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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Complex behavior models (plasticity, cracks, visco elascticity) face some theoretical difficulties for the determination of the behavior law at the continuous scale. When homogenization fails to give the right behavior law, a solution is to simulate the material at a meso scale in order to simulate directly a set of discrete properties that are responsible of the macroscopic behavior. The discrete element model has been developed for granular material. The proposed set shows how this method is capable to solve the problem of complex behavior that are linked to discrete meso scale effects. The first book solves the local problem, the second one presents a coupling approach to link the structural effects to the local ones, this third book presents the software workbench that includes all the theoretical developments.
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Seitenzahl: 189
Veröffentlichungsjahr: 2015
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Table of Contents
Cover
Title
Copyright
List of Figures
List of Tables
Introduction
I.1. The black box problem
I.2. A numerical tool to study a tribological problem
I.3. Why have we chosen a free license?
I.4. Discrete element methods
I.5. Application to tribological problems
I.6. A brief history of the workbench GranOO
I.7. A design to serve versatility
I.8. Choice of the programming language
I.9. Book organization
1: Object Oriented Approach and UML
1.1. Object Oriented (OO) paradigms
1.2. OO analysis and design
1.3. UML diagrams
2: Operating Architecture
2.1. The GranOO package
2.2. Compilation process of the executable file
2.3. Launching a GranOO executable
2.4. The input files
2.5. The magic world of the plugins
2.6. The output files
3: Focus on Libraries
3.1. The geometrical library
3.2. The DEM library
3.3. The libMySandbox library
3.4. Conclusion
4: Tools and Practical Examples of Use of GranOO
4.1. Tool overview
4.2. Granular simulation: the bluewave example
4.3. The continuous discrete element model
4.4. Conclusion
Conclusion
Appendices
Appendix 1: Using Quaternions
A1.1. Introduction
A1.2. Norm transformation
A1.3. Direction transformation
A1.4. Quaternion definition
A1.5. Mathematical properties
A1.6. Quaternion and attitude
A1.7. Quaternion and angular velocity
A1.8. Application to dynamics
A1.9. Numerical integration
A1.10. Conclusion
Appendix 2: Pendulum Problem Complete Code
Bibliography
Index
End User License Agreement
Guide
Cover
Table of Contents
Begin Reading
List of Illustrations
Introduction
Figure I.1. Example of packing problems of spheres
Figure I.2. Number of citations of the initial paper of Cundall and Strack [CUN 79] in the last two decades
Figure I.3. The discrete element method and its main variants
Figure I.4. Examples of granular and lattice model simulations
Figure I.5. The hybrid lattice-particle for solving tribological problems
Figure I.6. The layered architecture of the GranOO workbench
Chapter 1: Object Oriented Approach and UML
Figure 1.1. The template class SetOf (from the libDEM library)
Figure 1.2. Encapsulation mechanism
Figure 1.3. Example of global class diagram view showing the class DiscreteElementShaped (from the libDEM library) and the Interaction hierarchy
Figure 1.4. Example of class diagram view showing the class DiscreteDomain (from the libDEM library) and its relations with these classes Point, Vector, etc. (from the libGeometrical library)
Figure 1.5. Class diagram view showing the list of methods of the class DiscreteDomain (from the libDEM library)
Figure 1.6. Sequence diagram involving the ComputeProblem singleton class (from the libDEM library) and the object theComputeProblem instantiated from this class
Chapter 2: Operating Architecture
Figure 2.1. General view of the GranOO operating architecture. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 2.2. UML global view of the plugin class diagram hierarchy
Figure 2.3. UML diagram of the sensor classes hierarchy
Chapter 3: Focus on Libraries
Figure 3.1. Comparison of the GranOO geometrical library and blitz++ library performances on elementary operations. The elapsed time corresponds to cpu time (clock ticks). Each operation was repeated one million times
Figure 3.2. UML diagram of the plugin class hierarchy
Figure 3.3. Illustration of the changing frame operation processed on a point P and a vector V
Figure 3.4. UML diagram of the
libGeometrical
shapes
Figure 3.5. Initial configuration of the elastic pendulum problem
Figure 3.6. Simplified class diagram of the GranOO DEM library
Figure 3.7. UML class diagram of the SetOf environment
Figure 3.8. UML diagram of the discrete element classes
Figure 3.9. UML diagram of the PhysicalProperty class that implements thermal properties
Figure 3.10. UML diagram of the interaction classes
Figure 3.11. Example of disable bond view (simulation of a refractory microstructure in 2D). For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 3.12. UML diagram of the discrete shape classes
