離散元法分析理論
2016-08-29 by:CAE仿真在線 來源:互聯(lián)網(wǎng)
離散元方法(DEM)首次于19世紀70年代由CundallandStrack在《A discrete numerical model for granular assemblies》一文提出,并不斷得到學者的關注和發(fā)展。離散元在我國起步比較晚,但是發(fā)展迅速,1986年第一屆全國巖石力學數(shù)值計算及模型試驗討論會上,王泳嘉首次向我國巖石力學與工程界介紹了離散元法的基本原理及幾個應用例子。
離散元基本原理
離散元法是專門用來解決不連續(xù)介質(zhì)問題的數(shù)值模擬方法。該方法把節(jié)理巖體視為由離散的巖塊和巖塊間的節(jié)理面所組成,允許巖塊平移、轉(zhuǎn)動和變形,而節(jié)理面可被壓縮、分離或滑動。因此,巖體被看作一種不連續(xù)的離散介質(zhì)。其內(nèi)部可存在大位移、旋轉(zhuǎn)和滑動乃至塊體的分離,從而可以較真實地模擬節(jié)理巖體中的非線性大變形特征。離散元法的一般求解過程為:將求解空間離散為離散元單元陣,并根據(jù)實際問題用合理的連接元件將相鄰兩單元連接起來;單元間相對位移是基本變量,由力與相對位移的關系可得到兩單元間法向和切向的作用力;對單元在各個方向上與其它單元間的作用力以及其它物理場對單元作用所引起的外力求合力和合力矩,根據(jù)牛頓運動第二定律可以求得單元的加速度;對其進行時間積分,進而得到單元的速度和位移。從而得到所有單元在任意時刻的速度、加速度、角速度、線位移和轉(zhuǎn)角等物理量。
離散元應用領域
離散元技術在巖土、礦冶、農(nóng)業(yè)、食品、化工、制藥和環(huán)境等領域有廣泛地應用,可分為分選、凝聚、混合、裝填和壓制、推鏟、儲運、粉碎、爆破、流態(tài)化等過程。顆粒離散元法在上述領域均有不少應用:料倉卸料過程的模擬;堆積、裝填和壓制;顆?;旌线^程的模擬。
相關計算機軟件
目前開發(fā)離散元商用程序最有名的公司要屬由離散元思想首創(chuàng)者Cundall加盟的ITASCA國際工程咨詢公司.該公司開發(fā)的二維UDEC(universal distinct element code)和三維3DEC(3-dimensional distinct elementcode)塊體離散元程序,主要用于模擬節(jié)理巖石或離散塊體巖石在準靜或動載條件下力學過程及采礦過程的工程問題.該公司開發(fā)的PFC2D和PFC3D(particle flow code in 2/3 dimensions)則分別為基于二維圓盤單元和三維圓球單元的離散元程序.它主要用于模擬大量顆粒元的非線性相互作用下的總體流動和材料的混合,含破損累計導致的破裂、動態(tài)破壞和地震響應等問題.Thornton的研究組研制了GRANULE程序,可進行包括不同形狀的干、濕顆粒結塊的碰撞一破裂規(guī)律研究,離散本構關系的細觀力學分析,料倉料斗卸料規(guī)律研究等.國內(nèi)離散元軟件的開發(fā)相對還比較落后,但隨著離散元方法研究在國內(nèi)的升溫,也出現(xiàn)了用于土木工程設計的塊體離散元分析系統(tǒng)2D—Block[oJ和三維離散單元法軟件TRUDEC及應用,以及北京大學劉凱欣研究小組開發(fā)的基于二維圓盤單元和三維球單元為基礎的SUPER-DEM離散元力學分析系統(tǒng)。
最近,中國科學院非連續(xù)介質(zhì)力學與工程災害聯(lián)合實驗室與極道成然科技有限公司聯(lián)合開發(fā)了國內(nèi)最新的離散元大型商用軟件GDEM,該軟件基于中科院力學所非連續(xù)介質(zhì)力學與工程災害聯(lián)合實驗室開發(fā)的CDEM算法,將有限元與塊體離散元進行有機結合,并利用GPU加速技術,可以高效的計算從連續(xù)到非連續(xù)整個過程。GDEM軟件擁有完全獨立的自主知識產(chǎn)權,代表了離散元的最高發(fā)展水平,讓國人和世界站在了同一起跑線上。
參考文獻:
A GPU Accelerated Continuous-based Discrete Element Method for Elastodynamics Analysis.
