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.     

A semi-analytical model for the effective thermal conductivity of a multi-component polydisperse granular bed

A theoretical model to predict the effective thermal conductivity of a multi-component polydisperse granular bed is presented. A simple energy balance analysis is used to arrive at an approximate analytical expression for the effective thermal conductivity. Simulation of heat transfer in a granular bed is carried out using an open source Discrete Element Method (DEM) package called LIGGGHTS. The derived analytical expressions for the effective thermal conductivity compares well with the results obtained from DEM simulations for granular beds comprising of different components with different sizes.     

拆除爆破研究中数值分析方法的比较与选择

概述了数值分析法的分类。介绍了平面杆系有限元法、离散元法、数值流形法和不连续变形分析等几种数值分析方法。简单地讨论了平面杆系有限元法的分析步骤以及在拆除爆破中适于解决的问题 ;同时叙述了流形分析中采用的有限覆盖技术。通过分析和比较这几种方法在拆除爆破研究中的应用 ,作者认为 ,当前应用传统的有限元法进行爆破理论研究或拆除爆破模拟存在一些困难 ;离散元法用于拆除爆破理论的研究是可行的 ;不连续变形分析法对于拆除爆破模拟研究是一种具有良好前景的数值方法     

拆除爆破研究中数值分析方法的比较与选择

概述了数值分析法的分类。介绍了平面杆系有限元法、离散元法、数值流形法和不连续变形分析等几种数值分析方法。简单地讨论了平面杆系有限元法的分析步骤以及在拆除爆破中适于解决的问题 ;同时叙述了流形分析中采用的有限覆盖技术。通过分析和比较这几种方法在拆除爆破研究中的应用 ,作者认为 ,当前应用传统的有限元法进行爆破理论研究或拆除爆破模拟存在一些困难 ;离散元法用于拆除爆破理论的研究是可行的 ;不连续变形分析法对于拆除爆破模拟研究是一种具有良好前景的数值方法     

A multiscale DEM-FEM approach to investigate the tire–pavement friction

Abstract

Fundamental understandings of the pavement-tire friction are vital to improve the design of asphalt pavements. Most of the current research on pavement-tire friction is based on Finite Element Method (FEM), which is relatively complex and difficult to simulate the discontinuity during friction. To overcome the limitations, in this paper, the pavement–tire friction process is investigated using a coupled Multi-scale Discrete Element Method (DEM) – FEM approach. The benefit of such a multiscale method is that DEM has the advantage of simulating the discontinuity behaviour during friction, and FEM is good at simulating the continuum material with low computation consumption. The multi-scale approach provides an innovative and promising approach to simulate the tire-pavement friction behaviour.     

三维离散元与壳体有限元耦合的时空多尺度方法

壳体结构的局部失效及其对整体结构稳定性影响涉及到跨宏细观多尺度力学问题。该文推导出元/网格动量传递的多尺度算法,建立了三维离散元与壳体有限元耦合的时空多尺度数值计算方法。通过激光辐照下充内压圆柱壳局部失效算例的数值模拟,验证该多尺度方法能够完善地并行实现时间多尺度与空间多尺度计算,不仅能够准确模拟壳体结构局部细观非均匀演化及其对整体结构的影响,而且计算时间很少,有效地发挥了时空多尺度模拟高效率优势。     

Comprehensive numerical modelling of the hot isostatic pressing of Ti-6Al-4V powder: From filling to consolidation

Hot Isostatic Pressing (HIP) is a manufacturing process for production of near-net-shape components, where models based on Finite Element Method (FEM) are generally used for reducing the expensive experimental trials for canister design. Researches up to date implement in the simulation a uniform powder relative density distribution prior HIPping. However, it has been experimentally observed that the powder distribution is inhomogeneous after filling, leading to a non-uniform tool shrinkage. In this study a comprehensive numerical model for HIPping of Ti-6Al-4V powder is developed to improve model prediction by simulating powder filling and pre-consolidation by means of a two-dimensional Discrete Element Method (DEM). Particles’ dimension has been scaled up in order to reduce the computational cost of the analysis. An analytical model has been developed to calculate the relative density distribution from powder particle distribution provided by DEM, which is then passed in information to a three-dimensional FEM implementing the Abouaf and co-workers model for simulating powder densification during HIPping. Results obtained implementing the initial relative density distribution calculated from DEM are compared with those obtained considering a uniform relative density distribution over the powder domain (classic approach) at the beginning of the analysis. Experimental work has been carried out for validating the DEM (filling) and FEM (HIP) model. Comparison between experimental and numerical results shows the ability of the DEM model to represent the powder flow during filling and pre-consolidation, providing also a reliable values of the relative density distribution. It also highlights that taking into account the non-uniform powder distribution inside the canister prior HIP is vital to improve numerical results and produce near-net-shape components.     