Figure 3.13. View of discrete shapes with their associated surface boundaries. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 3.14. UML diagram of the contact management
Chapter 4: Tools and Practical Examples of Use of GranOO
Figure 4.1. The gddViewer window. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 4.2. Example of item selection in the 3D viewer
Figure 4.3. Snapshots of some gddviewer GUI details
Figure 4.4. Example of plot rendering with the plot-sensor-data.py Python script
Figure 4.5. Spectral analysis of sensor data given by post-treatment that uses plot-sensor-data.py as a module
Figure 4.6. A spherical compact domain given by the cooker packing program
Figure 4.7. The initial a) and final b) discrete domain
Figure 4.8. Successive spots of the blue wave simulation
Figure 4.9. Macroscopic Poisson’s ratio versus the microscopic radius ratio
Figure 4.10. Macroscopic versus microscopic Young’s modulus
Figure 4.11. Macroscopic versus microscopic failure stress
Figure 4.12. The discrete cylindrical specimen used for the tensile and torsion tests. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 4.13. The two bond sets created by the InitBondSet plugin of the failure tensile test. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 4.14. Evolution of the number of broken beams and normal stresses versus strain. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 4.15. Illustration of the failure torsion test. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 4.16. Overview of the loose abrasive grinding simulation. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 4.17. Subsurface damage distribution versus length approximated by a decreasing exponential function
Figure 4.18. Maximal SSD length versus the abrasive concentration for different abrasive radii. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Figure 4.19. Maximal SSD length versus average abrasive radius for different abrasive concentrations. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
Appendix 1: Using Quaternions
Figure A1.1. Point transformation with vector
Figure A1.2. Vector transformation with quaternion
Figure A1.3. Norm transformation
Figure A1.4. Direction transformation
Figure A1.5. Rotation as produced by two symmetries
Figure A1.6. The three Euler’s angles. For a color version of this figure, see www.iste.co.uk/andre/discrete.zip
List of Tables
Chapter 2: Object Oriented Approach and UML
Table 2.1. Available XML tags
Chapter 4: Tools and Practical Examples of Use of GranOO
Table 4.1. The macroscopic failure shear stresses computed in torsion tests
Appendix 1: Using Quaternions
Table A1.1. Multiplication table of unit quaternion
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3D Discrete Element Workbench for Highly Dynamic Thermo-mechanical Analysis
GranOO
Volume 3
Damien André
Jean-Luc Charles
Ivan Iordanoff
Discrete Element Model and Simulation of Continuous Materials Behavior Set
coordinated by Ivan Iordanoff
First published 2015 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUK
www.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2015
The rights of Damien André, Jean-Luc Charles and Ivan Iordanoff to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
Library of Congress Control Number: 2015951440
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-84821-772-0
List of Figures
I.1. Example of packing problems of spheres
I.2. Number of citations of the initial paper of Cundall and Strack [CUN 79] in the last two decades
I.3. The discrete element method and its main variants
I.4. Examples of granular and lattice model simulations
I.5. The hybrid lattice-particle for solving tribological problems
I.6. The layered architecture of the GranOO workbench
Chapter 1
1.1. The template class SetOf (from the libDEM library)
1.2. Encapsulation mechanism
1.3. Example of global class diagram view showing the class DiscreteElementShaped (from the libDEM library) and the Interaction hierarchy
1.4. Example of class diagram view showing the class DiscreteDomain (from the libDEM library) and its relations with these classes Point, Vector, etc. (from the libGeometrical library)
1.5. Class diagram view showing the list of methods of the class DiscreteDomain (from the libDEM library)
1.6. Sequence diagram involving the ComputeProblem singleton class (from the libDEM library) and the object theComputeProblem instantiated from this class
Chapter 2
2.1. General view of the GranOO operating architecture
2.2. UML global view of the plugin class diagram hierarchy
2.3. UML diagram of the sensor classes hierarchy
Chapter 3
3.1. Comparison of the GranOO geometrical library and blitz++ library performances on elementary operations. The elapsed time corresponds to cpu time (clock ticks). Each operation was repeated one million times
3.2. UML diagram of the plugin class hierarchy
3.3. Illustration of the changing frame operation processed on a point P and a vector V
3.4. UML diagram of the
libGeometrical
shapes
3.5. Initial configuration of the elastic pendulum problem
3.6. Simplified class diagram of the GranOO DEM library
3.7. UML class diagram of the SetOf environment
3.8. UML diagram of the discrete element classes