基于CDEM的高樁碼頭承載力數(shù)值模擬
離散元法及其在巖土工程中的應用綜述
顆粒流的離散元法模擬及其進展
離散元法研究的評述
離散元的歷史
離散元(discrete element method, distinct element method)是一種數(shù)值計算方法,主要用來計算大量顆粒在給定條件下如何運動。1971年Cundall提出此方法時采用ditinct element method是為了和連續(xù)介質(zhì)力學中的finite element method相區(qū)別。后來用discrete element method取代了distinct element method,以反映系統(tǒng)是離散的之一本質(zhì)特征。
1971年Cundall提出適于巖石力學的離散元法, 1979年Cundall和Strack又提出適于土力學的離散元法,并推出二維圓盤(disc)程序BALL和三維圓球程序TRUBAL(后發(fā)展成商業(yè)軟件PFC-2D/3D),形成較系統(tǒng)的模型與方法,被稱為軟顆粒模型;
離散元與分子動力學的比較
從本質(zhì)上來講,離散元和分子動力學方法類似(molecular dynamics),以至于有些作者在文獻中不加區(qū)別的使用MD和DEM兩個名字。然而離散元和分子動力學相似性只體現(xiàn)在形式上的相似(顆粒和牛頓定理)。二者還是有很大差別,在于分子動力學計算原子如何在給定相互作用勢下如何運動,而離散元計算的顆粒通常為微米及毫米量級。此外,離散元方法中需要考慮顆粒體在外力作用下的旋轉(zhuǎn)運動,顆粒的形狀,顆粒尺寸分布,以及顆粒之間填充氣體,液體對顆粒材料宏觀性能都有很大的影響??傊?即使計算模擬一個最簡單的顆粒系統(tǒng),單一尺寸的球形顆粒考慮摩擦作用下的運動問題都涉及到許多需要仔細考慮的細節(jié),然而正如其他模擬方法一樣,這些細節(jié)往往不會被作者在文章中出版,大多靠自己在實踐中去不斷領悟。
計算流程
第一步:建立所需要的幾何模型并產(chǎn)生顆粒。
幾何模型可以根據(jù)實際計算模型需要建立,顆粒產(chǎn)生通常為隨機產(chǎn)生,及在給定的幾何空間內(nèi)隨機產(chǎn)生所需要的顆粒。產(chǎn)生顆粒時需要實時監(jiān)測新產(chǎn)生的顆粒和已有顆粒之間的位置關系,任意兩顆粒之間不能有重疊,否則顆粒之間相互作用力可能很大而導致系統(tǒng)崩潰。所以如果幾何模型尺寸,顆粒尺寸以及顆粒數(shù)目之間關系不合適,有可能導致顆粒產(chǎn)生失敗。顆粒的初始速度需要根據(jù)模擬需要而給定。
第二步:確定接觸模型。
接觸模型是離散元計算的核心。所謂接觸模型就是確定顆粒接觸時的相互作用力。離散元計算中首先把相互作用力分解為法向力和切向力(法向指的是兩接觸顆粒中心之間的連線),所以接觸模型一般包含法向相互作用和切向相互作用。
中文名稱:離散元法英文名稱:distinct element method
定義:由康德爾建立的應用于不連續(xù)巖體的數(shù)值求解方法。即將含不連續(xù)面的巖體看作若干塊剛體組成,塊體之間靠角點作用力維持平衡。角點接觸力用彈簧和黏性元件描述,并服從牛頓第二定律。塊體的位移和轉(zhuǎn)動根據(jù)牛頓定律用動力松弛法按時步進行迭代求解。
應用學科:水利科技(一級學科);巖石力學、土力學、巖土工程(二級學科);巖石力學(水利)(三級學科)
離散元法(distinct element method,dem)是由cundall[1]提出的1種處理非連續(xù)介質(zhì)問題的數(shù)值模擬方法,其理論基礎是結合不同本構關系的牛頓第二定律,采用動態(tài)松弛法求解方程.
