In this paper, the authors analyse numerical and experimental results concerning either dry or saturated granular flows under steady, simple shear conditions. A new constitutive model is introduced, on the base of the mixture theory, according to which granular and liquid phases are considered separately. The constitutive relationship refers to the representative elementary volume and assumes that the mean values of all kinematic variables, of both granular and liquid phases, coincide. For the two phases, a parallel scheme is chosen. As regards the granular contribution, the authors employ an already conceived constitutive model where the critical state concept and the kinetic theory of granular gases are merged, and in which the granular temperature plays the role of state variable for the material. Under saturated conditions, the new model accounts for granular–liquid coupling effects. In fact, the liquid viscosity is a function of granular concentration, whereas the evolution of granular temperature is influenced by the liquid molecular viscosity. The model is validated against numerical results and critically discussed. For sufficiently small values of concentration, the transition from a Newtonian to a Bagnoldian regime, for increasing values of strain rate, is correctly reproduced.

中文翻译：

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饱和颗粒流：稳定简单剪切条件下的本构模型

在本文中，作者分析了在稳定，简单剪切条件下有关干燥或饱和颗粒流的数值和实验结果。在混合理论的基础上，引入了一种新的本构模型，根据该模型分别考虑了颗粒和液相。本构关系是指代表性的基本体积，并假定颗粒和液相的所有运动变量的平均值均重合。对于这两个阶段，选择并行方案。关于颗粒的贡献，作者采用了已经构想的本构模型，其中将临界状态概念和颗粒气体的动力学理论融合在一起，并且其中颗粒温度在材料中起着状态变量的作用。在饱和条件下，新模型考虑了颗粒-液体耦合效应。实际上，液体粘度是颗粒浓度的函数，而颗粒温度的变化受液体分子粘度的影响。该模型针对数值结果进行了验证，并进行了严格讨论。对于足够小的浓度值，正确地再现了从牛顿状态到巴格诺德状态的过渡，从而增加了应变率。