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Despite the industrial importance of dense suspensions of hard particles, fewconstitutive models for them have been proposed or tested. Most of these areeffectively "fabric evolution models" (FEMs) based on a stress rule connectingthe bulk stress to a rank-2 microstructural fabric tensor Q and a closedtime-evolution equation for Q. In dense suspensions most of the stress comesfrom short-ranged pairwise steric or lubrication interactions at near-contacts,so a natural choice for Q is the deviatoric 2nd moment of the distribution P(p)of the near-contact orientations p. Here we test directly whether a closedtime-evolution equation for such a Q can exist for inertialess non-Brownianhard spheres in a Newtonian solvent. We perform extensive numerical simulationsfor the evolution of P(p) under shear reversal, providing a stringent test forFEMs. We consider a generic class of these as defined by Hand (1962)constrained only by frame indifference. Motivated by the small microstructuralanisotropy in the dense regime, we start with linear models and successivelyconsider increasingly nonlinear ones. Based on these results we suggest that noclosed FEM properly describes the dynamics of Q under reversal. We attributethis to the fact that Q gives a poor description of the microstructure duringlarge parts of the microstructural evolution following shear reversal.Specifically, the truncation of P(p) at 2nd spherical harmonic level describestwo-lobed distributions of near-contact orientations, whereas on reversal weobserve distributions that are markedly four-lobed; moreover dP/dt (p) hasoblique axes, not collinear with those of Q in the shear plane. This structurelikely precludes any adequate closure at second-rank level. Instead, ournumerical data suggest that closures involving the coupled evolution of both afabric tensor and a fourth-rank tensor might be reasonably accurate.

Shear Reversal in Dense Suspensions: The Challenge to Fabric Evolution Models from Simulation Data