dem自問世以來,其主要應用領域集中在巖體工程和粉體(顆粒散體)工程.首先,在巖體計算力學方面,由于離散單元能更真實地表達節(jié)理巖體的幾何特點,便于處理所有非線性變形和破壞都集中在節(jié)理面上的巖體破壞問題,被廣泛應用于模擬邊坡、滑坡和節(jié)理巖體地下水滲流等力學過程.其次,在粉體工程方面,顆粒離散元被廣泛應用于粉體在復雜物理場作用下的復雜動力學行為的研究和多相混合材料介質(zhì)或具有復雜結構的材料力學特性研究中.它涉及到粉末加工、研磨技術、混合攪拌等工業(yè)加工領域以及糧食等顆粒離散體的倉儲和運輸?shù)壬a(chǎn)實際領域.
巖體工程中的dem與顆粒dem并無本質(zhì)不同,但在接觸處理以及一些概念的認識上有一定區(qū)別.例如,在節(jié)理巖體問題中,單元之間總是處于相互接觸或存在接觸—斷開的過程,均可視為準靜態(tài)情況,在此基礎上引入動態(tài)松弛法[2]將該準靜態(tài)問題化為動力學問題進行求解.動態(tài)松弛法要求選取合適的阻尼,使函數(shù)收斂于靜態(tài)值.在顆粒體問題中,顆粒間并不一定總存在接觸,顆粒體間的相互碰撞也表現(xiàn)為動態(tài)的過程,此時采用動態(tài)松弛法進行求解并非為了得到靜態(tài)值,而是為了引入阻尼系數(shù)以提供耗能裝置,達到最大程度的模擬效果.
本文旨在對顆粒dem中阻尼等計算參數(shù)的選取方法進行闡述,有關dem原理的詳細論述可參考文獻[3].
1阻尼系數(shù)選取
顆粒dem中阻尼系數(shù)的選取可參考連續(xù)介質(zhì)中阻尼的取法,引入工程中的黏性阻尼概念,采用rayleigh線性比例阻尼.rayleigh線性比例阻尼可以表示為
常用的系統(tǒng)振動阻尼比ζ的確定方法有半功率法和對數(shù)減量法等.
如前所述,rayleigh阻尼理論適用于連續(xù)介質(zhì)系統(tǒng),不完全適用于顆粒體這樣的非連續(xù)介質(zhì)系統(tǒng),因為非連續(xù)介質(zhì)系統(tǒng)隨著單元之間的滑移或分離,其振型不確定,但阻尼卻仍然存在,并可以用圖1所示的物理模型解釋.可以想象圖中質(zhì)量阻尼dm為把整個系統(tǒng)浸泡在黏性液體中,在物理意義上等價于用黏性活塞將顆粒單元與一不動點相連,使塊體單元的絕對運動受到阻尼.剛度阻尼ds在物理意義上等價于用黏性活塞把兩個接觸塊體相連,使顆粒單元之間的相對運動受到阻尼.
當顆粒之間接觸完全脫離,即不存在顆粒之間的相互接觸時,阻尼不再存在,或者將此時的阻尼理解為顆粒在空氣中受到的質(zhì)量阻尼.所以,在顆粒dem中,實際存在一個變阻尼的概念,包含至少兩套阻尼,即接觸時的質(zhì)量阻尼加剛度阻尼和無接觸時的空氣質(zhì)量阻尼.
對于連續(xù)介質(zhì)來說,其振型、最小圓頻率ωmin和最小臨界阻尼系數(shù)ξmin等能夠經(jīng)過計算與實驗得到.但是,對于非連續(xù)介質(zhì),由于其振型不確定,只能用試算的辦法確定這些參數(shù)進而計算阻尼系數(shù).顆粒dem中引入阻尼系數(shù)是為了提供耗能裝置,并非為了得到準靜態(tài)解,因此,阻尼系數(shù)的選取具有一定的靈活性,以滿足最大程度模擬為原則.
