三方程线性弹性-阻尼DEM模型及碰撞参数确定

建立了一种考虑法向接触力、切向接触力(含静滑动摩擦力及动滑动摩擦力)和力矩(含由切向力产生的力矩及静滚动摩擦力矩和动滚动摩擦力矩)的三方程线性弹性-阻尼离散单元模型,并将该模型应用到颗粒物料的三维数值模拟中,讨论了模型中几个重要碰撞参数--刚性系数、阻尼系数及摩擦系数的选择及其对计算结果的影响,同时也探讨了时间步长等计算参数对模拟结果的影响.为了验证算法和参数选择的正确性,本文对几个有代表性的颗粒系统进行了数值试验研究,并对计算结果进行了细致的分析,验证了新模型和参数选择的正确性.     

考虑粗糙结合面弹塑性接触的黏滑摩擦建模

提出一种同时考虑粗糙面上微凸体弹性变形和塑性接触的切向黏滑摩擦建模方法.采用Hertz弹性理论和Mindlin解描述弹性接触微凸体的切向载荷和相对变形的关系;采用AF(Abbott-Firstone)塑性理论和Fuji moto模型描述塑性接触微凸体切向载荷和相对变形的关系.再利用GW(Greenwood-Williamson)模型统计分析方法建立粗糙表面切向载荷和相对变形之间的关系.将模型与仅考虑微凸体弹性接触情况的模型进行对比,并研究了不同塑性指数对切向载荷和相对变形关系的影响.结果表明:与完全弹性接触模型相比,论文模型引入了塑性接触理论,能够更好地描述粗糙表面切向载荷和相对变形关系,并且考虑不同接触条件下弹性变形微凸体和塑性变形微凸体对切向接触载荷的贡献,在微滑移阶段,主要由弹性接触变形影响,而在进入宏观滑移阶段之后,切向行为主要由塑性变形影响.界面切向载荷由黏着和滑移接触作用共同决定,随着切向变形的增加,滑移接触力逐渐增加,而黏着接触力先增加后减少,反映了界面由微滑移逐渐向宏滑移演化的过程.随着塑性指数的增加,粗糙面上发生塑性接触的微凸体数目逐渐增加,切向黏滑行为主要受到塑性接触特征的控制.     

Viscous forces between two spheres colliding through interstitial power-law fluid

Interaction between two spheres with an interstitial fluid is essential in Discrete Element modeling for simulating the behaviors of ‘wet’ particulate materials. In this paper the interaction between two spheres with an interstitial Power-law fluid was approximately resolved as normal and tangential interactive models respectively, for which the governing equations were simplified on the basis of Reynolds approximation. These equations were then solved analytically together with the boundary conditions to obtain the pressure distributions for each individual model, and eventually solutions of the viscous squeeze force and the tangential viscous resistance were obtained, which provide a set of solutions for implementing into DEM code or other purposes.     

Multi-mechanism anisotropic model for granular materials

By representing the assembly by a simplified column model, a constitutive theory, referred to as sliding–rolling theory, was recently developed for a two-dimensional assembly of rods subjected to biaxial loading, and then extended to a three-dimensional assembly of spheres subjected to triaxial (equibiaxial) loading. The sliding–rolling theory provides a framework for developing a phenomenological constitutive law for granular materials, which is the objective of the present work. The sliding–rolling theory provides information concerning yield and flow directions during radial and non-radial loading. In addition, the theory provides information on the role of fabric anisotropy on the stress–strain behavior and critical state shear strength. In the present paper, a multi-axial phenomenological model is developed within the sliding–rolling framework by utilizing the concepts of critical state, classical elasto-plasticity and bounding surface. The resulting theory involves two yield surfaces and falls within the definition of the multi-mechanism models. Computational issues concerning the solution uniqueness for stress states at the corner of yield surfaces are addressed. The effect of initial and induced fabric anisotropy on the constitutive behavior is incorporated. It is shown that the model is capable of simulating the effect of anisotropy, and the behavior of loose and dense sands under drained and undrained loading.     