3.9. UML diagram of the PhysicalProperty class that implements thermal properties
3.10. UML diagram of the interaction classes
3.11. Example of disable bond view (simulation of a refractory microstructure in 2D)
3.12. UML diagram of the discrete shape classes
3.13. View of discrete shapes with their associated surface boundaries
3.14. UML diagram of the contact management
Chapter 4
4.1. The gddViewer window
4.2. Example of item selection in the 3D viewer
4.3. Snapshots of some gddviewer GUI details
4.4. Example of plot rendering with the plot-sensor-data.py Python script
4.5. Spectral analysis of sensor data given by post-treatment that uses plot-sensor-data.py as a module
4.6. A spherical compact domain given by the cooker packing program
4.7. The initial a) and final b) discrete domain
4.8. Successive spots of the blue wave simulation
4.9. Macroscopic Poisson’s ratio versus the microscopic radius ratio
4.10. Macroscopic versus microscopic Young’s modulus
4.11. Macroscopic versus microscopic failure stress
4.12. The discrete cylindrical specimen used for the tensile and torsion tests
4.13. The two bond sets created by the InitBondSet plugin of the failure tensile test
4.14. Evolution of the number of broken beams and normal stresses versus strain
4.15. Illustration of the failure torsion test
4.16. Overview of the loose abrasive grinding simulation
4.17. Subsurface damage distribution versus length approximated by a decreasing exponential function
4.18. Maximal SSD length versus the abrasive concentration for different abrasive radii
4.19. Maximal SSD length versus average abrasive radius for different abrasive concentrations
Appendix 1
A1.1. Point transformation with vector
A1.2. Vector transformation with quaternion
A1.3. Norm transformation
A1.4. Direction transformation
A1.5. Rotation as produced by two symmetries
A1.6. The three Euler’s angles
List of Tables
Chapter 2
2.1. Available XML tags
Chapter 4
4.1. The macroscopic failure shear stresses computed in torsion tests
Appendix 1
A1.1. Multiplication table of unit quaternion
Introduction
I.1. The black box problem
In the last three decades, the price of personal computers has become increasingly accessible, while their performance has increased significantly. Today, computers are everywhere and their usages take a non-negligible part of our daily life. Similarly, in the domain of sciences and engineering, computers have become an essential tool. A part of this scientific usage is the simulation of natural phenomena. For engineers, the usage is quite limited to ready-to-use software that embed a set of predefined actions and functions. In this case, the area of usage is clearly defined and delimited. The advantages are a user friendly interface and a good trust in the given results. The time of the learning process is short and the users quickly become proficient.
But what happens if the user wants to do something that was not planned by the software developers? The user may contact software support. If a solution is not found by software support, the user must search for another software that includes the required functionality and start the learning process again. This is a deadlock situation that cannot happen if the user is also a software developer. Following this idea, the aim of this book is to turn software users into software developers. The main disadvantage of this approach is the high degree of investment. The learning process of software development is slower than the process of learning software. But the benefits regarding the degree of freedom and possibility are very high. After becoming a developer, the sole limitations are those of the user himself (scientific knowledge and imagination) and computer performance.
This book addresses scientific researchers, high-qualified engineers and individuals interested in Discrete Element Method (DEM) modeling and software development. Throughout this book, the software black box is opened and, more precisely, the GranOO free software, dedicated to DEM modeling, is dissected and described.
I.2. A numerical tool to study a tribological problem
Initially, GranOO was designed to study tribological problems. Briefly speaking, tribology is the science that studies the contact between two surfaces with a relative motion or an adhesion. More particularly, tribology focuses on wear, friction and lubrication principles. These phenomena are very common. They happen in machining process, mechanical guiding or power transmissions. Tribological phenomena involve a wide range of scales, typically from the nanometer (at the surface scale) to the meter scale (at the mechanism scale). From the physical point of view, mechanics must be coupled with thermal, material and physico-chemical behavior to understand these phenomena. To study such complex problems, adapted numerical tools must be used to understand and predict the contact behavior. The finite element method is often used for these problems, presenting advantages such as broadly available commercial software that is easy to use. However, it is difficult for the finite element method to describe multifracturation followed by debris, as occurs in wear studies.