2剛度系數(shù)選取
對剛度系數(shù)的考慮見圖2,顆粒體a與顆粒體b存在兩個角邊接觸,接觸力分別為f1和f2,對于塊體a有平衡方程
3時步選取
時步計算的理論基礎是求解單自由度有阻尼彈性體系的中心差分格式下的臨界時步δt.對于動力方程
由推導可知,采用上述方法計算的時步能夠達到足夠小,可以保證顆粒之間的接觸過程得到充分模擬,不會出現(xiàn)這個時步顆粒之間剛剛開始接觸,下個時步顆粒間的接觸就反彈開了的現(xiàn)象,保證了接觸模擬的真實性.
4算例
下面給出采用本文作者編制的顆粒dem筒倉計算程序sisolv-2[4],對某大型筒倉的裝、卸料過程進行模擬的算例.對原60 m直徑、20 m倉高的筒倉按25∶3縮小建立模型,模型尺寸見圖3.模擬中采用的計算參數(shù)見表1.
5討論
顆粒dem看似簡單,其實卻很難.如何選取上述幾個參數(shù)對于初學者是很棘手的問題.要得到正確的模擬結果,需要在深入理解某些相關概念的基礎上通過試算得到阻尼等計算參數(shù),只有選取合理的計算參數(shù)才能保證模擬的真實性.
Discrete element method
A discrete element method (DEM), also called a distinct element method is any of family of numericalmethods for computing the motion of a large number of particles of micrometre-scale size and above. Though DEM is very closely related to molecular dynamics, the method is generally distinguished by its inclusion of rotational degrees-of-freedom as well as stateful contact and often complicated geometries (including polyhedra). With advances in computing power and numerical algorithms for nearest neighbor sorting, it has become possible to numerically simulate millions of particles on a single processor. Today DEM is becoming widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, and rock mechanics.
Discrete element methods are relatively computationally intensive, which limits either the length of a simulation or the number of particles. Several DEM codes, as do molecular dynamics codes, take advantage of parallel processing capabilities (shared or distributed systems) to scale up the number of particles or length of the simulation. An alternative to treating all particles separately is to average the physics across many particles and thereby treat the material as a continuum. In the case of solid-like granular behavior as in soil mechanics, the continuum approach usually treats the material as elasticor elasto-plasticand models it with the finite element methodor a mesh free method. In the case of liquid-like or gas-like granular flow, the continuum approach may treat the material as a fluidand use computational fluid dynamics. Drawbacks to homogenizationof the granular scale physics, however, are well-documented and should be considered carefully before attempting to use a continuum approach.
The DEM family
The various branches of the DEM family are the distinct element methodproposed by Cundallin 1971, the generalized discrete element methodproposed by Hocking, Williamsand Mustoein 1985, the discontinuous deformation analysis(DDA) proposed by Shiin 1988 and the finite-discrete element method concurrently developed by several groups (e.g., Munjizaand Owen). The general method was originally developed by Cundall in 1971 to problems in rock mechanics. The theoretical basis of the method was established by Sir Isaac Newton in 1697. Williams, Hocking, and Mustoe in 1985 showed that DEM could be viewed as a generalized finite element method. Its application to geomechanics problems is described in the bookNumerical Modeling in Rock Mechanics, by Pande, G., Beer, G. and Williams, J.R.. The 1st, 2nd and 3rd International Conferences on Discrete Element Methods have been a common point for researchers to publish advances in the method and its applications. Journal articles reviewing the state of the art have been published by Williams, Bicanic, and Bobetet al. (see below). A comprehensive treatment of the combined Finite Element-Discrete Element Method is contained in the bookThe Combined Finite-Discrete Element Methodby Munjiza.
Applications
The fundamental assumption of the method is that the material consists of separate, discrete particles. These particles may have different shapes and properties. Some examples are:
- liquidsand solutions, for instance of sugaror proteins;
- bulk materialsin storage silos, like cereal;
- granular matter, like sand;
- powders, like toner.
