基于闵可夫斯基和理论的扩展离散元模型及其应用

发布时间：2018-06-29 05:30

  本文选题：离散单元法 + 闵可夫斯基和　； 参考：《大连理工大学》2017年博士论文

【摘要】：颗粒物质与人类的生产生活紧密相关,如谷物的存储和运输、铁路道床的沉降、沙丘的迁移以及滑坡泥石流等都属于颗粒物质的研究范畴。颗粒物质由离散的个体随机组合而成,其宏观表现既有固体的力学特性又有流体的流动特性,并随着条件的变化在两者间相互转化。在对颗粒物质宏观行为的研究中,可采用基于Cosserat连续体的有限元模型进行数值模拟,但这种连续模型在计算颗粒材料微结构的连续性假设使其不适用于颗粒物质发生大变形的情况。在对大变形的情况以及颗粒物质离散的特性研究中,离散单元法是以颗粒个体为研究对象,通过控制形状、尺寸、物理属性来构造颗粒单元并通过建立单元间相互作用的本构关系来描述颗粒物质的动力过程。该方法无需对颗粒物质进行诸多假设和限制,在研究颗粒物质时具有特有的优势。离散单元法研究中,球形单元因其简单的几何描述以及成熟的接触模型成为离散单元法中最经典的颗粒单元模型之一。采用球体单元可以满足对颗粒物质研究的一般要求。然而颗粒单元的几何形态对其宏观力学行为的影响不可忽略,在自然界中颗粒物质形态主要是以非规则颗粒为主。如何构造接近真实颗粒形态的复杂单元,进而提高颗粒单元之间接触过程的计算精度是离散单元法需要解决的重要问题。本文在离散单元球形单元的基础上,研究了扩展圆盘单元和扩展多面体单元两种非规则单元模型,以及这里种单元的应用。扩展圆盘单元是由球体和圆盘经过闵可夫斯基和运算得到的非规则单元。在计算扩展圆盘单元间的接触力时,根据扩展圆盘单元的几何特点将单元间的接触简化为两类:面-面接触和弧面-面接触。参考渤海莲叶冰的形状和冰的物理属性特征,将扩展圆盘单元作为冰块单元对海冰进行模拟研究。文中模拟了碎浮冰与直立桩腿结构的碰撞过程,分析了浪高和潮流对冰荷载的影响,研究表明碎浮冰产生的冰荷载明显低于波浪荷载。为研究平整冰对海洋结构的作用,通过粘结带将圆盘冰单元连接以模拟平整冰在潮流作用下与锥体结构发生接触碰撞而产生冰荷载的过程。模拟结果和现场实测数据对比分析发现,用这种粘结破碎冰模型得到的冰荷载特点与现场实测数据具有较高的一致性。针对铁路道砟碎石块等具有复杂几何形态的颗粒单元,用球形单元和多面体单元进行闵可夫斯基和运算得到扩展多面体单元模型,这种模型有尖锐的棱角和不规则的形态。根据单元模型的特点,将单元间的接触类型分成三类:面-面接触,点-面接触,棱-棱接触。文中用这种单元模型对铁路道砟在循环加载下的道砟箱试验进行模拟,研究道床沉降与循环荷载频率的关系,构造了不同尖锐度的道砟颗粒,研究了道砟颗粒尖锐程度对道床性能的影响。研究结果表明道砟颗粒尖锐度对道床的初始体密度和道床在循环荷载下的沉降量有显著影响。颗粒材料的剪切流动行为广泛地存在于滑坡、泥石流等自然灾害以及矿物原料传输、泵送等工业过程中。本文用扩展多面体单元模拟了块石的滑坡过程,研究了块石滑坡过程中颗粒堆的能量耗散情况。研究发现滑动摩擦是颗粒系统耗能的主要原因,在同样的工况下由于颗粒堆内部坍塌的原因,滑坡的移动速度比质量块的滑动速度快。颗粒材料在不同体积分数、剪切速率和应力约束下会表现出不同的流动状态并发生相互转化。本文研究了球形颗粒单元接触间的滚动阻尼,文中采用试验和数值模拟两种方法研究球形单元滚动阻尼的大小以及滚动阻尼对颗粒单元运动形态的影响。研究发现滚动摩擦和滑动阻尼将对颗粒或发生滚动或发生滑动的不同运动形态有很大影响。对颗粒材料在剪切流动过程中力学特性的研究有助于加深理解其发生不同流动状态的内在机理,为解决相应的颗粒材料问题提供理论依据。为此,本文研制了颗粒材料剪切流动的中型环剪仪,并对颗粒材料在不同法向约束应力和剪切速率下的剪切应力和体积膨胀率进行了测试。结果表明,剪切应力和体积膨胀率均随剪切速率的增加而增大,但增长速率在临界剪切速率处发生转变,使其随剪切速率的平方呈分段式线性增长。通过对颗粒材料在不同剪切速率和惯性数下有效摩擦系数变化趋势的分析,讨论了颗粒材料由慢速流向快速流转化的基本规律,以及在临界剪切速率处发生流动状态转化的内在条件。最后,对本文在扩展离散元模型方面的研究工作进行总结,并指出了后续工作的研究重点。
[Abstract]:Particulate matter is closely related to the production and life of human beings, such as the storage and transportation of grain, the settlement of the railway bed, the migration of sand dunes, and the landslide and debris flow. The particle material is composed of discrete individuals, and its macroscopic performance has both the mechanical properties of the solid and the fluid flow characteristics. In the study of macroscopic behavior of particulate matter, the finite element model based on Cosserat continuum can be used for numerical simulation in the study of macroscopic behavior of particulate matter. However, this continuous model is not suitable for large deformation of particulate matter by calculating the continuity hypothesis of the micro structure of granular materials. In the study of the discrete properties of particulate matter, the discrete element method is based on the particle individual as the research object. The particle elements are constructed by controlling the shape, size and physical properties, and the dynamic process of the particles is described by establishing the constitutive relation of the interaction between the units. In the study of the granular material, the spherical element is one of the most classical particle element models in the discrete element method because of its simple geometric description and mature contact model in the study of the discrete element method. The influence of morphology on its macroscopic mechanical behavior can not be ignored. In nature, the main form of granular material is irregular particles. How to construct complex elements close to the real particle shape and improve the calculation accuracy of contact process between particles is an important problem to be solved by discrete element method. On the basis of the form element, two irregular element models of the extended disk unit and the extended polyhedron element are studied, and the application of the unit is given. The extended disk unit is an irregular unit which is obtained by the sphere and the disk through Minkowski and the operation. The geometric features simplify the contact between the units into two categories: surface to surface contact and arc surface contact. Referring to the shape of the Bohai lotus Ye Bing and the physical properties of ice, the extended disk unit is used as an ice unit