SPH and FEM Investigation of Hydrodynamic Impact Problems

Simulation of hydrodynamic impact problems and its effect on surrounding structures, can be considered as a fluid structure coupling problem. The application is mainly used in automotive and aerospace engineering and also in civil engineering. Classical FEM and Finite Volume methods were the main formulations used by engineers to solve these problems. For the last decades, new formulations have been developed for fluid structure coupling applications using mesh free methods as SPH method, (Smooth Particle Hydrodynamic) and DEM (Discrete Element Method). Up to these days very little has been done to compare different methods and assess which one would be more suitable. In this paper the mathematical and numerical implementation of the FEM and SPH formulations for hydrodynamic problem are described. From different simulations, it has been observed that for the SPH method to provide similar results as FEM Lagrangian formulations, the SPH meshing, or SPH particle spacing needs to be finer than FEM mesh. To validate the statement, we perform a simulation of a hydrodynamic impact on an elasto-plastic plate structure. For this simple, the particle spacing of SPH method needs to be at least two times finer than FEM mesh. A contact algorithm is performed at the fluid structure interface for both SPH and FEM formulations. In the paper the efficiency and usefulness of two methods, often used in numerical simulations, are compared.     

A numerical algorithm for simulation of the electric corona discharge in the triode system

A numerical algorithm is described to calculate the charge density, electric field and corona current distribution in the corona triode. The algorithm employs a hybrid technique based on the Boundary and Finite Element Methods (FEM). FEM is used to determine the electric field because of free space charge produced by the corona discharge. The Boundary Element Method (BEM) is applied for calculating the other component of electric filed as a result of the voltage applied to the electrodes. The Method of Characteristics (MOC) is used to update the space charge density distribution. The characteristic lines are traced backwards from points of the analysed domain to the corona wire. The current density, electric field and space charge density distributions can be controlled by changing the configuration of the system. Results of calculations in a few different cases show the influence of different parameters on the work of the corona triode.     

散状物料转载系统设计DEM仿真方法的研究

颗粒仿真技术可以对散状物料的运动进行观察、机理分析、受力分析、磨损(寿命)估计和系统优化.比较了散状物料转载计算方法,给出了采用DEM方法的建模与模型检验的基本步骤.针对DEM计算方法存在所需计算时间过长的问题,实验比较了降低剪切模量和增大颗粒粒度等方法对DEM计算时间和实验结果的影响,结果表明,在不影响计算结果的前提下可通过降低剪切模量和增大颗粒粒度来缩短DEM仿真计算时间.利用EDEM软件实现了散料转载过程的可视化,比较分析了直线型溜槽、折线型溜槽和曲线型溜槽中物料转载效果.仿真表明：采用变曲率半径效果更好;U型溜槽截面能够减少物料不对中情况的发生.     

Velocity fields of granular flows down a rough incline: a DEM investigation

This paper describes a statistical method to explore the velocity profiles of granular flows down rough inclines. Using 3D Discrete Element Method (DEM), granular material is released from a box onto a slope and allowed to flow indefinitely. Fluctuating velocity fields are observed, as particle motions become more dynamic and agitated. Linear regression is used to decompose the fluctuating velocity field into a best-fit velocity profile and a fluctuating component. Analysis shows that the slope inclination has a considerable influence on the rheology, in terms of both the fluctuating velocity and the shear rate of the flow.     

Calibration and verification of DEM parameters for dynamic particle flow conditions using a backpropagation neural network

The Discrete Element Method (DEM) requires input parameters to be calibrated and validated in order to accurately model the physical process being simulated. This is typically achieved through experiments that examine the macroscopic behavior of particles, however, it is often difficult to efficiently and accurately obtain a representative parameter set. In this study, a method is presented to identify and select a set of DEM input parameters by applying a backpropagation (BP) neural network to establish the non-linear relationship between dynamic macroscopic particle properties and DEM parameters. Once developed and trained, the BP neural network provides an efficient and accurate method to select the DEM parameter set. The BP neural network can be developed and trained for one or more laboratory calibration experiments, and be applied to a wide range of bulk materials under dynamic flow conditions.     

