We develop a constitutive model allowing for the description of the rheology of two-dimensional soft dense suspensions above jamming. Starting from a statistical description of the particle dynamics, we derive, using a set of approximations, a nonlinear tensorial evolution equation linking the deviatoric part of the stress tensor to the strain-rate and vorticity tensors. The coefficients appearing in this equation can be expressed in terms of the packing fraction and of particle-level parameters. This constitutive equation rooted in the microscopic dynamic qualitatively reproduces a number of salient features of the rheology of jammed soft suspensions, including the presence of yield stresses for the shear component of the stress and for the normal stress difference. More complex protocols like the relaxation after a preshear are also considered, showing a smaller stress after relaxation for a stronger preshear.

中文翻译：

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堵塞软悬浮液流变学的微观理论

我们开发了一个本构模型，可以描述干扰上方的二维软致密悬浮液的流变学。从粒子动力学的统计描述开始，我们使用一组近似推导出非线性张量演化方程，该方程将应力张量的偏部分与应变率和涡度张量联系起来。该方程中出现的系数可以用填充率和粒子级参数来表示。这个基于微观动力学的本构方程定性地再现了卡住的软悬架流变学的许多显着特征，包括应力的剪切分量和法向应力差的屈服应力的存在。还考虑了更复杂的协议，例如预剪切后的松弛，