密集颗粒系统的离散单元模型及其宏观力学行为特征的理论研究
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摘要
颗粒物质是自然界存在最多、工程应用最为广泛的物质类型之一,这类物质通常会表现出许多非常复杂的物理性质。作为这一领域的基础性课题,颗粒物质的力学行为研究成为当前科学研究中遇到的最棘手问题之一。系统内粒子的离散性和粒子间作用的非线性耗散性,使得颗粒物质的许多宏观特性都与系统内部的微观力学行为有着密切的联系,因此要研究和揭示颗粒系统产生宏观静态、动态性质的机理,就必须对系统内粒子的排列、接触、碰撞、运动等微观力学性质进行深入分析。本文基于改进的颗粒离散元模型,针对密集颗粒系统在准静态加载下的变形特征及剪切颗粒流的动力学行为等基础性问题,通过对微观尺度下粒子间力学行为的分析与统计,研究和揭示了系统在宏观尺度下的变形及流动行为,在此基础上分析了颗粒系统内接触力网的分布及演化特征。主要工作如下:
首先,考虑颗粒间发生滚动时的接触特征,给出了一种简化的颗粒滚动接触模型,在此基础上建立了分析和模拟密集颗粒系统的改进离散元模型。同时,给出了不同条件下密集颗粒样本的生成方法,分析了边界应力、初始构型、加载速率、粒子间的摩擦系数等对颗粒系统目标构型的影响。通过对微观尺度下粒子运动的分析与统计,研究了随机分布的密集颗粒系统在平面应变加载状态下的变形特征,得到的宏观变形模式与相应的实验结果吻合良好。数值模拟结果表明:在准静态加载状态下各种材料参数和因素如空隙比、围压、粒子间的摩擦系数等都会对系统的变形特征、承载能力和整体稳定性产生重要的影响。
其次,从微观尺度下粒子的运动特征出发,利用统计分析的方法研究了环形剪切颗粒流的宏观动力学特性。建立的离散动力学模型和统计方法可以较好的预测已有的实验结果。根据初始体积分数、剪切率、摩擦系数等对系统内剪切速度廓线、局部体积分数和配位数等的影响规律,分析了剪切颗粒系统的平均流动特征。同时,利用概率统计的方法研究了系统内切向速度、法向速度、自旋角速度的分布特征,揭示了不同局部区域内微观粒子的特殊运动现象。最后通过考虑粒子的速度波动,分析了剪切颗粒流内粒子的自扩散系数及其输运特征。通过从不同方面对系统内微观特征量的统计分析,可以为准确有效的描述和刻画不同流动状态下的密集颗粒系统提供重要的理论依据。
最后,分析了密集颗粒系统内接触力网的分布及演化特征。对系统内接触力网的分析统计有助于从机理上揭示颗粒系统的许多静、动态性质。为此,本文给出了一种颗粒系统内不同力尺度下接触力网的统计方法,并通过与相关实验结果的对比,验证了计算和统计方法的有效性。根据微观尺度下粒子的排列及接触特征,研究了静态堆积颗粒系统和围压约束下静态颗粒系统中接触力网的分布特征,同时分析了粒径分布、体积分数、边界条件等对接触力分布特征的影响。最后对动态剪切颗粒流中的接触力分布进行了研究,主要考虑了不同力尺度下接触力网的演化特征,模拟结果表明在剪切颗粒流内边界剪切会促使系统发生明显的状态转变,强接触力网沿着剪切方向也会表现出各向异性的特征。
总之,通过本文对密集颗粒系统在准静态条件下的微观变形特征、剪切作用下的流动特征以及系统内接触力网分布特征的研究,可以为揭示和分析密集颗粒系统不同加载状态下的宏观力学行为特征提供微观尺度下的理论依据。此外,开展这方面的基础研究也可以为地质、化工、能源、医药等学科研究和工业部门提供基本的分析方法和定量成果,同时对完善力学自身研究框架体系也具有重要的意义。
Granular matter is widely encountered in the nature and engineering applications, and usually may exhibit many complex and special features. At present, studies of granular material have become a very important research field as such matter has wide applications and scientific implications. The macroscopic behavior of granular material is mostly dependent on the interaction operating between particles. So the understanding on the fundamental properties granular material can only be obtained on the basis of micro-mechanical consideration, for example, arrangement, contact, collision and motion of the discrete particles in space. Based the modified discrete element method, this thesis mainly investigates the localized deformation of stochastic distributed granular material under plain strain conditions and dynamical features of shearing granular flow. Though analysis and statistics of micro-mechanical quantities, we investigate deformation and flow features of granular system on the macro scale. At last, we also investigate the distributing and evolution features of contact force network in dense granular systems. The main works are concluded as follows:
Firstly, Considering the rolling resistance between particles, a modified discrete element model(MDEM) is established to simulate the dense granular system. For different packing fractions and loading conditions, we have presented several specimen generation methods. The influences of boundary stress, initial configuration, loading rate and friction coefficient between particles on the state and configuration of dense granular system are also examined. Moreover, the features of the localized deformation in stochastically granular material are investigated under plain strain conditions, and obtained pattern of the macro deformation is well consist with measurements. The numerical results show that various material parameters or factors have significant influences on localized deformation features, capacity of carrying loading and whole stability of granular materials.
