颗粒流动力学及其离散模型评述

颗粒流是由众多颗粒组成的具有内在相互作用的非经典介质流动. 自然界常见颗粒流 都是密集流, 颗粒间接触形成力链, 诸多力链相互交接构成支撑整个颗粒流重量和外载荷的 网络, 其局部构型及强度在外载荷下演化, 是颗粒流摩擦特性和接触应力的来源.本文 介绍球形颗粒间无粘连作用时的Hertz法向接触理论和Mindlin-Deresiewicz切向接触 理论. Campbell依据是否生成较为稳定的力链把颗粒流分为弹性流和惯性流两大 类, 其中弹性-准静态流和惯性-碰撞流分别对应准静态流和快速流, 作为两种极端流动情况通常处理成连续体, 分 别采用摩擦塑性模型和动理论予以描述, 但是表征接触力链的颗粒弹性参数并不出现这两个 模型和理论框架中, 如何进一步考虑颗粒弹性参数将非常困难. 目前离散动力学方法逐渐 成为复现其复杂颗粒流动现象、提取实验不可能获得的内部流动信息进而综合起来探索颗粒 流问题的一种有效工具, 其真实性强于连续介质理论的描述. 软球模型对颗粒间接触力简化 处理, 忽略了切向接触力对法向接触力及其加载历史的依赖, 带来了法向和切向刚度系数 如何标度等更艰难的物理问题, 但由于计算强度小而广泛应用于工程问题中. 硬球模型不考虑 颗粒接触变形, 因而不能描述颗粒流内在接触应变等物理机理, 仅适用于快速颗粒流, 这不 仅仅是由于两体碰撞的限制. 因此基于颗粒接触力学的离散颗粒动力学模型是崭新的模型, 适用于准静态流到快速流整个颗粒流态的模拟, 可以细致考虑接触形变及接触力的细节, 建立更为合理的颗粒流本构关系, 进而有力的促进颗粒流这一非经典 介质流动的研究.

REVIEW ON GRANULAR FLOW DYNAMICS AND ITS DISCRETE ELEMENT METHOD

Granular flow concerns large assemblages of individual solids, and is fundamentally different from any other type of flow. Common granular flows in nature, such as debris flow, landslides and chutes, are densely packed with solid fractions, over 50{\%} by volume. The interparticle contact forces are found not evenly distributed throughout the granular material, but are concentrated in force chains supporting the bulk of internal compressive stress. Therefore, contact mechanics of particles and dynamic evolution of force chains have a significant effect on the rheological properties of granular flows. In this review paper, we first introduce Hertzian law and Mindlin-Deresiewicz theory for normal and tangential contact forces between non-adhesion particles. We then discuss the new granular flowmap proposed by Campbell (2002; 2005; 2006), based on the relative importance of Bagnold's inertial stress to the elastic stress of force chains. The limitations of Mohr--Coulomb theory and kinetics for quasistatic and the rapid-flow regimes, respectively, are also discussed. For intermediate flow regimes, no appropriate theory is proposed so far. Over 30 years' development, discrete element methods (DEM), a package of numerical techniques to model granular materials, may well be used to study granular flows. The potential value of DEM is the ability to obtain information that is normally inaccessible and to perform rigorous parametric studies. The soft-sphere model, one of the widely used DEM models in engineering applications, simplifies sophisticated contact mechanics and deformation details into an easy-to-use contact model. However, one of tricky problems arising from this simplification is the calibration of introduced parameters with realistic physical quantities. The hard-sphere model is further simplified and has very limited applications so far. We conclude that only the DEM based on rigorous contact mechanics on individual particles could help the fundamental study on granular flows, such as internal force chains properties related with constitutive relation, and eventually be applicable in natural process.