Discrete element representation of continua: Proof of concept and determination of the material parameters

A common approach for the modelling of metal or microfibre reinforced materials is to see these materials as a continuum on the macro scale. A major drawback is that an equation based on the continuum theory is unable to predict the various complicated microscopic effects, even though those effects have a strong influence on the macroscopic behaviour, e.g. on fracture, fatigue and life time. A large number of attempts has been made to correct the shortcomings of the continuum-based theories. One interesting alternative to common approaches for the numerical modelling of discontinuous materials is the Discrete Element Method (DEM). Within the DEM, the individual particles are modelled as stiff (or rigid) bodies which interact via contact forces. This simplification has the advantage of the complicated microscopic behaviour being represented by a simple system of linear equations based on a relatively small number of parameters.This paper describes the requirement for new computational methods for the modelling of fracture mechanics. First of all a proof of the described method will be shown. Then two examples are presented in order to verify the Discrete Element Method. Furthermore it will be shown how the corresponding material parameters are gained and implemented and how the boundary conditions have to be modelled in order to achieve exact results for the stress and strain fields of 2D shells.     

Modelling of Woven Fabrics with the Discrete Element Method

The mechanical behaviour of woven fabrics is dominated by the kinematics of the constituents on the microscopic scale. Their macroscopic response usually shows non-linearities which are due to the mobility of the interlaced yarns. The major deformation mechanisms of fabrics, i.e. the crimp interchange in case of biaxial tension and the trellising motion of the yarns in case of shear, reflect the dependency of the macroscopic material behaviour on the microstructural deformation mechanisms.
We present a novel modelling approach for woven fabrics which is capable to represent directly and locally the microstructure and its kinematics at yarn level. With only a small set of assumptions on the micro-scale the complex macroscopic material behaviour can be directly obtained. The proposed model uses the Discrete Element Method (DEM) for the representation of the fabric's microstructure. It is intrinsically dynamic since the equations of motion are solved numerically for every mass point through an application of an explicit finite difference technique. The model covers the full mobility of the fabric's microstructure while being efficiently enough to model macroscopic patches of the material.
With this model we can study the influence of the different material features of the micro-scale on the macroscopic material behaviour. With some further extensions accounting for coatings or embeddings, the range from pure fabrics to fabric reinforced membranes and composites can be covered. Problems related to large deformations and localization as well as damage can be addressed with the presented modelling approach.     

颗粒流的离散元法模拟及其进展

颗粒流问题是众多工农业生产领域中的常见问题,然而人们至今对颗粒流机理认识不深。目前一种基于离散元的数值模拟方法被用以模拟和分析颗粒流问题,研究实践表明该方法是散体力学分析的一种有效的工具。本文介绍了颗粒流研究的背景以及离散元法的发展过程,概述了颗粒流动力学研究的动理论模型和摩擦塑性模型,综述了离散元法的理论和各种颗粒作用模型及其在粉体工程领域的应用,讨论了颗粒流研究的主要困难和离散元法发展中亟待解决的问题。     

On the determination of material parameters in crack initiation laws

Crack initiation along slip bands can be described by the Tanaka–Mura relation and its extensions. These relations are based on dislocation theory and determine the number of load cycles to reach a critical dislocation density for a given value of the resolved shear stress along the potential crack path. An important material parameter in these relations is the critical shear stress which is a threshold value for crack initiation, i.e. the number of cycles to crack initiation becomes infinitely high if the resolved shear stress along the potential crack path stays below this threshold value. This critical shear stress is determined using a database for microcrack initiation, microcrack growth, and coalescence obtained with a martensitic steel. The number of cracks per unit area, the so‐called crack density, was derived from this database as a function of the number of load cycles. These experimentally observed values of the crack density are compared to values obtained by simulating the crack initiation process using a random cell structure as a mesoscopic unit cell. A best fit is obtained for values of the critical shear stress between 110 and 160 MPa with the uncertainty both related to simplifications in the model and to limitations of the experimental analysis.     

