DOCSLIB.ORG

Discrete Element Simulation of the Behavior of Bulk Granular Material During Truck Braking

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Discrete Element Simulation of the Behavior of Bulk Granular Material During Truck Braking The current issue and full text archive of this journal is available at www.emeraldinsight.com/0264-4401.htm EC 23,1 Discrete element simulation of the behavior of bulk granular material during truck braking 4 Shu-chun Zuo, Yong Xu and Quan-wen Yang Department of Applied Mechanics, China Agricultural University, Beijing, Received July 2004 Revised May 2005 People’s Republic of China, and Accepted June 2005 Y.T. Feng Civil & Computational Engineering Centre, School of Engineering, University of Wales Swansea, Swansea, UK Abstract Purpose – To simulate the dynamic feature of bulk granular material (such as agricultural products) during sudden braking of a truck by applying discrete element method. Design/methodology/approach – The bulk granular material was modeled by the discrete element approach, in which the spherical elements were used to represent the granular particles; the interaction between two in-adhesive particles was modeled by Hertz for normal interaction, and by Mindlin and Deresiewicz for tangential interaction; the interaction between two particles with adhesion was modeled by the JKR theory for normal interaction, and by Thornton’s theory for the tangential interaction. Different initial conditions (braking speeds/accelerations) were considered. The dynamic system was numerically solved by the central difference based explicit time integration, and the dynamic impact forces were recorded to further analysis. Findings – The computation predicted that the resultant dynamic force acting upon the front wall behaves in four stages, i.e. increasing, plateau, sharp increasing and drop with damped fluctuation. It was observed that, the shorter the breaking time is, the faster the force reaches its peak, and the greater the peak value is. The phenomenon was in good agreement with physical principals and common knowledge. Research limitations/implications – It is an application of the discrete element method and, therefore, no important contribution is made to advance the methodology. Practical implications – The proposed modeling approach may serve as a useful tool for advanced design of trucks. Originality/value – This paper is the first to apply the advanced discrete element method to the problem concerned. Keywords Land transport, Linear motion, Mechanical properties of materials Paper type Research paper 1. Introduction Transport of particulate materials with trucks is common in various industries and road freight. Such a granular matter has its special characteristics, e.g. flow-ability and Engineering Computations: International Journal for fluctuation in physical properties. Therefore, its macroscopic responses and behavior Computer-Aided Engineering and may differ from other solid structured products during braking, pitching or turning, Software Vol. 23 No. 1, 2006 pp. 4-15 This work is funded by the Natural Science Foundations of China under Grant No. 10372113. q Emerald Group Publishing Limited 0264-4401 The authors gratefully acknowledge the encouragement from Dr C. Thornton at Birmingham DOI 10.1108/02644400610638943 University. and these responses could significantly affect the dynamic load on the truck frame and Discrete element on the operation by drivers. Consequently it may cause potential strength problems or simulation even accidents. Therefore, the estimation of the workload involving the additional dynamic load is of great importance. In addition, inter-particle interaction of a particle bed is also important if the carrying goods are agricultural products, such as fruits or other vulnerable particle-shaped products, since damage the breakage will result in the loss of commercial profits. 5 To the authors’ best knowledge, up to date the workload value of the particulate materials used by the conventional truck design is still considered as a point mass and how to deal with the dynamic effect is unclear. It seems lack reports on the microscope mechanism of granular matter and the description of the dynamic interactions between the assembly and the truck box due to the difficulties inherent in the conventional theory which assumes the particulate material as a continuum media. The discrete element method (DEM), originated by Cundall and Strack (1979a), is a numerical method for analyzing a discrete system, which consists of an assembly of blocky or particulate elements. Over the past 20 years the method has been significantly developed and successfully applied to solve many practical problems (Couroyer et al., 2000; Owen and Feng, 2001; Han et al., 2002). Thornton (1991, 1993) presented a new model for adhesive spherical particles and modified the TRUBAL program originated by Cundall and Strack (1979b) into a new version known as Aston-TRUBAL or GRANULE. In this work, an assembly of spherical particles within a truck box in motion was simulated under a sudden braking using GRANULE. The effects of inertia dynamic force with different braking speeds and inter-particle interactions were considered. 