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Addresses the very topical, crucial and original subject of parameter identification and optimization within multiscale modeling methods
Multiscale Modelling and Optimization of Materials and Structures presents an important and challenging area of research that enables the design of new materials and structures with better quality, strength and performance parameters as well as the creation of reliable models that take into account structural, material and topological properties at different scales. The authors' approach is four-fold; 1) the basic principles of micro and nano scale modeling techniques; 2) the connection of micro and/or nano scale models with macro simulation software; 3) optimization development in the framework of multiscale engineering and the solution of identification problems; 4) the computer science techniques used in this model and advice for scientists interested in developing their own models and software for multiscale analysis and optimization.
The authors present several approaches such as the bridging and homogenization methods, as well as the general formulation of complex optimization and identification problems in multiscale modelling. They apply global optimization algorithms based on robust bioinspired algorithms, proposing parallel and multi-subpopulation approaches in order to speed-up computations, and discuss several numerical examples of multiscale modeling, optimization and identification of composite and functionally graded engineering materials and bone tissues. Multiscale Modelling and Optimization of Materials and Structures is thereby a valuable source of information for young scientists and students looking to develop their own models, write their own computer programs and implement them into simulation systems.
* Describes micro and nano scale models developed by the authors along with case studies of analysis and optimization
* Discusses the problems of computing costs, efficiency of information transfer, effective use of the computer memory and several other aspects of development of multiscale models
* Includes real physical, chemical and experimental studies with modern experimental techniques
* Provides a valuable source of information for young scientists and students looking to develop their own models, write their own computer programs, and implement them into simulation systems.
List of contents
Preface ix
Biography xi
1 Introduction to Multiscale Modelling and Optimization 1
1.1 Multiscale Modelling 2
1.1.1 Basic Information on Multiscale Modelling 2
1.1.2 Review of problems connected with multiscale modelling techniques 3
1.1.3 Prospective Applications of the Multiscale Modelling 6
1.2 Optimization 6
1.3 Contents of the Book 7
References 7
2 Modelling of Phenomena 9
2.1 Physical Phenomena in Nanoscale 9
2.1.1 The Linkage Between Quantum and Classical Molecular Mechanics 10
2.1.2 Atomic Potentials 15
2.1.2.1 Lennard-Jones Potential 15
2.1.2.2 Morse Potential 16
2.1.2.3 Stillinger-Weber Potential 17
2.1.2.4 Reactive empirical bond order (REBO) potential 18
2.1.2.5 Reactive force fields (ReaxFF) 19
2.1.2.6 Murrell-Mottram Potential 20
2.1.2.7 Embedded Atom Method 21
2.2 Physical Phenomena in Microscale 22
2.2.1 Microstructural Aspects of Selection of a Microscale Model 22
2.2.1.1 Plastometric Tests 23
2.2.1.2 Inverse Analysis 26
2.2.2 Flow Stress 26
2.2.2.1 Procedure to Determine Flow Stress 26
2.2.2.2 Flow Stress Model 28
2.2.2.3 Identification of the Flow Stress Model 30
2.2.3 Recrystallization 32
2.2.3.1 Static Microstructural Changes 33
2.2.3.2 Dynamic Softening 38
2.2.3.3 Grain Growth 41
2.2.3.4 Effect of Precipitation 42
2.2.4 Phase Transformations 43
2.2.4.1 JMAK-Equation-Based Model 47
2.2.4.2 Differential Equation Model 49
2.2.4.3 Numerical Solution 50
2.2.4.4 Additivity Rule 50
2.2.4.5 Phase Transformation During Heating 51
2.2.4.6 Identification of the Model 52
2.2.4.7 Case Studies 56
2.2.5 Fracture 57
2.2.5.1 Fundamentals of Fracture Mechanics and Classical Fracture and Failure Hypotheses 58
2.2.5.2 Empirical Fracture Criteria 60
2.2.5.3 Fracture Mechanics 61
2.2.5.4 Continuum Damage Mechanics (CDM) 62
2.2.6 Creep 66
2.2.7 Fatigue 71
References 73
3 Computational Methods 81
3.1 Computational Methods for Continuum 81
3.1.1 FEM and XFEM 81
3.1.1.1 Principles of Computational Modelling Using FEM 81
3.1.1.2 Principles of Computational Modelling Using FEM 83
3.1.1.3 Extended Finite Element Method 88
3.1.2 BEM and FEM/BEM Coupling 91
3.1.2.1 BEM 91
3.1.2.2 Coupling FEM and BEM 95
3.1.3 Computational Homogenization 96
3.2 Computational Methods for Nano and Micro 101
3.2.1 Classical Molecular Dynamics 101
3.2.1.1 Equations of Motion 101
3.2.1.2 Discretization of Equations of Motion 102
3.2.1.3 Temperature Controller 105
3.2.1.4 Evaluation of the Time Step 108
3.2.1.5 Cutoff Radius and Nearest-Neighbour Lists 109
3.2.1.6 Boundary Conditions 111
3.2.1.7 Size of the Atomistic Domain - Limitations of the Molecular Simulations 112
3.2.2 Molecular Statics 114
3.2.2.1 Equilibrium of Interatomic Forces 114
3.2.2.2 Solution of the Molecular Statics Problem 116
3.2.2.3 Numerical Example of the Molecular Statics 118
3.2.3 Cellular Automata 119
3.2.3.1 Cellular Automata Definitions 119
3.2.4 Monte Carlo Methods 125
3.3 Methods of Optimization 127
3.3.1 Optimization Problem Formulation 127
3.3.2 Methods of Conventional Optimization 1
Summary
Addresses the topical, crucial and original subject of parameter identification and optimization within multiscale modeling methods. This book presents an area of research that enables the design of materials and structures with better quality, strength and performance parameters. It describes micro and nano scale models along with case studies.
