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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. 

In a recent paper (Zhao et al., Phys Rev X, 2022, 12: 031,021), we reported experimental observations of “ultrastable” states in a shear-jammed granular system subjected to small-amplitude cyclic shear. In such states, all the particle positions and contact forces are reproduced after each shear cycle so that a strobed image of the stresses and particle positions appears static. In the present work, we report further analyses of data from those experiments to characterize both global and local responses of ultrastable states within a shear cycle, not just the strobed dynamics. We find that ultrastable states follow a power-law relation between shear modulus and pressure with an exponentβ≈ 0.5, reminiscent of critical scaling laws near jamming. We also examine the evolution of contact forces measured using photoelasticimetry. We find that there are two types of contacts: non-persistent contacts that reversibly open and close; and persistent contacts that never open and display no measurable sliding. We show that the non-persistent contacts make a non-negligible contribution to the emergent shear modulus. We also analyze the spatial correlations of the stress tensor and compare them to the predictions of a recent theory of the emergent elasticity of granular solids, the Vector Charge Theory of Granular mechanics and dynamics (VCTG) (Nampoothiri et al., Phys Rev Lett, 2020, 125: 118,002). We show that our experimental results can be fit well by VCTG, assuming uniaxial symmetry of the contact networks. The fits reveal that the response of the ultrastable states to additional applied stress is substantially more isotropic than that of the original shear-jammed states. Our results provide important insight into the mechanical properties of frictional granular solids created by shear.