2. Discrete element method models The GRANULE code for a spherical dry particle system provides mainly two contact models. The interaction between two in-adhesive particles was modeled by Hertz ( Johnson, 1985) for normal interaction, and by Mindlin and Deresiewicz (1953) for tangential interaction. The interaction between two particles with adhesion was modeled by the JKR theory (Johnson et al., 1971) for normal interaction, and by Thornton’s theory (1991, 1993) for the tangential interaction, which is a combination of the theory by Mindlin and Deresiewicz (1953) and the theory by Savkoor and Briggs (1977). In reality the term “adhesion” is normally used to describe the adhesive property of very small particles with surface energy. However, the adhesive interaction model can be used to take into account of the non-spherical and “sticky” effects, since the element is modeled as perfect round sphere. Besides adhesion, the effects of other properties, e.g. friction, were also considered and their significance to the modelling was also investigated. Note that in the context of DEM, each particle is assumed rigid and that its deformability is modeled via penalty springs. Therefore, Young’s modulus of particles in the model is used to determine the penalty value. Also a central difference explicit time integration is employed to numerically solve the dynamic system of equations. The critical time step is selected automatically in the program. EC 3. Problem description 23,1 3.1 Problem and the related data Our study on the behavior of the particle assembly during braking was focused on the interaction between the particle bed and the wall of the truck box and the movement of the assembly. Here a truck box with 4.0 m in length, 2.0 m in width, and 1.0 m in height was considered. The discrete element model contains 102,000 mono-size, soft spherical 6 particles with a radius of 4.5 cm. The term “soft” refers to a kind of agricultural products with Young’s modulus of around 70 MPa, which is 1/1000 of the elastic property of the wall. Previous work by Xu et al. (2002) indicates that the use of a smaller material modulus in the model has insignificant effect on the physical behaviour of the system but could substantially reduce the simulation time due to the increase of the critical time step. The values of the selected parameters used in the modelling are listed in Table I. The interaction between a sphere and a wall is treated as the interaction between a sphere and another sphere with an infinite radius. In our DEM simulation, a proper workspace is needed to contain all the particles and allow them to move in all possible ways. The workspace is divided into a certain number of cubic cells so as to detect the movement of any particle and identify their contact status. The dimensions of the workspace are the key factor affecting the overall computing efficiency and, therefore, it is impractical to specify a very large workspace to allow the box to move with a normal speed and then to stop in a certain distance. In our approach, an equivalent transformation was employed to allow the truck box being stationary and the relative motion of the particles with respect to the box was analyzed. In the simulation the speed of a truck before braking was chosen as 72 km/h, and four cases of different braking time durations were selected and the corresponding braking distances and de-accelerations were listed in Table II. Radius (particle) 0.045 m Density (particle) 1,200 kg/m3 Young’s modulus (particle) 70 MPa Poisson’s ratio (particle) 0.25 Friction (particle to particle) 0.35 Number of particles 102,000 Total mass of particles 5,726 kg Table I. Young’s modulus (wall) 70 GPa Properties of particle Poisson’s ratio (wall) 0.3 and wall Friction (wall to particle) 0.35 Case Braking time (s) Braking distance (m) De-acceleration (m/s2) 1 1 10 20 2 0.8 8 25 3 0.667 6.67 30 4 0.5 5 40 Table II. Kinetic properties Note: Motion speed before braking is 72 km/h 3.2 Initial preparation of the particle bed Discrete element The particles were generated randomly within the specified volume. A large number of simulation preliminary iterative cycles were performed under the gravity, during which the positions of the particles and contact links were repeatedly updated until all the particles settle down to form a bed. Then an additional acceleration due to the de-acceleration of the truck was assigned to each particle, the height of the simulation domain was reduced to the original value and the real cyclic computation began. It is 7 noted that a top wall was introduced to avoid the escape of the particles during the simulation. The initial particle bed is shown in Figure 1. During the simulation the “real time” state of the system was continuously fed back to an interface platform in the form of graphic output or data files.
