Thermal Ensemble for Stresses in Dense Suspensions*

We develop a predictive framework for the macroscopic stress properties of dense suspensions
in two dimensions, based on correlations in a dual space representing forces. Working with the
ensemble of steady state configurations obtained from simulations of suspensions, we find an
emerging anisotropy in the pair correlation function in force space as the confining shear stress
(σ_xy) and the packing fraction (φ) are varied. Using these microscopic correlations, we build
a statistical theory of the forces and relate this to the macroscopic stress tensor of the system.
We find that (i) the stress anisotropy τ /P decreases as φ is increased and (ii) the normal stress
N₁ = σ_xx− σ_yy changes sign near the discontinuous shear thickening transition (DST). We provide
evidence for a first order transition occurring near the DST point, with a coexistence of ‘fluid’
regions with low stresses and ‘solid’ regions with high stresses.