CFD-DEM simulation of the hole cleaning process in a deviated well drilling: The effects of particle shape

We investigate the effect of particle shape on the transportation mechanism in well-drilling using a three-dimensional model that couples computational fluid dynamics (CFD) with the discrete element method (DEM). This numerical method allows us to incorporate the fluid–particle interactions (drag force, contact force, Saffman lift force, Magnus lift force, buoyancy force) using momentum exchange and the non-Newtonian behavior of the fluid. The interactions of particle−particle, particle−wall, and particle−drill pipe are taken into account with the Hertz–Mindlin model. We compare the transport of spheres with non-spherical particles (non-smooth sphere, disc, and cubic) constructed via the multi-sphere method for a range of fluid inlet velocities and drill pipe inclination angles. The simulations are carried out for laboratory-scale drilling configurations. Our results demonstrate good agreement with published experimental data. We evaluate the fluid–particle flow patterns, the particle velocities, and the particle concentration profiles. The results reveal that particle sphericity plays a major role in the fluid–solid interaction. The traditional assumption of an ideal spherical particle may cause inaccurate results.     

机械结合面切向接触阻尼计算模型

针对两粗糙表面在法向力和切向力共同作用下相互接触时结合面切向阻尼的问题进行了研究。首先,根据KE模型对单个微凸体在弹性、弹塑性、塑性变形阶段的切向接触行为进行了分析,获得了微凸体在三个变形阶段的黏滑特性;然后,基于GW统计模型建立了一种在微凸体法向弹性、弹塑性和塑性变形机制基础上,考虑微凸体黏滑摩擦行为的机械结合面切向接触阻尼统计模型;最后,分别讨论了机械结合面的法向预载荷、切向激振频率和切向动态位移幅值对机械结合面切向阻尼的影响。研究表明:结合面切向接触阻尼系数随着结合面法向载荷的增大而增大,随着切向激振频率和切向动态位移幅值的增大而减小;在高频率、大幅值下,结合面切向接触阻尼系数几乎与动态位移幅值和激振频率无关。为了验证模型的准确性,构建了动态切向力作用下的结合面切向阻尼试验,其试验结果与理论仿真变化规律与量级基本一致,从而证明了本文所提出的切向阻尼模型的有效性。      

A hysteretic model of localized frictional contacts with instrumental stiffness

The steady-state dynamic response of a single-degree-of-freedom system comprising both a hysteretic element and a spring is considered. The Hertz–Cattaneo–Mindlin theoretical framework for modeling of local tangential contact with friction is applied in conjunction with the Masing model of hysteresis to describe the hysteretic behavior of the multiple localized frictional contact interface. The steady-state tangential displacement amplitude of a rigid body under harmonic tangential force excitation is approximately determined by means of the equivalent linearization technique, based on the harmonic balance principle. A special attention is paid to the evaluation of the frictional damping and the determination of the backbone curve of the Masing model from the dissipation-amplitude relation.

     

Theory of rolling: Solution of the Coulomb problem

A theory of rolling of round bodies in the normal mode with adhesion conditions satisfied on the entire contact area is proposed. This theory refines the classical Coulomb’s theory of rolling in which the rolling moment is directly proportional to the pressing force (e.g., the weight of the rolling body). The rolling moment of cylinders is found to be directly proportional to the pressing force raised to a power of 3/2, and the rolling moment of balls and tori is proportional to the pressing force raised to a power of 4/3. It is shown that the normal mode of uniform rolling can only be provided for a certain ratio of the elastic constants of the materials of the round body and the base forming an ideal pair. The Coulomb problem is solved for the cases of rolling of an elastic cylinder over an elastic half-space, of an elastic ball over an elastic half-space, of an elastic torus over an elastic half-space, and of a cylinder and ball over a tightly stretched membrane. The rolling law is derived for such cases. The rolling friction coefficients, the rolling moment, and the rolling friction force are calculated.     