Load more

Recommended publications
  • Application of Discrete-Element Methods to Approximate Sea-Ice
    Confidential manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) 1 Application of discrete-element methods to approximate sea-ice 2 dynamics 1 1 1 3 A. Damsgaard , A. Adcroft , and O. Sergienko 1 4 Program in Atmospheric and Oceanic Sciences, Princeton University, Princeton, New Jersey, USA 5 Key Points: • 6 Abrupt strengthening under dense ice-packing configurations induces granular jam- 7 ming • 8 Cohesive bonds can provide similar behavior as Coulomb-frictional parameteriza- 9 tions • 10 A probabilistic model characterizes the likelihood of jamming over time Corresponding author: A. Damsgaard, [email protected] –1– Confidential manuscript submitted to Journal of Advances in Modeling Earth Systems (JAMES) 11 Abstract 12 Lagrangian models of sea-ice dynamics have several advantages over Eulerian continuum 13 models. Spatial discretization on the ice-floe scale are natural for Lagrangian models and 14 offer exact solutions for mechanical non-linearities with arbitrary sea-ice concentrations. 15 This allows for improved model performance in ice-marginal zones. Furthermore, La- 16 grangian models can explicitly simulate jamming processes such as sea ice movement 17 through narrow confinements. Granular jamming is a chaotic process that occurs when 18 the right grains arrive at the right place at the right time, and the jamming likelihood over 19 time can be described by a probabilistic model. While difficult to parameterize in contin- 20 uum formulations, jamming emerges spontaneously in dense granular systems simulated 21 in a Lagrangian framework. Here, we present a flexible discrete-element framework for 22 approximating Lagrangian sea-ice mechanics at the ice-floe scale, forced by ocean and at- 23 mosphere velocity fields.
    [Show full text]
  • Contact Dynamics As a Nonsmooth Discrete Element Method Farhang Radjai, Richefeu Vincent
    Contact dynamics as a nonsmooth discrete element method Farhang Radjai, Richefeu Vincent To cite this version: Farhang Radjai, Richefeu Vincent. Contact dynamics as a nonsmooth discrete element method. Me- chanics of Materials, Elsevier, 2009, 41, pp.715–728. 10.1016/j.mechmat.2009.01.028. hal-00689866 HAL Id: hal-00689866 https://hal.archives-ouvertes.fr/hal-00689866 Submitted on 20 Apr 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Contact dynamics as a nonsmooth discrete element method Farhang Radjai and Vincent Richefeu Laboratoire de M´ecanique et G´enieCivil, CNRS - Universit´eMontpellier 2, Place Eug`eneBataillon, 34095 Montpellier cedex 05 Abstract The contact dynamics (CD) method is presented as a discrete element method for the simulation of nonsmooth granular dynamics at the scale of particle rear- rangements where small elastic response times and displacements are neglected. Two central ingredients of the method are detailed: 1) The contact laws expressed as complementarity relations between the contact forces and velocities and 2) The nonsmooth motion involving velocity jumps with impulsive unresolved forces as well as smooth motion with resolved static forces. We show that a consistent descrip- tion of the dynamics at the velocity level leads to an implicit time-stepping scheme together with an explicit treatment of the evolution of the particle configuration.
    [Show full text]
  • A Coupled SPH-DEM Model for Fluid-Structure Interaction Problems with Free-Surface Flow and Structural Failure
    This is a repository copy of A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure. White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/103460/ Version: Accepted Version Article: Wu, K, Yang, D and Wright, N (2016) A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure. Computers and Structures, 177. pp. 141-161. ISSN 0045-7949 https://doi.org/10.1016/j.compstruc.2016.08.012 © 2016 Elsevier Ltd. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ Reuse This article is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) licence. This licence only allows you to download this work and share it with others as long as you credit the authors, but you can’t change the article in any way or use it commercially. More information and the full terms of the licence here: https://creativecommons.org/licenses/ Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ A coupled SPH-DEM model for fluid-structure interaction problems with free-surface flow and structural failure Ke Wu1, Dongmin Yang1,*, Nigel Wright2 1 School of Civil Engineering, University of Leeds, LS2 9JT, UK 2 Faculty of Technology, De Montfort University, LE1 9BH, UK Abstract An integrated particle model is developed to study fluid-structure interaction (FSI) problems with fracture in the structure induced by the free surface flow of the fluid.