Molecular dynamic methods are increasingly applied to the study of tribological problems [KOM 00, YAN 07, SOD 12]. Free software exists in that field that can be used by a large number of scientists. However, the simulated time and space scales are often small compared to the scales of tribological phenomena. Over the past 10 years, DEM have been shown to be an interesting tool that can take contacts into account at the right scale and solve multiphysical problems. Unfortunately, discrete element commercial software is often restricted to a closed list of physical applications and is difficult to extend to complex problems. The consequence is that tribological studies using discrete element models are limited by software difficulties. The GranOO workbench has been developed to offer the scientific community a free, powerful and rather easy-to-use discrete element software.
I.3. Why have we chosen a free license?
GranOO is distributed under the free General Public License1 (GNU). In few words, it means that the source code can be freely read and edited. However, any modification of the source code must be placed under a free license. In our opinion, this kind of license encourages scientific sharing of numerical tools. In addition, opening the source code encourages user contributions, increases the number of bug fixes and improves the software quality. From a user point of view, it ensures a good level of trust. If a concern is raised, users can read the source code and check the validity of the coded algorithms.
I.4. Discrete element methods
DEM was initiated in the early 1980s. The article written by Cundall and Strack in 1979 [CUN 79] is considered as the first implementation of DEM to model granular medias. The media was modeled by a set of pseudo-rigid bodies that interact by contacts. In the literature, these bodies are named grains, elements or discrete elements. In this book, the term discrete element is preferred because it does not presuppose the real nature of the body. Originally, the aim of this method was to solve a class of problems that cannot be treated by continuous or analytic approaches such as packing problems and hourglass flows. Figure I.1 illustrates the problem of packing spheres. It can be formulated as: what is the maximal number of spheres that can be introduced in a finite volume? In the case of equal spheres contained inside parallelepiped shapes, the problem is well known and analytic solutions exist. Figure I.1(a) shows an example of a perfect arrangement in two dimensions called hexagonal close-packing. For bounding volumes other than box-shaped, the solutions are not trivial. In the case of unequal spheres (for instance, random radius), even if the statistical distribution of the sphere sizes is known, an analytic solution does not exist and the arrangement cannot be predicted by an analytic formula. Figure I.1(b) shows an example of this disordered arrangement of unequal spheres. To solve this problem, a DEM simulation must be performed. The simulation considers each sphere as a rigid body. The interpenetrations between the spheres are forbidden2 due to contact management. The chosen DEM simulation must model a compaction process such as iterative growth algorithm [LUB 90] and isotropic compression [MAR 03]. As a result of these boundary conditions and mechanical loadings, the volume occupied by the discrete domain becomes minimal.
Figure I.1.Example of packing problems of spheres
To ensure that the solution is reproducible, the domain must contain a high number of discrete elements. These statistical considerations are of a high level of importance in DEM. To ensure the convergence of the solutions, the number of discrete elements to manage is high and it requires computational resources. In the last two decades, with the spectacular improvement of computer performances, DEM has met growing interest in the scientific community. Figure I.2 plots the evolution of the number of citations of the initial paper of Cundall and Strack about DEM [CUN 79] in the last 20 years. It clearly shows the enthusiasm of the scientific community for this numerical method.
Figure I.2.Number of citations of the initial paper of Cundall and Strack [CUN 79] in the last two decades
The growth of interest about DEM can also be explained by the emergence of novel methods based on the original approach by Cundall and Strack. Because DEM is a discontinuous method, it can be used to study discontinuous phenomena. In this case, the discrete elements are always present and can model a grain or just a part of a material. According to the problem to study, microscopic interaction laws are introduced at the scale of discrete elements and their neighbors. These interactions can be contacts, bonds or distant interactions such as the Lennard–Jones potential [VER 67].
Classifying the ecosystem of discrete methods is not easy. These methods interact with each other and new branches are often created. Readers can refer to the first volume of this book series where a classification of the DEM according to its respective spatial scales is proposed in the second chapter. The next section recalls the main aspects of this classification.
Following the DEM approach, two main algorithms and numerical schemes are distinguished:
–
the smooth
methods [CUN 79] based on
regular
interaction laws and explicit time integration algorithms. These methods are well adapted to model quick and time-short phenomena through dynamic simulations;
–
the non-smooth
[MOR 88] methods based on
non-regular
interaction laws and implicit time integration algorithms. These methods are well adapted to model slow phenomena through quasi-static simulations.
Again, depending on the phenomena to simulate, two main variants can be distinguished:
–
the particle