A goal-oriented field measurement filtering technique for the identification of material model parameters

The post-processing of experiments with nonuniform fields is still a challenge: the information is often much richer, but its interpretation for identification purposes is not straightforward. However, this is a very promising field of development because it would pave the way for the robust identification of multiple material parameters using only a small number of experiments. This paper presents a goal-oriented filtering technique in which data are combined into new output fields which are strongly correlated with specific quantities of interest (the material parameters to be identified). Thus, this combination, which is nonuniform in space, constitutes a filter of the experimental outputs, whose relevance is quantified by a quality function based on global variance analysis. Then, this filter is optimized using genetic algorithms.     

基于离散元方法的RDX-Al颗粒混合数值模拟分析

基于离散元方法,以旋转筒内RDX-Al二元颗粒体系的搅拌过程为研究对象进行模拟。采用离散元软件(EDEM),首先研究RDX-Al二元颗粒各自随转速的变化趋势,并进一步得出二元颗粒变化率的特点,做出分布上的拟合,得出最吻合模拟试验的函数为指数函数。然后,将旋转筒细分为多个单元空间,考察旋转轴与单元空间之间的距离对二元颗粒混合效果的影响。结果表明:单元空间离旋转轴越远,即旋转半径越大,颗粒之间的变化率也就越快,越容易达到均匀状态。最后,考察加入抄板的影响,结果表明:RDX-Al二元颗粒趋于的稳定值分别发生了改变。     

EMC材料参数对微电子封装器件热应力的影响

利用动态机械分析仪测定环氧模塑封(EMC)材料的粘弹性数据,并用广义麦克斯韦模型表征了EMC材料的粘弹松弛特性;利用热机械分析仪获得了EMC材料在不同温度时的尺寸变化量,并通过线性拟合得到了EMC材料的热膨胀系数。使用有限元软件MSC Marc分别模拟了基于EMC粘弹性、弹性两种不同性质时,QFN器件在-55~+125℃温度条件下热应力分布,并分析了热膨胀系数对热应力的影响。结果表明:QFN器件的最大热应力出现在粘接剂、芯片和EMC材料的连接处,有限元分析中EMC的材料性质和热膨胀系数会对热应力产生较大影响。     

离散单元法在行星式球磨机仿真中的应用

为了认识与系统结构、操作条件以及材料性能相关的参数对行星式球磨机研磨性能的影响,对国内外将离散单元法用于模拟和分析行星式球磨机球磨过程的研究进行归纳和总结,阐述从物料运动、能量转换、磨损和大型化等领域的研究与应用成果。结果表明:操作条件的优化可使有效碰撞和高能碰撞处于较优的比例;具体环境下,冲击和研磨对于物料细化的效果有待探索;粉体的团聚和润滑作用会阻碍粉体的细化;几何相似大型化后的介质碰撞能量正比于规模化比例的4.87次方。     

Discrete Element Method Analysis of Railtrack Ballast Degradation during Cyclic Loading

Ballast materials forming part of railway structures are subjected to cyclic loads. As a result of these loads, ballast densification, aggregate degradation, and lateral spread of the ballast material underneath the ties takes place inducing permanent deformations on the railways. Maintenance and rehabilitation costs of railtracks due to problems related with ballast performance are substantial, and millions of dollars are annually spent around the world in these activities. Understanding the crushable behavior of railtrack ballast could lead to the design of better railways that will reduce these costs. This paper presents the results of two discrete element method simulations intended to study the effect of crushing on the behavior of a simulated track ballast material forming part of a simulated track section. Even though the two simulations consider the same idealized material, crushing was allowed only in one simulation. The simulated track sections were subjected to a cyclic load, and the values of permanent deformation as a function of number of cycles were recorded. The obtained results showed that the induced permanent deformation strongly increased when considering particle crushing even though only a few particles were broken. Moreover, it was found that crushing concentrated underneath the simulated sleepers. Snap shots of the track sections are presented allowing a visualization of the evolution of crushing.     