- Blocky or jointed rock masses
Typical industries using DEM are:
- Agriculture and food handling
- Chemical
- Civil Engineering
- Oil and gas
- Mining
- Mineral processing
- Pharmaceutical
- Powder metallurgy
Outline of the method
A DEM-simulation is started by first generating a model, which results in spatially orienting all particles and assigning an initial velocity. The forces which act on each particle are computed from the initial data and the relevant physical laws and contact models. Generally, a simulation consists of three parts: the initialization, explicit time-stepping, and post-processing. The time-stepping usually requires a nearest neighbor sorting step to reduce the number of possible contact pairs and decrease the computational requirements; this is often only performed periodically.
The following forces may have to be considered in macroscopic simulations:
- friction, when two particles touch each other;
- contact plasticity, or recoil, when two particles collide;
- gravity, the force of attraction between particles due to their mass, which is only relevant in astronomical simulations.
- attractive potentials, such as cohesion, adhesion, liquid bridging, electrostatic attraction. Note that, because of the overhead from determining nearest neighbor pairs, exact resolution of long-range, compared with particle size, forces can increase computational cost or require specialized algorithms to resolve these interactions.
On a molecular level, we may consider
- the Coulomb force, the electrostaticattraction or repulsion of particles carrying electric charge;
- Pauli repulsion, when two atoms approach each other closely;
- van der Waals force.
All these forces are added up to find the total force acting on each particle. An integration methodis employed to compute the change in the position and the velocity of each particle during a certain time step from Newton's laws of motion. Then, the new positions are used to compute the forces during the next step, and this loopis repeated until the simulation ends.
Typical integration methods used in a discrete element method are:
- the Verlet algorithm,
- velocity Verlet,
- symplectic integrators,
- the leapfrog method.
Long-range forces
When long-range forces (typically gravity or the Coulomb force) are taken into account, then the interaction between each pair of particles needs to be computed. The number of interactions, and with it the cost of the computation,increases quadraticallywith the number of particles. This is not acceptable for simulations with large number of particles. A possible way to avoid this problem is to combine some particles, which are far away from the particle under consideration, into one pseudoparticle. Consider as an example the interaction between a star and a distant galaxy: The error arising from combining all the stars in the distant galaxy into one point mass is negligible. So-called tree algorithms are used to decide which particles can be combined into one pseudoparticle. These algorithms arrange all particles in a tree, a quadtreein the two-dimensional case and an octreein the three-dimensional case.
However, simulations in molecular dynamics divide the space in which the simulation take place into cells. Particles leaving through one side of a cell are simply inserted at the other side (periodic boundary conditions); the same goes for the forces. The force is no longer taken into account after the so-called cut-off distance (usually half the length of a cell), so that a particle is not influenced by the mirror image of the same particle in the other side of the cell. One can now increase the number of particles by simply copying the cells.
Algorithms to deal with long-range force include:
- Barnes–Hut simulation,
- the fast multipole method.
Combined finite-discrete element method
Following the work by Munjiza and Owen's earlier work, the combined-discrete element method has been further developed to various irregular and deformable particles in many applications including pharmaceutical tableting,[1]packaging and flow simulations,[2]and concrete and impact analysis,[3]and many other applications.
Advantages and limitations
Advantages
- DEM can be used to simulate a wide variety of granular flow and rock mechanics situations. Several research groups have independently developed simulation software that agrees well with experimental findings in a wide range of engineering applications, including adhesive powders, granular flow, and jointed rock masses.
- DEM allows a more detailed study of the micro-dynamics of powder flows than is often possible using physical experiments. For example, the force networks formed in a granular media can be visualized using DEM. Such measurements are nearly impossible in experiments with small and many particles.
Disadvantages
- The maximum number of particles, and duration of a virtual simulation is limited by computational power. Typical flows contain billions of particles, but contemporary DEM simulations on large cluster computing resources have only recently been able to approach this scale for sufficiently long time (simulated time, not actual program execution time).
