Multiphysics and Multiscale Modeling

Techniques and Applications

Young W. Kwon

• Publisher: CRC Press
• Year: 2015
• ISBN:
  9781498782524
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

Written to appeal to a wide field of engineers and scientists who work on multiscale and multiphysics analysis, Multiphysics and Multiscale Modeling: Techniques and Applications is dedicated to the many computational techniques and methods used to develop man-made systems as well as understand living systems that exist in nature. Presenting a body

1

Introduction

1.1    Overview

There are systems that exist in nature and there are systems developed by human beings. For example, the bodies of humans and animals are living systems in nature, and power plants are man-made systems. To understand or develop such systems, it is necessary to conduct multiphysics and multiscale analyses.

Multiphysics analysis is the study of multiple physical behaviors as they interact with one another. For example, the human body is a good example of something that requires multiphysics analyses. Chemistry and biology are basic knowledge necessary to understand living cells, tissues, organs, and the like. However, those subjects are not considered in this book because they are outside of the scope of the study. Only the physical aspects are considered in multiphysics analysis.

Considering the blood circulation system in the human body, blood vessels require fluid mechanics analysis to study blood flow and blood pressure; the system also requires structural analysis to investigate contraction and dilation as well as aneurysms and potential ruptures of the blood vessels. In this case, both analyses should be coupled because blood and vessels interact. As a result, multiphysics analysis is required. As an example for a man-made system, a power plant contains many heat pipes that carry hot fluid, which also requires fluid mechanics analysis and structural analysis, leading to multiphysics analysis. When there is an exchange of heat between the fluids inside and outside the heat pipes, heat transfer analysis should also be considered.

In many cases, a single analysis is conducted, neglecting the interactive aspect of multi-physics because the single analysis is much simpler. However, if the interaction is strong and influencing each participant, a single analysis may not provide reliable results. In that case, multiphysics analysis must be undertaken even though it is more complex and requires more effort. With advances in computing power as well as computational techniques, multiphysics analysis has been more common in engineering design and analysis.

On the other hand, almost every material and living organism has a complex hierarchical structure in different length scales. Human bones are good examples. They consist of simple elements at the nanoscale from a mechanics point of view. However, through the complex hierarchical structures in different length scales, bones are optimized and provide necessary strength and stiffness for the human skeleton. Likewise, man-made composite materials consist of fibers and matrix materials. Through aligning or weaving the fibers, the fiber composite structures become strong, stiff, and light for use for new technology. Metals also have many different characteristics at the different length scales.

To understand and predict their behaviors as well as to develop new materials, it is necessary to undertake multiscale analysis. This analysis links the main characteristics at different length scales so that we can have more fundamental understanding of their behavior as well as knowledge of what are the most important hierarchical structures influencing the macroscale behavior.

1.2    Computational Methods

Advances in computing capabilities as well as computational techniques contribute to the study of multiphysics and multiscale analysis. In this section, we discuss some computational methods used for multiscale and multiphysics analyses. There is no intention to list and discuss all the available computational methods here. Some computational methods are presented that are relevant to the contents of the book.

The finite element method is arguably the most popular and powerful computational technique to analyze continuous media [1, 2, 3]. This technique can solve virtually any differential equation with proper boundary and initial conditions for complex shapes of domains. The finite element method was developed initially for structural analysis, and the technique has spread to other types of applications, including problems in fluid mechanics, electromagnetic waves, and so on. As a result, the finite element method is useful for multiphysics problems.

The finite element technique is useful for solving continuous domain problems; the molecular dynamics technique is applicable to discrete domain problems such as atomistic and molecular modeling [4,5]. As a result, the length scale of the molecular dynamics problems is much smaller than the length scale of the finite element analysis problems. In order to combine the two techniques, a coupling technique is necessary for multiscale analyses.

The lattice Boltzmann method as well as cellular automata can be applied to both continuous and discrete domain problems [6, 7, 8, 9]. These are the advantages of the techniques. However, those methods are based on rules, and those rules are not straightforward for development for any differential equation. As a result, the lattice Boltzmann method and the cellular automata have been applied to a limited number of problems. Because those methods are based on rules, they are easy to program and are computationally efficient.

1.3    Organization of This Book

This book is organized in the following manner: first, multiple computational techniques are presented in Chapters 2 through 5, respectively: the finite element method, lattice Boltzmann method, cellular automata, and molecular dynamics technique. Then, Chapter 6 presents coupling techniques to take advantage of these methods. Finally, several example problems are discussed for multiphysics and multiscale problems in Chapters 7 through 12. The first three of these chapters are for multiscale analyses, and the last three chapters are for multiphysics problems.

Multiscale analysis for composite materials and structures is provided in Chapter 7; fibrous composite, particulate composite, and woven fabric composite materials and structures are presented as examples. Multiscale analysis for metals is given in Chapter 8. In this chapter, a simplified analysis is provided for crystalline structures using the finite element method and molecular dynamics. Then, Chapter 9 discusses multiscale analysis of biomaterials using human bones as an example.

Multiphysics problems are discussed for composite structures in Chapter 10. Fluid–structure interaction is presented for composite structures surrounded by water. Ship structures are examples of these structures. Chapter 11 provides an example of the multi-physics analysis of electromechanical problems. A rail gun is selected as an example problem; this couples electromagnetic waves, heat transfer, and rigid body dynamics. Finally, Chapter 12 presents a multiphysics analysis of biomechanics using the example of blood vessels, for which there is fluid–structure interaction.

2

Finite Element Method

2.1 Introduction

The finite element method (FEM) is one of the most widely used numerical solution techniques [1, 2, 3]. Especially, the FEM has been used almost exclusively for analyses of solids and structures. This chapter introduces the basic finite element concepts and presents formulation...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgments
• Author
• 1. Introduction
• 2. Finite Element Method
• 3. Lattice Boltzmann Method
• 4. Cellular Automata
• 5. Molecular Dynamics
• 6. Coupling Techniques
• 7. Multiscale Analysis of Composite Structures
• 8. Multiscale Analysis of Metallic Materials
• 9. Multiscale Analysis of Biomaterials
• 10. Multiphysics Analysis of Composite Structures
• 11. Multiscale Analysis of Electromechanical System
• 12. Multiphysics Analysis of Biomechanics
• References
• Index