    [Show full text]
  • Virtual Experiments of Particle Mixing Process with the SPH-DEM Model
    materials Article Virtual Experiments of Particle Mixing Process with the SPH-DEM Model Siyu Zhu, Chunlin Wu and Huiming Yin * Department of Civil Engineering and Engineering Mechanics, Columbia University, 610 S.W. Mudd, 500 West 120th Street, New York, NY 10027, USA; [email protected] (S.Z.); [email protected] (C.W.) * Correspondence: [email protected]; Tel.: +1-212-851-1648 Abstract: Particle mixing process is critical for the design and quality control of concrete and composite production. This paper develops an algorithm to simulate the high-shear mixing process of a granular flow containing a high proportion of solid particles mixed in a liquid. DEM is employed to simulate solid particle interactions; whereas SPH is implemented to simulate the liquid particles. The two-way coupling force between SPH and DEM particles is used to evaluate the solid-liquid interaction of a multi-phase flow. Using Darcy’s Law, this paper evaluates the coupling force as a function of local mixture porosity. After the model is verified by two benchmark case studies, i.e., a solid particle moving in a liquid and fluid flowing through a porous medium, this method is applied to a high shear mixing problem of two types of solid particles mixed in a viscous liquid by a four-bladed mixer. A homogeneity metric is introduced to characterize the mixing quality of the particulate mixture. The virtual experiments with the present algorithm show that adding more liquid or increasing liquid viscosity slows down the mixing process for a high solid load mix. Although the solid particles can be mixed well eventually, the liquid distribution is not homogeneous, especially when the viscosity of liquid is low.
    [Show full text]
  • Modelling Complex Particle–Fluid Flow with a Discrete Element Method Coupled with Lattice Boltzmann Methods (DEM-LBM)
    chemengineering Article Modelling Complex Particle–Fluid Flow with a Discrete Element Method Coupled with Lattice Boltzmann Methods (DEM-LBM) Wenwei Liu and Chuan-Yu Wu * Department of Chemical and Process Engineering, University of Surrey, Guildford GU2 7XH, UK; [email protected] * Correspondence: [email protected] Received: 1 July 2020; Accepted: 29 September 2020; Published: 7 October 2020 Abstract: Particle–fluid flows are ubiquitous in nature and industry. Understanding the dynamic behaviour of these complex flows becomes a rapidly developing interdisciplinary research focus. In this work, a numerical modelling approach for complex particle–fluid flows using the discrete element method coupled with the lattice Boltzmann method (DEM-LBM) is presented. The discrete element method and the lattice Boltzmann method, as well as the coupling techniques, are discussed in detail. The DEM-LBM is thoroughly validated for typical benchmark cases: the single-phase Poiseuille flow, the gravitational settling and the drag force on a fixed particle. In order to demonstrate the potential and applicability of DEM-LBM, three case studies are performed, which include the inertial migration of dense particle suspensions, the agglomeration of adhesive particle flows in channel flow and the sedimentation of particles in cavity flow. It is shown that DEM-LBM is a robust numerical approach for analysing complex particle–fluid flows. Keywords: particle–fluid flow; discrete element method; lattice Boltzmann method 1. Introduction Particulate flows are extensively encountered in nature and industrial processes, attracting tremendous engineering research interests in almost all areas of sciences [1–3], including astrophysics, chemical engineering, biology, life science and so on.