Assessment of empirical formulas for prediction of the effects of projectile impact on concrete structures

The prediction of the response of structures subjected to projectiles impact may often be accomplished by means of empirical or semi‐empirical formulas available in the technical literature, which address mainly cases of relevance in engineering practice in terms of the observed failure modes. The paper presents an evaluation of the performance of the equations most widely used in predictions of penetration, scabbing and perforation of concrete and rock structures by comparing the predicted results with experimentally observed response and with the results of detailed numerical analyses employing the truss‐like Discrete Element Method (DEM). Numerical DEM predictions were shown to be close to the experimentally determined responses of concrete plates subjected to impact throughout the range of velocities examined and were also consistent with the empirical formulas. In all cases the authors attempted to quantify the uncertainty inherent both in the predictions of empirical formulas and of the numerical analysis.     

Simulation of potash cake strength by discrete element method

After potash ore has been mined and processed it is stored and shipped as bulk granular particles. If these particle beds are exposed to a relative humidity that is above 50%, moisture will accumulate in the bed. This causes the formation of concentrated brines on the surfaces of the particles that migrate toward the contact points between particles. If drying occurs crystal bridges at or near the contact points will form between particles. When large numbers of crystal bridges are formed per unit volume of bed, the bed is said to be caked. In this paper, the Discrete Element Method (DEM) is used to analyze the micro-mechanical behaviour of ideal spherical or ellipsoidal particles inside a potash bed and these results can be used to determine the cake strength. Hertz contact compressive stress theory is applied at each contact point between particles to resolve the stiffness matrix in the DEM analysis. The results of the DEM analysis compare well to those obtained using continuum mechanics for the case of a caked test ring in a centrifuge, especially when Poisson’s ratio has a low value.     

Superconductor Stability Revisited: Impacts from Coupled Conductive and Thermal Radiative Transfer in the Solid

Standard stability calculations following the Stekly, adiabatic or dynamic stability models apply purely solid thermal conduction mechanism, derive predictions under (quasi-) stationary and adiabatic conditions and assume ideal (mostly centrosymmetric) location of disturbances. Instead, the present paper takes into account also thermal radiative heat transfer in the superconducting solid, pool boiling, and considers the impact of random location and intensity of disturbances on the stability problem. The analysis is based on interplay between Monte Carlo radiative transfer calculations and a rigorous Finite Element method to calculate the resulting transient temperature field and stability functions. The combined Monte Carlo/Finite Element method is applied to 1G filament and 2G thin-film-coated high temperature superconductors. Results are strongly different from solutions achieved with standard, solely solid conduction thermal transport. It is not realistic, even in thin films, to assume uniform conductor temperature under transient disturbances. This may have significant consequences for design and simulation of performance of superconducting fault current limiters. There are doubts whether superconducting fault current limiters under any operation conditions could work in either pure flux flow or Ohmic resistive states.     

NOPD的椭球状散体元建模

提出了能模拟不同颗粒形状的微颗粒组合体的椭球状散体元模型,从理论上解决了椭球单元的接触判断及运动学、动力学问题。采用该模型对NOPD复合阻尼结构进行了动力学计算,计算结果与实验结果具有很好的一致性,为进一步研究NOPD的阻尼机理提供了一种理论分析方法。     

Packing of fine particles in an electrical field

A numerical model based on the Discrete Element Method (DEM) is developed to study the packing of fine particles in an electrical field related to the dust collection in an electrostatic precipitator (ESP). The particles are deposited to form a dust cake mainly under the electrical and van der Waals forces. It is shown that for the packing formed by mono-sized charged particles, increasing either particle size or applied electrical field strength increases packing density until reaching a limit corresponding to the density of random loose packing obtained under gravity. The corresponding structural changes are analyzed in terms of coordination number, radial distribution function and other topological and metric properties generated from the Voronoi tessellation. It is shown that these properties are similar to those for the packing under gravity. Such structural similarities result from the similar changes in the competition of the cohesive forces and the driving force in the packing. In particular, it is shown that by replacing the gravity with the electrical field force, the previous correlation between packing density and the ratio of the cohesive force to the packing-driven force can be applied to the packing of fine particles in ESP.     

单层网壳结构弹塑性屈曲分析的离散单元法研究

该文提出离散元塑性区法,即将任意2个球元的接触截面划分成若干小面积,通过各小面积的应力状态描述整个截面的塑性发展过程,较离散元塑性铰法更精确。该文推导了杆系离散元截面应变增量计算公式,建立了截面在三维应力-应变状态下的结构弹塑性本构方程、加卸载准则、截面内力积分公式以及计算分析流程。离散元弹塑性屈曲分析的追踪策略与弹性屈曲分析完全相同,即仍采用离散元力控制法或位移控制法。采用Fortran语言自编程序对若干单层网壳结构算例进行弹塑性屈曲分析,验证了离散元塑性区法的正确性和适用性,拓宽了离散单元法在工程领域的应用范围,为结构分析提供了新路径。