On the Origin of Spatial Stress Correlations in Disordered Media

It has been recently shown^1,2 that coarse-grained stress fields in amorphous media exhibit long range spatial correlations. It has been proposed³ that these correlations stem from the nature of the dynamical processes that occur during the formation of these systems. Using numerical simulations of simple lattice-based models we show that the minimal ingredients for the emergence of stress correlations are mechanical equilibrium and some form of disorder, and therefore stress correlations are not a consequence of dynamical processes. In addition, we demonstrate that any arbitrarily small degree of disorder leads to the emergence of stress correlations, and that positional disorder is not a necessary ingredient for their emergence. Finally, we introduce a lattice model in which the functional form of the spatial decay of stress correlations can be exactly derived.

[1] S. Chowdhury, S. Abraham, T. Hudson, and P. Harrowell, The J. of Chem. Phys. 144, 124508 (2016)
[2] B. Wu, T. Iwashita and T. Egami, Phys. Rev. E 91, 032301 (2015)
[3] A. Lemaître, The J. of Chem. Phys. 143, 164515 (2015)