References
- ^ R W Lewis, D T Gethin, X-S Yang, R. Rowe, A Combined Finite-Discrete Element Method for Simulating Pharmaceutical Powder Tableting, Int. J. Num. Method in Engineering, 62, 853–869 (2005)
- ^ D T Gethin, X-S Yang and R W Lewis; A Two Dimensional Combined Discrete and Finite Element Scheme for Simulating the Flow and Compaction of Systems Comprising Irregular Particulates, Computer Methods in Applied Mechanics and Engineering, 195, 2006, 5552–5565 (2006)
- ^ I. M. May, Y. Chen, D. R. J. Owen, Y.T. Feng and P. J. Thiele: Reinforced concrete beams under drop-weight impact loads, Computers and Concrete, 3 (2–3): 79–90 (2006).
Bibliography
Book
- Ante Munjiza,The Combined Finite-Discrete Element MethodWiley, 2004, ISBN 0-470-84199-0
- Bicanic, Ninad,Discrete Element Methodsin Stein, de Borst, HughesEncyclopedia of Computational Mechanics, Vol. 1. Wiley, 2004. ISBN 0-470-84699-2.
- Griebel, Knapek, Zumbusch, Caglar:Numerische Simulation in der Molekulardynamik. Springer, 2004. ISBN 3-540-41856-3.
- Williams, J.R., Hocking, G., and Mustoe, G.G.W., “The Theoretical Basis of the Discrete Element Method,” NUMETA 1985, Numerical Methods of Engineering, Theory and Applications, A.A. Balkema, Rotterdam, January 1985
- Pande, G., Beer, G. and Williams, J.R.,Numerical Modeling in Rock Mechanics, John Wiley and Sons, 1990.
- Farhang Radja? and Frédéric Dubois, "Discrete-element Modeling of Granular Materials", Wiley, 2011, ISBN 978-1-84821-260-2
- Thorsten P?schel and Thomas Schwager,Computational Granular Dynamics, models and algorithms. Springer, 2005. ISBN 3-540-21485-2.
Periodical
- A. Bobet, A. Fakhimi, S. Johnson, J. Morris, F. Tonon, and M. Ronald Yeung (2009) "Numerical Models in Discontinuous Media: Review of Advances for Rock Mechanics Applications", J. Geotech. and Geoenvir. Engrg., 135 (11) pp. 1547–1561
- P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies.Geotechnique,29:47–65, 1979.
- Kawaguchi, T., Tanaka, T. and Tsuji, Y., Numerical simulation of two-dimensional fluidized beds using the discrete element method (comparison between the two- and three-dimensional models)Powder Technology,96(2):129–138, 1998.
- Williams, J.R. and O’Connor, R.,Discrete Element Simulation and the Contact Problem, Archives of Computational Methods in Engineering, Vol. 6, 4, 279–304, 1999
- Zhu HP, Zhou ZY, Yang RY, Yu AB. Discrete particle simulation of particulate systems: Theoretical developments. Chemical Engineering Science. 2007;62:3378-3396
- Zhu HP, Zhou ZY, Yang RY, Yu AB. Discrete particle simulation of particulate systems: A review of mayor applications and findings. Chemical Engineering Science. 2008;63:5728-5770.
Proceedings
- Shi, G, Discontinuous deformation analysis – A new numerical model for the statics and dynamics of deformable block structures, 16pp. In1st U.S. Conf. on Discrete Element Methods, Golden. CSM Press: Golden, CO, 1989.
- Williams, J.R. and Pentland, A.P., "Superquadric and Modal Dynamics for Discrete Elements in Concurrent Design," National Science Foundation Sponsored 1st U.S. Conference of Discrete Element Methods, Golden, CO, October 19–20, 1989.
- 2nd International Conference on Discrete Element Methods, Editors Williams, J.R. and Mustoe, G.G.W., IESL Press, 1992 ISBN 0-918062-88-8
Software
Open source and non-commercial software:
- AscalaphMolecular dynamicswith fourth order symplectic integrator.
- BALL & TRUBAL (1979–1980) distinct element method (FORTRAN code), originally written by P.Cundall and currently maintained by Colin Thornton.