基于离散元法的催化剂密相装填过程数值模拟

基于颗粒离散元法,对一种椭圆形密相装填器的催化剂密相装填过程进行数值模拟研究,分析布料盘转速和颗粒直径对装填过程的影响。结果表明:催化剂颗粒装填速度不等于布料盘上方料斗下料速度,而是随着布料盘转速增大而增大,随颗粒直径增大而减小。催化剂颗粒在反应器底部分布的直径范围与颗粒直径大小无关,它随着布料盘转速增大而增大。颗粒与反应器的碰撞是造成颗粒破碎的主要因素。利用该设备装填球形催化剂颗粒时,催化剂床层中心会出现凹陷现象,当颗粒直径较小时,床层中心附近会出现驼峰状的凸起。     

基于离散元法的果粒灌装输送过程仿真

目的 针对甜橙果粒灌装效率低的问题,提出一种高效精确的果粒灌装输送设备.方法 建立灌装设备的三维模型,研究螺旋叶片几何参数以及果粒特性对果粒罐装过程的影响.结果 果粒灌装设备能够较好地完成果粒灌装,颗粒质量流率比初始值提高了6倍以上;粘性物料颗粒在螺旋输送的过程中能保持较稳定的聚团性,这一特性只与颗粒的表面能有关;在螺旋输送过程中可通过工艺优化增大颗粒的表面能,以达到颗粒在螺旋输送过程中保持明显的稳定性和提高输送效率的目的,当颗粒表面能为0.1 J/m2时,颗粒之间表现出稳定性,在表面能为1.3 J/m2时螺旋输送效率达到最大.结论 经过分析优化,文中提出的灌装设备能够有效实现果粒的高效灌装.     

岩石爆炸增渗模型实验及DEM数值模拟研究

岩体中爆炸提高矿石的渗透性可以极大地提高采矿效率,是碎裂岩型矿床预裂浸出法的关键技术.混凝土与岩体都具有脆性材料的特性,因此用浇筑于铁桶中的混凝土试件进行模型实验研究岩体的爆炸增渗效果.铁桶可以提高实验效率,使边界条件更为简单和易于操作,但是,实验和原型的差异需要论证.用自主开发的基于连续介质力学模型的离散元方法,模拟了有铁桶边界的模型实验,验证了数值模拟方法的可行性及有效性,给出了有弹性侧限边界约束的混凝土和较大尺度无反射边界条件的岩石中的爆炸差别.在此基础上,分析了岩石中爆炸造成的岩石破坏规律.计算结果表明:岩石破坏面总面积和破坏区的最大裂缝宽度受药量和岩石的抗拉强度影响,破坏面总面积和裂缝宽度随药量增加而增大,随抗拉强度增大而减小;在药量相同的条件下,实际岩石环境下的岩块破坏程度比铁桶约束的大.模型实验和数值模拟相结合的办法可以对混凝土和岩石的爆炸破坏给出较为合理的结果.     

Simulation of fresh concrete flow using Discrete Element Method (DEM): theory and applications

This article provides an overview of the development and the contemporary state of research in the field of simulating fresh concrete flow using the Discrete Element Method (DEM). First, this work originating from TC 222-SCF simulation of fresh concrete flow, covers the mathematical methodology, the identification of the model parameters and the link between the rheological properties of fresh concrete and the parameters of DEM-based models. Various examples of the estimation of model parameters and calibration of the model were demonstrated, followed by verifications by comparing the numerical results and the corresponding predictions by analytical formula and laboratory experiments. Furthermore, software used in concrete engineering and existing industrial applications of the developed particle models were described, showing the potential of DEM.     

An inverse method for material parameters determination of titanium samples under tensile loading

Different approaches used for the simulation of woven reinforcement forming are investigated. Especially several methods based on finite element approximation are presented. Some are based on continuous modelling, while others, called discrete or mesoscopic approaches, model the components of the fabric. A semi discrete finite element made of woven unit cells under biaxial tension and in-plane shear is detailed. In continuous approaches, the difficulty lies in the necessity to take the strong specificity of the fibrous material into account. The yarn directions must be strictly followed during the large strains of the fabric. This is the main goal of the non-orthogonal model and of the hypoelastic constitutive model based on the yarn rotation presented in this paper. In the case of discrete and semi-discrete approaches the directions of the yarns are “naturally” followed because the yarns are modeled. Explicitly, however, modeling each component at the mesoscopic scale can lead to high numerical cost.     