    [Show full text]
  • Numerical Modelling of Deformation Within Accretionary Prisms
    IT 12 022 Examensarbete 45 hp Juni 2012 Numerical modelling of deformation within accretionary prisms Ting Zhang Institutionen för informationsteknologi Department of Information Technology Abstract Numerical modelling of deformation within accretionary prisms Ting Zhang Teknisk- naturvetenskaplig fakultet UTH-enheten A two dimensional continuous numerical model based on Discrete Element Method is used to investigate the behaviour of accretionary wedges with different basal frictions. Besöksadress: The models are based on elastic-plastic, brittle material and computational granular Ångströmlaboratoriet Lägerhyddsvägen 1 dynamics, and several characteristics of the influence of the basal friction are analysed. Hus 4, Plan 0 The model results illustrate that the wedge’s deformation and geometry, for example, fracture geometry, the compression force, area loss, displacement, height and length Postadress: of the accretionary wedge etc., are strongly influenced by the basal friction. In general, Box 536 751 21 Uppsala the resulting wedge grows steeper, shorter and higher, and the compression force is larger when shortened above a larger friction basement. Especially, when there is no Telefon: basal friction, several symmetrical wedges will distribute symmetrically in the domain. 018 – 471 30 03 The distribution of the internal stress when a new accretionary prime is forming is Telefax: also studied. The results illustrate that when the stress in a certain zone is larger than 018 – 471 30 00 a critical number, a new thrust will form there. Hemsida: http://www.teknat.uu.se/student Key words: Discrete Element Method, accretionary wedge, basal friction, compression force, area loss, displacement, height and length Handledare: Hemin Koyi Ämnesgranskare: Maya Neytcheva Examinator: Jarmo Rantakokko IT 12 022 Tryckt av: Reprocentralen ITC Numerical modelling of deformation within accretionary prisms Zhang Ting Content Abstract Content 1.
    [Show full text]
  • Hammering Beneath the Surface of Mars – Modeling and Simulation Of
    URN (Paper): urn:nbn:de:gbv:ilm1-2014iwk-155:2 58th ILMENAU SCIENTIFIC COLLOQUIUM Technische Universität Ilmenau, 08 – 12 September 2014 URN: urn:nbn:de:gbv:ilm1-2014iwk:3 Hammering beneath the surface of Mars – Modeling and simulation of the impact-driven locomotion of the HP3-Mole by coupling enhanced multi-body dynamics and discrete element method Roy Lichtenheldt1, Bernd Schäfer2, Olaf Krömer3 1 German Aerospace Center (DLR), Institute of System Dynamics and Control 1 Ilmenau University of Technology, Department of Mechanical Engineering, Mechanism Technology Group 2 German Aerospace Center (DLR), Institute of Robotics and Mechatronics 3German Aerospace Center (DLR), Institute of Space Systems ABSTRACT As the formation of the rocky planets in our inner solar system has always been a major sub- ject of scientific interest, NASA’s discovery mission InSight (Interior Seismic Investigations, Geodesy and Heat Transport) intends to gain further knowledge about the interior structure of Mars. In order to understand the processes that lead to planetary evolution, Mars’ seismic as well as thermal properties will be measured. DLR’s HP3-Mole (Heat Flow and Physical Prop- erties Package), an innovative self impelling nail, will hammer itself into the red planet deeper than any other instrument before, in order to measure the heat flux and thermal gradient down to a final depth of 5 m. To achieve this challenging goal, high fidelity simulation models have been used throughout the whole development process. To meet the demands on accuracy, two detailed models were created based on enhanced multi-body dynamics and discrete element techniques. For the most detailed analysis both methods are coupled to enable further understanding of the interaction between Mole mechanism and soil dynamics.
    [Show full text]
  • Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) Applied to Centrifuges
    6 Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) Applied to Centrifuges Xiana Romani Fernandez, Lars Egmont Spelter and Hermann Nirschl Karlsruhe Institute of Technology, Campus South, Institute for Mechanical Process Engineering and Mechanics, Karlsruhe Germany 1. Introduction The simulation of fluid flow in e.g. air channels, pipes, porous media and turbines has been the emphasis of many research projects and optimization processes in the academic and industrial community during the last years. A key advantage of the calculation of fluid flow through a given geometry when compared to the experimental determination is the efficient identification of disadvantages of the current state and the fast cycle of change in geometry and analysis of its effects. This saves time and costs and furthermore opens up new fields of research and development. There are, however, few drawbacks of the new optimisation and research methods. The numerically obtained results need validation before it can be stated whether they are correct or misrepresent the true state. In some cases, such as the optimisation of existing systems, the experience of the user may be sufficient to evaluate the calculated flow pattern. In the case of the prediction of flow in new geometries or process conditions, the numerical result can be validated only by measuring the flow pattern at representative process conditions (flow velocity, pressure, and temperature). For non- moving geometries, many measurements have been conducted in order to determine the flow behaviour in various geometries and for different process conditions. These measurements are readily available for the evaluation of new simulations. However, only little research has been conducted to evaluate the flow conditions in centrifuges, especially at high rotational speeds.
