Abstract: Theoretical treatments of frictional granular matter often assume that it is legitimate to invoke classical elastic theory to describe its coarse-grained mechanical properties. Here, we show, based on numerical simulations, that this is generically not the case since stress autocorrelation functions decay more slowly than what is expected from elasticity theory. We prove quite generally that mechanical balance and material isotropy constrain the stress autocorrelation matrix to be fully determined by two spatially isotropic functions: the pressure and torque autocorrelations. The pressure and torque fluctuations being, respectively, normal and hyperuniform force the stress autocorrelation to decay as the elastic Green’s function. However, generic compressed frictional assemblies exhibit abnormal pressure fluctuations, failing to conform with the central limit theorem. The physics of this failure is linked to correlations built in the material during compression from a dilute configuration prior to jamming. By changing the protocol of compression, one can observe different pressure fluctuations, and stress autocorrelations decay at large scales. Our study is experimentally verified.

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