【作者】 徐春晖；

【导师】 黄文彬；

【作者基本信息】 中国农业大学 ， 车辆工程， 2003， 博士

【摘要】 离散元法(DEM)是分析散体力学行为的数值方法，颗粒离散元法适用于单个几何形状可用圆球近似而不产生显著差异的情况。两圆盘问介质的挤压流动问题是分析两圆球间介质挤压流动的基础。当颗粒之间有法向或切向相对运动时，由于存在填隙流体，颗粒之间产生的法向的挤压力和切向阻力，是湿颗粒离散元法的理论基础。因此，研究存在填隙流体时颗粒之间的相互作用力具有重要的理论价值和实际意义。本文主要研究工作如下： 1．研究了存在壁面滑移时两刚性圆盘间刚塑性介质的挤压流动。首先对现有的库仑摩擦条件下的压力规律做了进一步的研究，找到了一种更合理的圆盘上的压力分布规律。同时，在圆盘边缘处滑移速度一定，介质的滑移速度随着半径线性变化的假设下，引入合理的速度场，得到了另一种圆盘上的压力分布规律，并对不同的摩擦条件及用不同方法计算得到的结果进行了对比。 2．以Reynolds润滑理论为基础，采用小参数法研究了存在滑移时两刚性圆盘间二阶流体的挤压流动，导出了流体的速度场和压力分布，进而求出圆盘间挤压力的解析表达式。 3．研究了存在壁面滑移时两圆盘间宾汉流体的挤压流动，得到了计算流体刚性区和挤压粘性力的公式。结果表明，圆盘上的挤压力随着滑移参数的增加而减小，当流体全部处于流动状态时，即为圆盘挤压牛顿流体时的情况；当流体全部处于刚性状态时，即为圆盘挤压理想刚塑性介质时的情况。 4．采用Reynolds润滑理论和小参数法等研究了存在填隙二阶流体时两球法向及切向运动时的运动，位移及压力分布规律，从而求出挤压力或切向阻力、阻力矩的解析解。结果表明，二阶流体的本构关系虽然比牛顿流体复杂得多，但法向挤压力与牛顿流体相比只有微小的偏离，而切向阻力和阻力矩与牛顿流体相同。所以，当两球间存在填隙二阶流体时，颗粒间的相互作用力可采用存在牛顿流体时的理论结果。 5．研究了存在填隙Herschel-Bulkley流体时两球法向运动时的挤压力，并且证明了法向挤压力的解分别可以退回到宾汉流体或幂律流体情形。 6．利用上述理论以及DEM TRUBAL程序，研究了存在填隙流体时颗粒规则排列单向压缩问题，得到了宏观应力应变曲线随流体性质、壁的运动速度等的变化规律；并对随机排列单向压缩问题进行了数值模拟，得到了宏观应力应变平均曲线；并对干、湿两种情况下颗粒的模拟结果进行了对比。 7．对存在填隙流体时离散元法的应用进行了初步探索，对块石土强夯过程和挡土墙问题等进行了简单的离散元模拟，可以看出采用存在填隙流体时球颗粒间的作用规律后，可以对一些问题定性分析。 本文从细观上得到了颗粒间的相互作用规律，为离散元法增加了新的理论模型，增加了新的思路，具有参考意义和潜在的广阔应用前景。更多还原

【Abstract】 The Discrete Element Method (DEM) is a powerful tool in analyzing granular assembly. The granular discrete element method can be applied to the partials, whose shape can be approximately described as a sphere. The research of the squeeze flow between two disks is the basic study on the squeeze flow between two spheres. Due to the interstitial fluid between the partials, the solutions of the pressure and tangential force between the two granules are the theoretical foundation of the wet granular discrete element method. Therefore, it is important to study the forces between two granules with interstitial fluid.1. Squeeze flow between two parallel disks is considered for small gaps for rigid-plastic material with partial wall slip. Firstly, the Coulombic friction condition is discussed, and a new pressure distribution is obtained. Moreover, based on the assumption that the slip velocity at the disks increases linearly with the radius up to the rim slip velocity, another pressure distribution is derived by introducing a appropriate velocity field. Then these different results by the different friction conditions and technique are compared.2. Based on the Reynolds’ lubrication approximation, the small parameter method is introduced to approximately analyze velocity field and stress distribution between the two parallel disks with an interstitial second-order fluid.3. Squeeze flow between two parallel plates of a Bingham fluid with partial wall slip is considered. The results show that the squeeze viscous force decreases with the slip parameter increases, rigid region of the fluid increases with the slip parameter increases. When the slip parameter tends to infinite, the results of the squeeze viscous force reduce to the case of the squeeze flow of rigid-plastic solid between two parallel disks.4. Based on the Reynolds’ lubrication approximation, and utilizing the small parameter method, the velocity and the pressure equations for two spheres translating normally and tangentially with an interstitial second-order fluid are derived for modeling wet granular assembles using the Discrete Element Method. As a result, analytical solution for the tangential force and the torque were obtained. It is interesting to find that, although the equations for the velocity and the pressure are more complicated in their form than a Newtonian fluid, however, the final results are simple and the same as those for a Newtonian fluid.5. When two spheres with an interstitial Herschel-Bulkley fluid translate normally, the velocity and the squeeze force distributions are investigated. It is shown that the solution of the squeeze force can reduced to the Bingham and power-law fluid cases, respectively.6. Applied the above theory and the DEM program TRUBAL, the unilateral compress problems for the regular generated particles with an interstitial fluid are studied, and the macro-strain-stress curves varied with the fluid properties and the velocity of the wall are gotten. Then, he unilateral compress problems for the random generated particles are numerically simulated, and the macro-strain-stress curves are obtained. Moreover, the numerical simulation results for the dry and moist cases are compared.7. Finally, the application of the discrete element method with an interstitial fluid is discussed. For this purpose, a dynamic compacting process and a retaining wall problem are simulated by DEM. It is shown that these problems can be qualitatively analyzed by DEM.The present results of the interaction between two particles with an interstitial fluid provide a new sight and model for DEM, and show a potential usage in application.更多还原