Secondly, based microscopic motions of particles inside granular system, we have analyzed the macroscopic mechanical features of annular shear granular flow using probability statistic method. The predictions of the proposed discrete dynamical model and statistical method are quite agreeable with the existing experimental results. By considering the influences of initial packing fraction, shear rate and friction coefficient on the shear velocity profile, local packing fraction and coordinate number, we have investigate the mean flow features inside shear granular flows. We have also analyzed the distributing features of tangential velocity, radial velocity and spin angular velocity, and revealed some special particle motions inside different local regions. At last, using velocity fluctuations of microscopic particles, we investigate the self-diffusivity and transport processes inside shear granular flows. Such different kind's statistical results can provide an important theoretical basis for describing the dense shear granular flow accurately.
Finally, the distributing and evolving features of contact force network in dense granular systems are investigated. The contact force network may provide a micro-mechanism for revealing the static, dynamic features in granular systems. So a statistical method under different force scales about the contact force network inside granular systems is presented, and it is also verified by comparing with the counterpart experiment results. We investigate the contact force distributions inside the static granular systems under the conditions of stochastic packing and confining pressure constraint. The influences of particle size distribution, packing fraction and constraint condition are also considered. Finally, we put our attention on the evolving features of contact force network inside a dynamical shear granular flow. From the numerical results we find a jamming transition and shear-induced anisotropy in dense shear granular flows.
After all, the theoretical investigations of localized deformations under quasi-static loading, dynamical features under shearing, and distributing features of contact force network in dense granular systems must be important and useful for precise revealing and prediction macro mechanical features of granular systems. Moreover, such fundamental researches can provide some basic analysis methods and quantitative results for geological, chemical, energy, and pharmaceutical engineering, et al, and it is very important for improving the research framework of mechanical system.
首先,考虑颗粒间发生滚动时的接触特征,给出了一种简化的颗粒滚动接触模型,在此基础上建立了分析和模拟密集颗粒系统的改进离散元模型。同时,给出了不同条件下密集颗粒样本的生成方法,分析了边界应力、初始构型、加载速率、粒子间的摩擦系数等对颗粒系统目标构型的影响。通过对微观尺度下粒子运动的分析与统计,研究了随机分布的密集颗粒系统在平面应变加载状态下的变形特征,得到的宏观变形模式与相应的实验结果吻合良好。数值模拟结果表明:在准静态加载状态下各种材料参数和因素如空隙比、围压、粒子间的摩擦系数等都会对系统的变形特征、承载能力和整体稳定性产生重要的影响。
其次,从微观尺度下粒子的运动特征出发,利用统计分析的方法研究了环形剪切颗粒流的宏观动力学特性。建立的离散动力学模型和统计方法可以较好的预测已有的实验结果。根据初始体积分数、剪切率、摩擦系数等对系统内剪切速度廓线、局部体积分数和配位数等的影响规律,分析了剪切颗粒系统的平均流动特征。同时,利用概率统计的方法研究了系统内切向速度、法向速度、自旋角速度的分布特征,揭示了不同局部区域内微观粒子的特殊运动现象。最后通过考虑粒子的速度波动,分析了剪切颗粒流内粒子的自扩散系数及其输运特征。通过从不同方面对系统内微观特征量的统计分析,可以为准确有效的描述和刻画不同流动状态下的密集颗粒系统提供重要的理论依据。
最后,分析了密集颗粒系统内接触力网的分布及演化特征。对系统内接触力网的分析统计有助于从机理上揭示颗粒系统的许多静、动态性质。为此,本文给出了一种颗粒系统内不同力尺度下接触力网的统计方法,并通过与相关实验结果的对比,验证了计算和统计方法的有效性。根据微观尺度下粒子的排列及接触特征,研究了静态堆积颗粒系统和围压约束下静态颗粒系统中接触力网的分布特征,同时分析了粒径分布、体积分数、边界条件等对接触力分布特征的影响。最后对动态剪切颗粒流中的接触力分布进行了研究,主要考虑了不同力尺度下接触力网的演化特征,模拟结果表明在剪切颗粒流内边界剪切会促使系统发生明显的状态转变,强接触力网沿着剪切方向也会表现出各向异性的特征。
总之,通过本文对密集颗粒系统在准静态条件下的微观变形特征、剪切作用下的流动特征以及系统内接触力网分布特征的研究,可以为揭示和分析密集颗粒系统不同加载状态下的宏观力学行为特征提供微观尺度下的理论依据。此外,开展这方面的基础研究也可以为地质、化工、能源、医药等学科研究和工业部门提供基本的分析方法和定量成果,同时对完善力学自身研究框架体系也具有重要的意义。