to simulate the sea ice. The collision process between the broken ice and the upright pile is simulated in this paper, and the wave height and the flow to the ice are analyzed. The study shows that the ice load produced by the crushed ice is obviously lower than the wave load. In order to study the effect of the ice on the ocean structure, the disc ice unit is connected by the bond zone to simulate the ice load caused by the contact collision of the flat ice with the cone structure under the action of the tide. The simulation results are compared with the field measured data. It is found that the ice load characteristics of the broken ice model are in good agreement with the field measured data. For the particle units with complex geometric shapes such as the railway ballast fragments, the spherical element and the polyhedron element are used for Minkowski and the extended polyhedral element model. This model has a sharp point. Sharp edges and irregular forms. According to the characteristics of the unit model, the contact types between units are divided into three types: face to face contact, point to surface contact, and prism contact. In this paper, the ballast box test of railway ballast under cyclic loading is simulated with this element model, and the relationship between the bed settlement and the frequency of cyclic loading is studied. The impact of the sharpness of ballast particles on the performance of ballast particles has been studied. The results show that the sharpness of ballast particles has a significant influence on the initial body density of the ballast bed and the settlement of the ballast bed under cyclic loading. The shear flow behavior of the granular materials is widely distributed in natural disasters such as landslides, debris flows and minerals. During the industrial process of raw material transmission and pumping. This paper simulates the landslide process of block stone with extended polyhedron element and studies the energy dissipation of the granular pile in the process of block stone landslide. It is found that the sliding friction is the main reason for the energy dissipation of the granular system. In the same working condition, the cause of the collapse of the particle heap and the speed of the landslide movement The sliding velocity of the mass is faster than the mass block. The particle material will show different flow states and transform each other under the different volume fraction, shear rate and stress constraint. In this paper, the rolling damping between the contact of spherical particles is studied. In this paper, two methods of experiment and numerical simulation are used to study the size of the rolling damping of the spherical element. It is found that the rolling friction and the sliding damping will have a great influence on the particle or the different motion patterns of the particles or rolling or sliding. The study of the mechanical properties of the granular material during the shear flow will help to deepen the understanding of the internal mechanism of the different flow state. This paper provides a theoretical basis for solving the corresponding particle material problem. Therefore, this paper has developed a medium ring shear apparatus for the shear flow of granular materials. The shear stress and volume expansion rate of the granular materials under different normal stress and shear rates were tested. The results showed that the shear stress and volume expansion rate increased with the shear rate. In addition, the growth rate is changed at the critical shear rate, which makes it linearly increase with the square of shear rate. By analyzing the change trend of the effective friction coefficient under different shear rate and inertia number, the basic law of the transformation from slow flow to fast flow is discussed, and the critical shear rate is discussed. The internal conditions for the transformation of the flow state at the cutting rate. Finally, the research work on the extended discrete element model is summarized, and the focus of the follow-up work is pointed out.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：O347.7
，

本文编号：2081054