Optimisation methods for the determination of cyclic material parameters from strain controlled uniaxial fatigue tests

Four new methods are presented for the determination of cyclic strain-life curves according to Manson/Coffin/Basquin/Morrow and of cyclic stress–strain curves according to Ramberg/Osgood from results of strain controlled uniaxial fatigue tests. The material parameters are assessed by combined linear regressions of linearised parts of these curves with the method of least squares either in strain–stress-life space or in stress–strain and strain-life planes. The compatibility terms are applied as constraints. Experimental data from fourteen test series of magnesium die-casting alloys AE42, AM50, and AZ91 at different elevated temperature levels between 30 °C and 140 °C is used exemplarily. The four new methods and two methods known from literature, which lack combined linear regression, are valuated with six different measures, which are based on the remaining absolute deviation. The comparison shows that the method that combines the linear regressions of the plastic part of the cyclic stress–strain curve and the elastic and plastic part of the strain-life curve in an optimisation leads to the best results.     

基于离散元方法的沥青混合料力链演化及分布量化分析

为了研究沥青混合料内部颗粒间力链的演化及分布规律,以AC-13沥青混合料作为研究对象,利用离散元方法重构沥青混合料数字试件,模拟简单性能试验,提取试件内部颗粒间的力链信息进行力链演化、概率分布和角度分布分析。结果表明,通过比较预测结果和实测结果,基于离散元方法重构的AC-13沥青混合料细观模型用于模拟其细观力学特性是可行的。试件内部力链空间分布具有各向异性,以垂直方向的压力力链为主,承受大部分的半正弦荷载。法向力链概率分布随加载时间的变化规律基本一致,法向接触力与平均法向接触力比值f最小时,概率分布出现最大值,f=1.75时,概率分布再次达到峰值,然后逐渐减小并趋于稳定。法向力链角度分布主要位于90°和270°附近,第一、二象限的角度分布比例远大于第三、四象限,60~120°、30~150°中法向力链角度分布比例均大于70%,最小为72.733%。     

基于离散单元法的砂轮磨料粉体流动性研究

目的在不同摩擦因数工况下进行磨料粉体自由卸料的流动性研究。方法根据粉体流动性评价方式,建立流动性表征指标;基于离散单元法原理,利用PFC3D软件建立料仓粉体自由卸料模型,仿真砂轮磨料在不同摩擦条件下的自由卸料运动过程;根据仿真结果,分析磨料粉体摩擦因数变化对其流动性的影响,利用表征指标评价流动性,建立流动性函数。结果摩擦因数为0.4时,磨料粉体的流动性能最佳。结论随着摩擦因数增大,砂轮磨料粉体流速减小,流动稳定性提高。     

Modeling the Dynamics of Fabric in a Rotating Horizontal Drum Using the Discrete Element Method

In order to provide a tool for designing more efficient methods of mixing fabric, a simplified discrete element computational model was developed for modeling fabric dynamics in a rotating horizontal drum. Because modeling the interactions between actual pieces of fabric is quite complex, a simplified model was developed where individual pieces of bundled fabric are represented by spherical particles. This model is essentially a ball mill. The simulations are used to investigate fabric bundle kinematics, the power required to drive the rotating drum, and the power dissipated through normal and tangential contacts. Parametric studies were performed to investigate the effects of fill percentage, baffles, rotation speed, friction coefficient, and coefficient of restitution. The simulation results indicate that fill percentage, drum rotation speed, and friction coefficient play significant roles in the fabric bundle dynamics. For example, the specific drum power increases by a factor of 600% to 800% as the fill percentage decreases from 75% to 25%. In addition, the maximum specific drum power occurs at a rotation speed just less than the speed at which centrifuging occurs. The friction coefficient does not play a significant role in the bundle dynamics for values greater than a critical value. The critical value decreases from a value of approximately 0.3 at a 25% fill percentage to 0.05 for a 75% fill percentage. For friction coefficients less than this critical value, the specific power decreases with decreasing friction coefficient. Drum baffles have a minor effect on the power dissipation and kinematics for fill percentages greater than 50%. Bundle size and coefficient of restitution have a relatively weak influence on the measured parameters.