Non-slipping adhesive contact between mismatched elastic spheres: A model of adhesion mediated deformation sensor

A generalized JKR model is established for non-slipping adhesive contact between two dissimilar elastic spheres subjected to a pair of pulling forces and a mismatch strain. We discuss the full elastic solution to the problem as well as the so-called non-oscillatory solution in which tension and shear tractions along the contact interface is decoupled from each other. The model indicates that the mismatch strain has significant effect on the contact area and the pull-off process. Under a finite pulling force, a pair of adhering spheres is predicted to break apart spontaneously at a critical mismatch strain. This study suggests an adhesion mediated deformation sensing mechanism by which cells and molecules can detect mechanical signals in the environment via adhesive interactions.     

车轮钢滚动剥离摩擦磨损特性研究

在NENE-2型摩擦磨损试验机上利用往复滚动试验装置研究了不同滚滑状态下车轮钢的剥离摩擦磨损特性和碳含量对车轮钢滚动剥离磨损性能的影响.结果表明:在不同滚滑状态下摩擦副之间的摩擦力不同,平面试样的表面磨痕形貌随着不同的切向摩擦力而明显不同,随着切向摩擦力的增大滚动磨损机制亦发生改变,剥离磨损加剧且磨损深度变大,当相对滑动量增大到一定程度后,磨损表现为明显的剥层机制;碳含量对车轮钢的滚动磨损表面磨痕形貌影响显著,碳含量低时磨痕以犁沟为主,碳含量高时剥离磨损发生的概率增加.     

Tangential interaction of elastic spherical particles in contact

The elastic interaction of spherical particles is studied. The distribution of the stress, normal to the contact plane, is determined by the rod model suggested recently, which is applicable in the more wide range of deformations as compared with the classical Hertz law. In the rod model context an inner part of compressed particles is regarded as an elastic cylindrical rod, which radius is equal to the contact radius. The rod reaction is added to the normal particle interaction corresponding with the Hertz solution. The resulting normal force passes into the Hertz solution for infinitesimal deformations and gives stronger particle repulsion for finite deformations. Here we solve the Mindlin problem for the rod model, i.e., derive the tangential interaction of initially compressed particles when a relative displacement takes place. The analytical expressions, which determine the total displacement of the sphere’s centers and the corresponding tangential force, are derived. So, the generalization of the classical Mindlin law is obtained for the rod model.     

Non-slipping adhesive contact between mismatched elastic cylinders

We have recently proposed a generalized JKR model for non-slipping adhesive contact between two elastic spheres subjected to a pair of pulling forces and a mismatch strain (Chen, S., Gao, H., 2006c. Non-slipping adhesive contact between mismatched elastic spheres: a model of adhesion mediated deformation sensor. J. Mech. Phys. Solids 54, 1548–1567). Here we extend this model to adhesion between two mismatched elastic cylinders. The attention is focused on how the mismatch strain affects the contact area and the pull-off force. It is found that there exists a critical mismatch strain at which the contact spontaneously dissociates. The analysis suggests possible mechanisms by which mechanical deformation can affect binding between cells and molecules in biology.     

Application of moment interaction to the construction of a stable model of graphite crystal lattice

The aim of the present paper is to construct and study a model of pair moment interaction between carbon atoms in the two-dimensional graphite lattice. The carbon atom is modeled by a structure consisting of three rigidly connected mass points located at the vertices of an equilateral triangle. The interaction between mass points is described by a pair force potential, but the total interatomic interaction contains moment components owing to the finite size of the structure modeling the atom. We compute rank 4 tensors characterizing the elastic properties of the graphite crystal lattice constructed on the basis of our model. We determine lattice stability criteria depending on the number of coordination spheres taken into account. We show that this model permits one to ensure stability of the graphite lattice but significantly underestimates the transverse-to-longitudinal interatomic coupling rigidity ratio. We construct a generalized moment potential that permits one to obtain a rigidity ratio consistent with experimental data.     

