Multiscale Modelling and Optimisation of Materials and Structures

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats. Limit of Liability/Disclaimer of Warranty The contents of this work are intended to further general scientific research, understanding, and discussion only and are not intended and should not be relied upon as recommending or promoting scientific method, diagnosis, or treatment by physicians for any particular patient. In view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of medicines, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each medicine, equipment, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Cover Title Page Copyright Page Contents Preface Biography Chapter 1 Introduction to Multiscale Modelling and Optimization 1.1 Multiscale Modelling 1.1.1 Basic Information on Multiscale Modelling 1.1.2 Review of Problems Connected with Multiscale Modelling Techniques 1.1.3 Prospective Applications of the Multiscale Modelling 1.2 Optimization 1.3 Contents of the Book References Chapter 2 Modelling of Phenomena 2.1 Physical Phenomena in Nanoscale 2.1.1 The Linkage Between Quantum and Classical Molecular Mechanics 2.1.2 Atomic Potentials 2.1.2.1 Lennard-Jones Potential 2.1.2.2 Morse Potential 2.1.2.3 Stillinger-Weber Potential 2.1.2.4 Reactive Empirical Bond Order (REBO) Potential 2.1.2.5 Reactive Force Fields (ReaxFF) 2.1.2.6 Murrell-Mottram Potential 2.1.2.7 Embedded Atom Method 2.2 Physical Phenomena in Microscale 2.2.1 Microstructural Aspects of Selection of a Microscale Model 2.2.1.1 Plastometric Tests 2.2.1.2 Inverse Analysis 2.2.2 Flow Stress 2.2.2.1 Procedure to Determine Flow Stress 2.2.2.2 Flow Stress Model 2.2.2.3 Identification of the Flow Stress Model 2.2.3 Recrystallization 2.2.3.1 Static Microstructural Changes 2.2.3.2 Dynamic Softening 2.2.3.3 Grain Growth 2.2.3.4 Effect of Precipitation 2.2.4 Phase Transformations 2.2.4.1 JMAK-Equation-Based Model 2.2.4.2 Differential Equation Model 2.2.4.3 Numerical Solution 2.2.4.4 Additivity Rule 2.2.4.5 Phase Transformation During Heating 2.2.4.6 Identification of the Model 2.2.4.7 Case Studies 2.2.5 Fracture 2.2.5.1 Fundamentals of Fracture Mechanics and Classical Fracture and Failure Hypotheses 2.2.5.2 Empirical Fracture Criteria 2.2.5.3 Fracture Mechanics 2.2.5.4 Continuum Damage Mechanics (CDM) 2.2.6 Creep 2.2.7 Fatigue References Chapter 3 Computational Methods 3.1 Computational Methods for Continuum 3.1.1 FEM and XFEM 3.1.1.1 Principles of Computational Modelling Using FEM 3.1.1.2 Principles of Computational Modelling Using FEM 3.1.1.3 Extended Finite Element Method 3.1.2 BEM and FEM/BEM Coupling 3.1.2.1 BEM 3.1.2.2 Coupling FEM and BEM 3.1.3 Computational Homogenization 3.2 Computational Methods for Nano and Micro 3.2.1 Classical Molecular Dynamics 3.2.1.1 Equations of Motion 3.2.1.2 Discretization of Equations of Motion 3.2.1.3 Temperature Controller 3.2.1.4 Evaluation of the Time Step 3.2.1.5 Cutoff Radius and Nearest-Neighbour Lists 3.2.1.6 Boundary Conditions 3.2.1.7 Size of the Atomistic Domain – Limitations of the Molecular Simulations 3.2.2 Molecular Statics 3.2.2.1 Equilibrium of Interatomic Forces 3.2.2.2 Solution of the Molecular Statics Problem 3.2.2.3 Numerical Example of the Molecular Statics 3.2.3 Cellular Automata 3.2.3.1 Cellular Automata Definitions 3.2.4 Monte Carlo Methods 3.3 Methods of Optimization 3.3.1 Optimization Problem Formulation 3.3.2 Methods of Conventional Optimization 3.3.3 Methods of Nonconventional Optimization 3.3.3.1 Evolutionary Algorithm 3.3.3.2 Artificial Immune System 3.3.3.3 Particle Swarm Optimization 3.3.3.4 Hybrid Optimization Algorithms References Chapter 4 Preparation of Material Representation 4.1 Generation of Nanostructures 4.1.1 Modelling of Polycrystals and Material Defects 4.1.1.1 Controlled Cooling 4.1.1.2 Adjustable Range of Atomic Interactions 4.1.1.3 Squeezing of the Nanoparticles 4.1.1.4 Modelling of Structures with Voids 4.1.1.5 Material Properties of the Nanostructures 4.1.1.6 Models and Mechanical Properties of 2D Materials with Point Defects 4.2 Microstructure 4.2.1 Generation of Microstructures 4.2.1.1 Voronoi Tessellation 4.2.1.2 Cellular Automata Grain Growth Algorithm 4.2.1.3 Close-Packed Sphere Growth CA-Based Grain Growth Algorithm 4.2.1.4 Monte Carlo Grain Growth Algorithm 4.2.1.5 DigiCore Library 4.2.1.6 Image Processing 4.2.2 Properties of the Microstructure Features References Chapter 5 Examples of Multiscale Simulations 5.1 Classification of Multiscale Modelling Methods 5.2 Case Studies 5.2.1 Nano–Micro 5.2.1.1 Multiscale Discrete-Continuum Model 5.2.1.2 Conversion of the Nodal Forces to Tractions 5.2.1.3 Examples of the Nanoscale–Microscale Modelling 5.2.2 Microscale–Macroscale 5.2.2.1 Dynamic Recrystallization 5.2.2.2 Phase Transformation 5.2.2.3 Microshear Bands, Shear Bands, and Strain Localization References Chapter 6 Optimization and Identification in Multiscale Modelling 6.1 Multiscale Optimization 6.1.1 Optimization of Atomic Clusters 6.1.1.1 Introduction to Optimization of Atomic Clusters 6.1.1.2 Optimization of Carbon Atomic Clusters 6.1.1.3 New Stable Carbon Networks X and Y 6.1.2 Material, Shape, and Topology Optimization 6.2 Identification in Multiscale Modelling 6.2.1 Material Parameters Identification 6.2.2 Multiscale Identification Problem in Stochastic Conditions 6.2.3 Shape and Topology Identification 6.2.4 Identification of Shape for Multiscale Thermomechanical Problems References Chapter 7 Computer Implementation Issues 7.1 Interactions Between the Analysis and Optimization Solutions 7.1.1 Example of Direct Problem Solver File Access 7.1.2 Examples of an Internal Script in Direct Problem Solver 7.2 Visualization of Large Data Sets 7.2.1 Implementation Aspects and Tools 7.2.1.1 Graphical Libraries 7.2.1.2 Software 7.2.1.3 Frameworks 7.2.1.4 Data Storing 7.2.2 High Efficiency of Visualization 7.2.2.1 Dedicated Algorithms 7.2.2.2 Hardware Parallelism 7.2.2.3 Quality Improvement 7.2.2.4 Material Data for Visualization Purposes 7.2.3 Visualization Based on Sectioning 7.2.3.1 Algorithm Idea 7.2.3.2 Background Buffering 7.2.3.3 Preferred Sections 7.2.4 Functional Assumptions 7.2.4.1 Data Preprocessing 7.2.4.2 Visualization 7.2.5 Case Studies 7.2.5.1 Digital Microstructures 7.2.5.2 Performance Tests References Chapter 8 Concluding Remarks Index EULA 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. "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."-- Provided by publisher. 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.