- dp3D(discrete powder 3D), DEM code oriented toward material science engineering applications (powder compaction, powder sintering, fracture of brittle materials...). Emphasis is put on the physics of the contact laws. dp3D is written in fortran 90 and heavily parallelised with OpenMP.
- ESyS-ParticleESyS-Particle is a high-performance computing implementation of the Discrete Element Method released under the Open Software License v3.0. To date, development focus is on geoscientific applications including granular flow, rock breakage and earthquake nucleation. ESyS-Particle includes a Python scripting interface providing flexibility for simulation setup and real-time data analysis. The DEM computing engine is written in C++ and parallelised using MPI, permitting simulations of more than 1 million particles on clusters or high-end workstations.
- LAMMPSis a very fast parallel open-source molecular dynamics package with GPU support also allowing DEM simulations. LAMMPS Website, Examples.
- LIGGGHTSis a code based on LAMMPS with more DEM features such as wall import from CAD, a moving mesh feature and granular heat transfer. Further a coupling to CFD is available. LIGGGHTS Website
- SDECSpherical Discrete Element Code.
- LMGC90Open platform for modelling interaction problems between elements including multi-physics aspects based on an hybrid or extended FEM – DEM discretization, using various numerical strategies as MD or NSCD.
- PasimodoPASIMODO is a program package for particle-based simulation methods. The main field of application is the simulation of granular media, such as sand, gravel, granulates in chemical engineering and others. Moreover it can be used for the simulation of many other Lagrangian methods, e.g. fluid simulation with Smoothed-Particle-Hydrodynamics.
- YadeYet Another Dynamic Engine (historically related to SDEC), modular and extensible toolkit of DEM algorithms written in c++. Tight integration with Python gives flexibility to simulation description, real-time control and post-processing, and allows introspection of all internal data. Can run in parallel on shared-memory machines using OpenMP.
- MechSysAlthough it is initially a package dedicated to the FEM method, it also contains a DEM module. It uses both spherical elements and spheropolyhedra to model collision of particles with general shapes. Both elastic and cohesive forces are included to model damage and fracture processes. Parallelization is achieved mostly by the new std::thread library of the new C++ standard. There is also a module dealing with the coupling between DEM and LBM still under development.
Commercially available DEM software packages include PFC3D, EDEM and Passage/DEM:
- Bulk Flow Analyst (Applied DEM)General-purpose 3D DEM tool for mechanical engineering applications. Imports many types of 3D modelling files (including DXF, IGES, and STEP) and integrates with AutoCAD and SolidWorks as well as providing its own 3D interface.
- Chute Analyst (Overland Conveyor Company)3D DEM tool for transfer chute engineering applications. Imports many types of 3D modelling files (including DXF, IGES, and STEP) and integrates with AutoCAD and SolidWorks as well as providing its own 3D interface.
- Chute Maven (Hustrulid Technologies Inc.)Spherical Discrete Element Modeling in 3 Dimensions. Directly reads in AutoCad dxf files and interfaces with SolidWorks.
- EDEM (DEM Solutions Ltd.)General-purpose DEM simulation with CAD import of particle and machine geometry, GUI-based model set-up, extensive post-processing tools, progammable API, couples with CFD, FEA and MBD software.
- ELFEN
- GROMOS 96
- MIMESa variety of particle shapes can be used in 2D
- PASSAGE/DEM(PASSAGE/DEM Software is for predicting the flow particles under a wide variety of forces.)
- PFC (2D & 3D)Particle Flow Code.
- SimPARTIXDEM and SPH simulation package from Fraunhofer IWM
- StarCCM+Engineering analysis suite for solving problems involving flow (of fluids or solids), heat transfer and stress.
- UDECand 3DECTwo- and three-dimensional simulation of the response of discontinuous media (such as jointed rock) that is subject to either static or dynamic loading.
- DEMpackDiscrete / finite element simulation software in 2D and 3D, user interface based on GiD.
- MFIX
See also
- Movable Cellular Automata
- Finite element method
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