamental variable. This theory allows microscopic prestress to vary for the same bond or contact configuration and is particularly convenient for nonconservative systems, such as granular packings and jammed suspensions, where there is no well-defined reference state, invalidating conventional elasticity. Using prestressed nonconservative triangular lattices and a computational model of amorphous solids, we show that drastically different mechanical responses can show up in amorphous materials at the same density, due to nonconservative interactions which evolve over time, or different preparation protocols. In both cases, the information is encoded in the prestress of the network and not visible at all from the configurations of the network in the case of nonconservative interactions.