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Considering the rheology of two-dimensional soft suspensions above thejamming density, we derive a tensorial constitutive model from the microscopicparticle dynamics. Starting from the equation governing the $N$-particledistribution, we derive an evolution equation for the stress tensor. Thisevolution equation is not closed, as it involves the pair and three-particlecorrelation functions. To close this equation, we first employ the standardKirkwood closure relation to express the three-particle correlation function interms of the pair correlation function. Then we use a simple and physicallymotivated parametrization of the pair correlation function to obtain a closedevolution equation for the stress tensor. The latter is naturally expressed asseparate evolution equations for the pressure and for the deviatoric part ofthe stress tensor. These evolution equations provide us with a non-lineartensorial constitutive model describing the rheological response of a jammedsoft suspension to an arbitrary uniform deformation. One of the advantages ofthis microscopically-rooted description is that the coefficients appearing inthe constitutive model are known in terms of packing fraction and microscopicparameters.

Derivation of a constitutive model for the rheology of jammed soft suspensions from particle dynamics