    [Show full text]
  • An Implementation of the Soft-Sphere Discrete Element Method in a High-Performance Parallel Gravity Tree-Code
    Granular Matter (2012) 14:363–380 DOI 10.1007/s10035-012-0346-z ORIGINAL PAPER An implementation of the soft-sphere discrete element method in a high-performance parallel gravity tree-code Stephen R. Schwartz · Derek C. Richardson · Patrick Michel Received: 20 January 2012 / Published online: 30 March 2012 © Springer-Verlag 2012 Abstract We present our implementation of the soft-sphere body surfaces, or at designing efficient sampling tools for discrete element method (SSDEM) in the parallel gravita- sample-return space missions. tional N-body code pkdgrav, a well-tested simulation pack- age that has been used to provide many successful results Keywords Bulk solids · Solar system · DEM · in the field of planetary science. The implementation of Hopper · SSDEM SSDEM allows for the modeling of the different contact forces between particles in granular material, such as var- ious kinds of friction, including rolling and twisting friction, 1 Introduction and the normal and tangential deformation of colliding par- ticles. Such modeling is particularly important in regimes The study of granular materials and their dynamics is of great for which collisions cannot be treated as instantaneous or as importance for a wide range of applications in industry, but occurring at a single point of contact on the particles’ sur- also in the field of planetary science. Most celestial solid faces, as is done in the hard-sphere discrete element method bodies’ surfaces are not bare rock, but are instead covered already implemented in the code. We check the validity by granular material. This material can take the form of fine of our soft-sphere model by reproducing successfully the regolith as on the Moon, or gravels and pebbles as on the dynamics of flows in a cylindrical hopper.
    [Show full text]
  • Numerical Methods in Geomechanics
    Antonio Bobet NUMERICAL METHODS IN GEOMECHANICS Antonio Bobet School of Civil Engineering, Purdue University, West Lafayette, IN, USA اﻟﺨﻼﺻـﺔ: ﺗﻘﺪم هﺬﻩ اﻟﻮرﻗﺔ وﺻﻔ ﺎً ﻟﻠﻄﺮق اﻟﻌﺪدﻳﺔ اﻷآﺜﺮ اﺳﺘﺨﺪاﻣﺎ ﻓﻲ اﻟﻤﻴﻜﺎﻧﻴﻜﺎ اﻟﺠﻴﻮﻟﻮﺟﻴﺔ. وهﻲ أرﺑﻌﺔ ﻃﺮق : (1) ﻃﺮﻳﻘﺔ اﻟﻌﻨﺼﺮ اﻟﻤﻤﻴﺰ (2) ﻃﺮﻳﻘﺔ ﺗﺤﻠﻴﻞ اﻟﻨﺸﻮة اﻟﻤﺘﻘﻄﻊ (3) ﻃﺮﻳﻘﺔ اﻟﺘﺤﺎم اﻟﺠﺴﻴﻤﺎت (4) ﻃﺮﻳﻘﺔ اﻟﺸﺒﻜﺔ اﻟﻌﺼﺒﻴﺔ اﻟﺼﻨﺎﻋﻴﺔ. وﺗﻀﻤﻨﺖ اﻟﻮرﻗﺔ أ ﻳ ﻀ ﺎً وﺻﻔ ﺎً ﻣﻮﺟﺰ اً ﻟﺘﻄﺒﻴﻖ اﻟﻤﺒﺎدئ اﻟﺨﻮارزﻣﻴﺔ ﻟﻜﻞ ﻃﺮﻳﻘﺔ إﺿﺎﻓﺔ إﻟﻰ ﺣﺎﻟﺔ ﺑﺴﻴﻄﺔ ﻟﺘﻮﺿﻴﺢ اﺳﺘﺨﺪاﻣﻬﺎ. ______________________ *Corresponding Author: E-mail: [email protected] Paper Received November 7, 2009; Paper Revised January 17, 2009; Paper Accepted February 3, 2010 April 2010 The Arabian Journal for Science and Engineering, Volume 35, Number 1B 27 Antonio Bobet ABSTRACT The paper presents a description of the numerical methods most used in geomechanics. The following methods are included: (1) The Distinct Element Method; (2) The Discontinuous Deformation Analysis Method; (3) The Bonded Particle Method; and (4) The Artificial Neural Network Method. A brief description of the fundamental algorithms that apply to each method is included, as well as a simple case to illustrate their use. Key words: numerical methods, geomechanics, continuum, discontinuum, finite difference, finite element, discrete element, discontinuous deformation analysis, bonded particle, artificial neural network 28 The Arabian Journal for Science and Engineering, Volume 35, Number 1B April 2010 Antonio Bobet NUMERICAL METHODS IN GEOMECHANICS 1. INTRODUCTION Analytical methods are very useful in geomechanics because they provide results with very limited effort and highlight the most important variables that determine the solution of a problem. Analytical solutions, however, have often a limited application since they must be used within the range of assumptions made for their development.