Investigation of elemental shape for 3D DEM modeling of interaction between soil and a narrow cutting tool

Discrete Element Method (DEM) has been applied in recent studies of soil cutting tool interactions in terramechanics. Actual soil behavior is well known to be inexpressible by simple elemental shapes in DEM, such as circles for 2D or spheres for 3D because of the excessive rotation of elements. To develop a more effective model for approximating real soil behavior by DEM, either the introduction of a rolling resistance moment for simple elemental shape or the combination of simple elements to form a complex model soil particle shape cannot be avoided. This study was conducted to investigate the effects of elemental shape on the cutting resistance of soil by a narrow blade using 3D DEM. Six elemental shapes were prepared by combining unit spheres of equal elemental radius. Moreover, cutting resistance was measured in a soil bin filled with air-dried sand to collect comparative data. The elemental shape, with an axial configuration of three equal spheres overlapped with each radius, showed similar results of soil cutting resistance to those obtained experimentally for the six elemental shapes investigated.     

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.      

填隙幂率流体下两刚性圆球相对错移时的粘性阻力

湿颗粒离散元模型以两球作用时填隙流体定常流动解为基础,其中切向作用是难点,国外仅有Goldman的牛顿流体渐近解.基于Reynolds润滑理论导出了两刚性球切向错动时填隙幂律流体的压力方程,并利用傅立叶级数展开简化,通过数值解法得到相应的压力分布、黏性阻力及阻力矩.该方程的解较之作者先前对速度场附加假定的结果精确,而当幂指数为1时等价于Goldman的牛顿流体渐近解.     

存在填隙幂律流体时圆球间切向作用的近似解

在Reynolds润滑理论的基础上，导出了存在填隙幂律流体时，两刚性圆球有相对切向运动时流体压力的近似方程，并进一步求得了圆球所受阻力矩的近似积分表达式，给出了问题的数值解。结果发现幂流体的幂指数、颗粒间最小间隙以及颗粒的大小都是流体压力和颗粒间切向阻力的重要因素。与Godman等人的牛顿流体下圆球平行于平面缓慢运动时圆球所受阻力以及阻力矩的渐近解作的比较表明，本文的数值解优于渐近解。     

柔性对多体系统中铰接副磨损的影响

通过集成柔性多体动力学与磨损计算程序,提出了一种用于对柔性多体系统中间隙铰接副部位的磨损进行了预测的方法.基于绝对节点坐标方法(ANCF)建立了柔性部件的多体动力学模型,引入Lankanrani和Nikravesh提出的连续接触力模型计算间隙铰接副部分的法向接触力,采用Lu Gre摩擦模型计算切向摩擦力,并利用基于Archard模型的迭代计算程序计算磨损.为了提高计算效率,引入了并行计算策略.最后,通过对一个含柔性连杆的曲柄滑块机构机构进行仿真计算,发现当考虑部件的柔性时,得到的间隙处的冲击力会大幅降低,预测的磨损量也随之降低,并且随着机构柔性的增强,这种效果更为明显.     

基于Iwan模型的接合面切向响应建模

针对工程中常见预紧力作用下的搭接接头,研究其在小幅切向位移激励时的切向位移响应问题,为此提出一种新的基于实际表面形貌和材料性能参数的滑移力密度分布函数.应用该分布函数得到搭接接头切向响应本构模型,并获得单位加载周期内的迟滞曲线和能量耗散值,通过与已出版的实验结果相对比,发现得到的模拟值与实验结果吻合,证明该模型的合理性.在此基础上利用该分布函数研究了接合面切向位移与切向力、切向接触刚度及能量耗散之间的关系,结果表明:建立的模型能很好地描述接合面间切向力与切向位移之间的关系,临界滑移力函数开始迅速上升,到达最大值后迅速收敛到零;切线力与切向位移之间表现出非线性特性,随着切向位移的增大,切向接触刚度表现出"软化"现象;初始切向刚度与法向载荷、粗糙度参数及塑性指数有关,对于确定的接触表面,法向力越大,初始切向刚度越大;初始切向刚度同样也随着塑性指数的增大而增大.