颗粒材料热力学理论在简单剪切流中的应用

Thermodynamic analysis of simple shear granular flows

颗粒物质由大量离散的粗大固体颗粒聚集而成,在外界作用下可能发生准静态变形、变形局部化和破坏,直至流动,其中采用固体力学和流体力学对准静态变形和流动开展的研究较为系统,而变形局部化和破坏的研究非常薄弱.分析内部结构演化规律,建立颗粒体系非平衡态热力学,统一描述颗粒体系力学行为是重要的基础研究课题,Granular Solid Hydrodynamics(GSH)理论为该研究提供了基础.本文完善了该理论涉及的颗粒温度表达式,确定了相应参数数值;与动理学理论和离散元模拟一起对恒定体积简单剪切流进行了分析,对比了三种方法得到的正应力与颗粒体积分数的关系,发现由于基本假设的限制,动理学理论只能适用于稀疏颗粒流,而完善后的颗粒体系热力学理论比动理学涵盖范围更广,可以从稀疏体系到密集体系.这样该理论可以连贯地描述颗粒体系准静态变形、变形局部化和破坏,直至流动的力学行为.

Granular flow is the collective moment of a large number of solid particles. A so-called Granular Solid Hydrodynamics （GSH） was recently proposed and expected to provide unifying descriptions of mechanical properties of granular materials. In this work, the simple shear flows with constant volume are firstly simulated with the discrete element method （DEM） where the volume fraction of solids ranges from 0.2 to 0.68. Meanwhile, the conventional kinetic theory is used for dilute systems analysis （i.e. volume fraction less than 0.6 in this study）. We found the kinetic theory results about the normal stress with different volume fractions and shear rates agree well with DEM results. After improve the expression of granular temperature, GSH theory is employed to study the granular flows and the obtained results coincide with DEM and kinetic results. It is concluded that the improved GSH theory could coherently describe mechanical behavior of granular flows from quasi-static deformation until rapid flows.