    [Show full text]
  • Discrete Element Modeling— a Promising Method for Refractory Microstructure Design
    Discrete element modeling— A promising method for refractory microstructure design efractory materials are required to Rkeep their structural stability when subjected to extreme mechanical and chemical environments. Thermal shock spalling, corro- sion, creep, and other complex phenomena may take place while using them. Therefore, mechanical behavior of refractory materials is of great interest. In recent years, researchers reported various technical problems and industrial challenges concerning refractory materials that are Credit: Moreira et al. not easily solved using conventional experimental methods. Thus, numerical computational tools emerged to better understand the physical problems and to analyze such complex conditions. The finite element method (FEM) is one of the most popu- lar approaches for studying thermomechanical problems. It is a numerical method that subdivides a large system into smaller, simpler parts for easier analysis through the use of a mesh, i.e., a geometrical representation of the domain of interest that comprises all elements to be analyzed. This technique is suitable to solve elliptic and parabolic prob- lems, and it is not restricted to linear or isotropic cases. The mesh makes it geometrically flexible and able to model complex domains. Additionally, this technique is easily implemented as computer codes and is also robust because most mathematical problems can be stated as a variational problem where FEM can be applied. However, one of the main disadvantages to FEM is the dif- ficulty of analyzing microscopic situations and material discontinui- ties, as the equations associated with the problem are derived based on a continuous materials assumption.1 Trying to overcome this issue, researchers developed the FEM remeshing technique, which solves complex problems by updating the mesh to consider discontinuities, but this procedure can affect 2 3 By M.
    [Show full text]
  • Introduction to the Combined Finite- Discrete Element Method Máté Hazay Budapest University of Technology and Economics, Hungary
    Introduction to the Combined Finite- Discrete Element Method Máté Hazay Budapest University of Technology and Economics, Hungary Ante Munjiza Queen Mary University of London, England ABSTRACT This chapter presents a general overview of the combined finite-discrete element method (FEM/DEM) which is considered as a state-of-the-art technique for the mechanical analysis of masonry structures. In a FEM/DEM simulation each discrete element representing a stone block is discretised into finite elements in order to describe the deformability of the blocks. This chapter deals with the main steps of the FEM/DEM including contact detection, contact interaction, fracture and fragmentation algorithms, calculation of deformations and the time integration of the equation of motion. The FEM/DEM is advantageously used to simulate transition from continua to discontinua processes which may lead to the collapse of the structure. Some examples for practical applications found in the literature are mentioned. Keywords: Contact detection, Contact interaction, Potential force concept, Green-St. Venant tensor, Fracture, Fragmentation, Central difference method, Parallelization, Ante Munjiza, Y3D INTRODUCTION The two basic types of mechanical models are the classical models of continuum mechanics and the models of discrete elements. The finite element method (FEM) is the most widely used technique to model continuum mechanical problems. On the other hand, the discrete element method (DEM) is able to describe discontinuum-based phenomena including the motion and interaction of individual particles. However in certain situations the two different phenomena arise at the same time, thus the development of a coupled numerical tool was required. Therefore, in the early 1990s the two above mentioned methods have been combined and the resulting method was termed the combined finite- discrete element method (FEM/DEM).
    [Show full text]