Discrete element model and simulation of continuous materials behavior set. Volume 1, Discrete element method to model 3D continuous materials

198 Pages·2015·6.518 MB·English

by  Mohamed Jebahi, Damien Andre, Inigo Terreros, Ivan Iordanoff

Discrete Element Method to Model 3D Continuous Materials

Discrete Element Model and Simulation
of Continuous Materials Behavior Set
coordinated by
Ivan Iordanoff
Volume 1
Discrete Element
Method to Model 3D
Continuous Materials

Mohamed Jebahi
Damien André
Inigo Terreros
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,
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ISTE Ltd John Wiley & Sons, Inc.
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© ISTE Ltd 2015
The rights of Mohamed Jebahi, Damien André, Inigo Terreros 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: 2015930631

British Library Cataloguing-in-Publication Data
A CIP record for this book is available from the British Library
ISBN 978-1-84821-770-6
Contents
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . xv
PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . xxi
CHAPTER 1. STATE OF THE ART: DISCRETE
ELEMENT MODELING . . . . . . . . . . . . . . . . . . . . 1
1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Classification of discrete methods . . . . . . . . . 3
1.2.1.Quantum mechanical methods . . . . . . . . . 4
1.2.2.Atomistic methods . . . . . . . . . . . . . . . . . 5
1.2.3.Mesoscopic discrete methods . . . . . . . . . . 8
1.3. Discrete element method for continuous
materials . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.4. Discrete-continuum transition: macroscopic
variables . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.4.1.Stress tensor for discrete systems . . . . . . . 18
1.4.2.Strain tensor for discrete systems . . . . . . . 21
1.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 31
vi DiscreteElementMethodtoModel3DContinuousMaterials
CHAPTER 2. DISCRETE ELEMENT MODELING
OF MECHANICAL BEHAVIOR OF
CONTINUOUS MATERIALS . . . . . . . . . . . . . . . . . 33
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 33
2.2. Explicit dynamic algorithm . . . . . . . . . . . . . 35
2.3. Construction of the discrete domain . . . . . . . . 37
2.3.1.The cooker compaction algorithm . . . . . . . 39
2.3.2.Geometrical characterization of the discrete
domain . . . . . . . . . . . . . . . . . . . . . . . . 44
2.4. Mechanical behavior modeling . . . . . . . . . . . 56
2.4.1.Cohesive beam model . . . . . . . . . . . . . . . 58
2.4.2.Calibration of the cohesive beam static
parameters . . . . . . . . . . . . . . . . . . . . . . 64
2.4.3.Calibration of the cohesive beam dynamic
parameters . . . . . . . . . . . . . . . . . . . . . . 79
2.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 87
CHAPTER 3. DISCRETE ELEMENT
MODELING OF THERMAL BEHAVIOR
OF CONTINUOUS MATERIALS . . . . . . . . . . . . . . . 93
3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 93
3.2. General description of the method . . . . . . . . . 95
3.2.1.Characterization of field variable
variation in discrete domain . . . . . . . . . . . 95
3.2.2.Application to heat conduction . . . . . . . . . 96
3.3. Thermal conduction in 3D ordered
discrete domains . . . . . . . . . . . . . . . . . . . . 97
3.4. Thermal conduction in 3D disordered
discrete domains . . . . . . . . . . . . . . . . . . . . 100
3.4.1.Determination of local parameters
for each discrete element . . . . . . . . . . . . . 102
3.4.2.Calculation of discrete element
transmission surface . . . . . . . . . . . . . . . . 103
3.4.3.Calculation of local volume fraction . . . . . . 104
3.4.4.Interactions between each discrete
element and its neighbors . . . . . . . . . . . . 105
Contents vii
3.5. Validation . . . . . . . . . . . . . . . . . . . . . . . . 106
3.5.1.Cylindrical beam in contact
with a hot plane . . . . . . . . . . . . . . . . . . . 106
3.5.2.Dynamically heated sheet . . . . . . . . . . . . 107
3.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 113
CHAPTER 4. DISCRETE ELEMENT MODELING
OF BRITTLE FRACTURE . . . . . . . . . . . . . . . . . . . 115
4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . 115
4.2. Fracture model based on the cohesive beam
bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4.2.1.Fracture criterion . . . . . . . . . . . . . . . . . 118
4.2.2.Calibration . . . . . . . . . . . . . . . . . . . . . 120
4.2.3.Convergence study . . . . . . . . . . . . . . . . 123
4.2.4.Validation . . . . . . . . . . . . . . . . . . . . . . 125
4.3. Fracture model based on the virial stress. . . . . 132
4.3.1.Fracture criterion . . . . . . . . . . . . . . . . . 132
4.3.2.Calibration . . . . . . . . . . . . . . . . . . . . . 134
4.3.3.Convergence study . . . . . . . . . . . . . . . . 134
4.3.4.Validation . . . . . . . . . . . . . . . . . . . . . . 136
4.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . 137
CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . 141
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . 145
INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161