Contents
Contributor contact details ix
Preface xi
1 The role of ab initio electronic structure calculations in multiscale modelling of materials 1
M. ŠOB, Masaryk University, Czech Republic and Academy of
Sciences of the Czech Republic
1.1 Introduction 1
1.2 Basic equations of electronic structure calculations 2
1.3 Illustrative examples 7
1.4 Conclusions 19
1.5 Acknowledgments 20
1.6 References 21
2 Modelling of dislocation behaviour at the continuum level 25
K. W. SCHWARZ, IBM Watson Research Center, USA
2.1 Introduction 25
2.2 Brief history 27
2.3 Implementation 28
2.4 Some current applications 44
2.5 Extensions of current discrete dislocation dynamics trends 54
2.6 Acknowledgments 57
2.7 References 57
3 Phase-field modelling of material microstructure 62
L.-Q. CHEN, Penn State University, USA
3.1 Introduction 62
3.2 Model description 63
3.3 Advantages and disadvantages 76
3.4 Recent developments and future opportunities 77
3.5 Acknowledgments 79
3.6 References 79
4 Mesoscale modelling of grain growth and microstructure in polycrystalline materials 84
D. MOLDOVAN, Louisiana State University, USA and D. WOLF,
Argonne National Laboratory, USA
4.1 Introduction 84
4.2 Molecular dynamics simulation of grain growth 87
4.3 Mesoscale simulation methodology 97
4.4 Validation of mesoscale simulations 103
4.5 Mesoscale simulation results 106
4.6 Summary and conclusions 114
4.7 Acknowledgments 117
4.8 References 117
5 Finite element and homogenization modelling of materials 121
J. LLORCA, C. GONZÁLEZ and J. SEGURADO, Polytechnic
University of Madrid, Spain
5.1 Introduction 121
5.2 Representative volume element 122
5.3 Homogenization techniques 125
5.4 Computational micromechanics 131
5.5 Multiscale coupling 136
5.6 Future directions 143
5.7 Acknowledgments 144
5.8 References 144
6 Grain–continuum modelling of material behaviour 148
M. O. BLOOMFIELD and T. S. CALE, Rensselaer Polytechnic Institute, USA
6.1 Introduction 148
6.2 Representations and models 154
6.3 Grain-continuum approach 161
6.4 Grain-continuum examples 165
6.5 Opportunities 174
6.6 References 180
7 Coupled atomistic/continuum modelling of plasticity in materials 189
R. E. MILLER, Carleton University, Canada
7.1 Introduction 189
7.2 Automatic adaption: the QC method 193
7.3 Kinematically identifying dislocations – the CADD method 202
7.4 Challenges and future trends 213
7.5 References 215
8 Multiscale modelling of carbon nanostructures 220
T. Y. NG, S. H. YEAK, and Y. X. REN, Nanyang Technological
University, Singapore; and K. M. LIEW, City University of
Hong Kong, Hong Kong
8.1 Introduction to carbon nanotube dynamics 220
8.2 Overlap TB/MD multiscale model 221
8.3 Simulation results of carbon nanotubes under axial loading 227
8.4 Introduction to hydrogen interaction with carbon nanostructures 239
8.5 Hybrid calculations with multiscale ONIOM scheme 241
8.6 Chemosorption of hydrogen atoms onto carbon nanotubes 249
8.7 References 259
9 Multiscale modelling of structural materials 261
D. PORTER, QinetiQ, UK
9.1 Introduction 261
9.2 Structural materials 262
9.3 Metals 264
9.4 Polymers 273
9.5 Ceramics 281
9.6 Time scales 282
9.7 Future trends 284
9.8 References 285
Index 288
Preface
Materials are fundamental building blocks of products and devices. Humans initially used materials that nature provided in finished or semi-finished forms such as flints, wood and natural fibres. This eventually progressed to engineering materials with sophisticated and heterogeneous structures due to both composition and processing. Continued harnessing of engineered materials and products in a timely and cost-effective manner requires the rapid development of new/improved processing techniques as well as indepth understanding and accurate control of materials chemistry, processing, structure, property, performance, durability and, more importantly, their relationships. This scenario usually involves multiple length and timescales and multiple processing and performance stages, which are, sometimes, accessible only via multiscale modelling. In the past, materials modelling has contributed greatly to our understanding of materials science and to advances in various technologies. However, many of the activities are usually confined within rather separate disciplines or communities, e.g. applied mathematics, physics, chemistry, materials, engineering or medicine, each of which usually concentrates on isolated problems involving rather narrow scales or aspects of materials. It is therefore essential to bring together modelling expertise across all the length/timescales to develop multiscalelinking methodologies to fulfil future industrial demands. Recent years have seen rapid development of computational technologies, both in terms of hardware and software. It is now possible to attempt seriously multiscale modelling and simulation using even desktop computers, and to predict accurately complex materials behaviours via computational methods. Under the theme of ‘Multiscale Modelling’, a wealth of new results has appeared that are either specific to one given scale or establish connections between different scales. A psychological barrier has been broken, taking advantage of the progress in available computing power, which now allows some overlap between different simulation methods: the realisation that thermodynamics and purely continuum frames cannot solve all problems; and the present drive in nanostructures/nanotechnology and in energy/environmental issues.
This book aims to provide a guiding tool for both academic researchers, who are developing or wish to apply appropriate modelling methodologies for a specific phenomenon in materials science, and industrialists, who would like to gain a comprehensive knowledge of multiscale materials modelling for product and/or process design and optimisation. The chapters are contributed by internationally recognised experts in the field, and cover the spectrum of scales in modelling methodologies. I wish to take the opportunity to thank all the contributing scientists and the staff at Woodhead Publishing Limited for untiring assistance in bringing the book to publication.
Professor Z. Xiao Guo