Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan.
Phys Rev E. 2017 Dec;96(6-1):062909. doi: 10.1103/PhysRevE.96.062909. Epub 2017 Dec 27.
We propose a constitutive model to describe the nonlocality, hysteresis, and several flow features of dry granular materials. Taking the well-known inertial number I as a measure of sheared-induced local fluidization, we derive a relaxation model for I according to the evolution of microstructure during avalanche and dissipation processes. The model yields a nonmonotonic flow law for a homogeneous flow, accounting for hysteretic solid-fluid transition and intermittency in quasistatic flows. For an inhomogeneous flow, the model predicts a generalized Bagnold shear stress revealing the interplay of two microscopic nonlocal mechanisms: collisions among correlated structures and the diffusion of fluidization within the structures. In describing a uniform flow down an incline, the model reproduces the hysteretic starting and stopping heights and the Pouliquen flow rule for mean velocity. Moreover, a dimensionless parameter reflecting the nonlocal effect on the flow is discovered, which controls the transition between Bagnold and creeping flow dynamics.
我们提出了一个本构模型来描述干颗粒材料的非局部性、滞后性和几种流动特征。以众所周知的惯性数 I 作为衡量剪切诱导局部流化的标准，我们根据雪崩和耗散过程中微结构的演化，推导出了一个关于 I 的弛豫模型。该模型为均匀流动产生了一个非单调的流动法则，解释了滞后性的固-流转变和准静态流动中的间歇性。对于非均匀流动，该模型预测了广义的 Bagnold 剪切应力，揭示了两种微观非局部机制之间的相互作用：相关结构之间的碰撞和结构内流化的扩散。在描述沿斜坡的均匀流动时，该模型再现了滞后性的起始和停止高度以及 Pouliquen 平均速度流动法则。此外，发现了一个反映对流动的非局部影响的无量纲参数，它控制着 Bagnold 流动和蠕动流动动力学之间的转变。
