We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalise the Integration Through Transients (itt) formalism to a fluid of dissipative, randomly driven granular particles. The stress relaxation function is computed approximately within a mode-coupling theory—based on the physical picture, that relaxation of shear is dominated by slow structural relaxation, as the glass transition is approached. The transient build-up of stress in steady shear is thus traced back to transient density correlations which are computed self-consistently within mode-coupling theory. The glass transition is signalled by the appearance of a yield stress and a divergence of the Newtonian viscosity, characterizing linear response. For shear rates comparable to the structural relaxation time, the stress becomes independent of shear rate and we observe shear thinning, while for the largest shear rates Bagnold scaling, i.e., a quadratic increase of shear stress with shear rate, is recovered. The rheological properties are qualitatively similar for all values of $\epsilon$, the coefficient of restitution; however, the magnitude of the stress as well as the range of shear thinning and thickening show significant dependence on the inelasticity.

中文翻译：

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通过瞬态积分实现非弹性硬球体流体

对于一般剪切速率和密度，我们计算了稳定剪切流中非弹性硬球的流变特性。从微观动力学出发，我们将通过瞬态积分（itt）形式化概括为耗散的，随机驱动的颗粒状流体。应力松弛函数大约是根据模式耦合理论计算得出的-根据物理图像，随着接近玻璃化转变，剪切的松弛主要由缓慢的结构松弛引起。因此，稳态剪应力的瞬态累积可以追溯到瞬态密度相关性，它们在模态耦合理论中是自洽计算的。玻璃化转变通过屈服应力的出现和牛顿粘度的发散来表示，表征线性响应。对于与结构弛豫时间相当的剪切速率，应力变得与剪切速率无关，并且我们观察到剪切变薄，而对于最大的剪切速率，则恢复了Bagnold结垢，即剪切应力随剪切速率的二次增加。流变特性在所有值上都相似。$\epsilon$，赔偿系数；然而，应力的大小以及剪切变薄和增厚的范围显示出对非弹性的显着依赖性。