颗粒间滚动阻力的离散元模型研究

The interaction of rolling among particles significantly influences the complex macroscopic behavior of a particle system, such as, the formation of shear band, the arching phenomenon and force chains existing in the shear band. Furthermore, the rolling resistance, which plays a key role to numerical stability and repeatability, determines the simulation results, and must be considered in the discrete element method (DEM). However, the method to model correctly the rolling resistance remains questionable, numerous articles have proposed different rolling resistance models, and even the same researchers used various models in different periods, what’s more, the definition of rolling is not unique. Hence, the merits and demerits of different models should be analyzed to determine the most feasible one. For this purpose, five models are adopted to simulate the simple shear flow by DEM. The force-displacement and contraction/dilatancy curves of the feasible model at different volume fractions should be in good agreement with the experimental findings, aside from in line with experiments, also satisfy the objectivity and rate-independent theory. Briefly, the correct model can be identified by criteria of objectivity and rate-independence, with an interpretable physical mechanism. On the base of spherical particles, the rolling deformation should be generalized to the case of non-spherical particles, and the general rolling resistance is useful for simulating a real particle system. We propose to figure out one of the most basic problems in DEM, discuss the mechanisms of sliding and rolling, and determine a standard of rolling resistance. All the related investigations make the simulation closer to the actual conditions of a particle system, and provide a reference to model particles of arbitrary shape.

颗粒间的滚动和体系表现出的复杂的宏观性质（如剪切带的形成，成链成拱现象等）有很大关系，滚动阻力还影响着颗粒流的模拟结果,是获取稳定和可重复结果的关键，是离散元模拟必须考虑的一种作用形式。但滚动模型很多，不同的研究者甚至相同的研究者在不同的时期使用的模型也不同，且滚动的定义也有矛盾，模型的优劣和对错需要甄别。本项目对球形颗粒单剪体系用离散元模拟常用的五种滚动模型，获取应力-应变、剪胀/剪缩曲线，通过和实验对比来确定模型的优劣，结合率无关和客观性来确定最合理的模型，解释模型的物理机制。在确定球形颗粒间正确的滚动形变的基础上，向非球形颗粒推广，推导普遍情形的滚动形变公式，用于程序的编写。本项目研究的是离散元中最基础的一个问题，探讨颗粒间滚动和滑动机制，澄清符合客观性的正确的滚动形变表达式，确定一个标准的滚动阻力模型，使模拟结果更接近实验，为模拟任意形状的颗粒体系提供参考。

通过本项目的执行，按计划完成了预定的研究目标。用离散元模拟中常用的五种滚动阻力模型对球形颗粒剪切体系进行了研究。五种模型的应力-应变、剪胀曲线都和实验一致，但只有一种模型（Luding模型）同时满足率无关和客观性。分析了Luding模型中球形颗粒间滚动形变的物理机制，并向非球形颗粒进行了推广，给出了普遍情形下的滚动形变公式和滚动阻力模型，并编写了相应的程序。用该滚动阻力模型，结合四种不同的法向、切向力接触模型，对非球形颗粒剪切体系进行了离散元模拟，得到了满足率无关的剪切曲线。本项目得到的非球形颗粒间滚动阻力模型对不同的法向、切向力接触模型是普适的。用组合球体、椭圆、椭球、超椭球、心形颗粒体系对该滚动阻力模型进行了验证，得到了重力和应力作用下动能耗散为零的平衡态，验证了模型对不同颗粒形状的普适性。除了适用于剪切体系，该滚动阻力模型还可以用来研究单轴压缩体系的声学性质。

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