Granular matter is widely encountered in the nature and engineering applications, and usually may exhibit many complex and special features. At present, studies of granular material have become a very important research field as such matter has wide applications and scientific implications. The macroscopic behavior of granular material is mostly dependent on the interaction operating between particles. So the understanding on the fundamental properties granular material can only be obtained on the basis of micro-mechanical consideration, for example, arrangement, contact, collision and motion of the discrete particles in space. Based the modified discrete element method, this thesis mainly investigates the localized deformation of stochastic distributed granular material under plain strain conditions and dynamical features of shearing granular flow. Though analysis and statistics of micro-mechanical quantities, we investigate deformation and flow features of granular system on the macro scale. At last, we also investigate the distributing and evolution features of contact force network in dense granular systems. The main works are concluded as follows:
Firstly, Considering the rolling resistance between particles, a modified discrete element model(MDEM) is established to simulate the dense granular system. For different packing fractions and loading conditions, we have presented several specimen generation methods. The influences of boundary stress, initial configuration, loading rate and friction coefficient between particles on the state and configuration of dense granular system are also examined. Moreover, the features of the localized deformation in stochastically granular material are investigated under plain strain conditions, and obtained pattern of the macro deformation is well consist with measurements. The numerical results show that various material parameters or factors have significant influences on localized deformation features, capacity of carrying loading and whole stability of granular materials.
Secondly, based microscopic motions of particles inside granular system, we have analyzed the macroscopic mechanical features of annular shear granular flow using probability statistic method. The predictions of the proposed discrete dynamical model and statistical method are quite agreeable with the existing experimental results. By considering the influences of initial packing fraction, shear rate and friction coefficient on the shear velocity profile, local packing fraction and coordinate number, we have investigate the mean flow features inside shear granular flows. We have also analyzed the distributing features of tangential velocity, radial velocity and spin angular velocity, and revealed some special particle motions inside different local regions. At last, using velocity fluctuations of microscopic particles, we investigate the self-diffusivity and transport processes inside shear granular flows. Such different kind's statistical results can provide an important theoretical basis for describing the dense shear granular flow accurately.
Finally, the distributing and evolving features of contact force network in dense granular systems are investigated. The contact force network may provide a micro-mechanism for revealing the static, dynamic features in granular systems. So a statistical method under different force scales about the contact force network inside granular systems is presented, and it is also verified by comparing with the counterpart experiment results. We investigate the contact force distributions inside the static granular systems under the conditions of stochastic packing and confining pressure constraint. The influences of particle size distribution, packing fraction and constraint condition are also considered. Finally, we put our attention on the evolving features of contact force network inside a dynamical shear granular flow. From the numerical results we find a jamming transition and shear-induced anisotropy in dense shear granular flows.
After all, the theoretical investigations of localized deformations under quasi-static loading, dynamical features under shearing, and distributing features of contact force network in dense granular systems must be important and useful for precise revealing and prediction macro mechanical features of granular systems. Moreover, such fundamental researches can provide some basic analysis methods and quantitative results for geological, chemical, energy, and pharmaceutical engineering, et al, and it is very important for improving the research framework of mechanical system.
引文
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