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Advanced Reading

Advanced reading is not required for a Modeling Materials short course, but will enhance the student experience and learning outcomes. Below is a list of select chapters from the course textbooks:
  • MM: Modeling Materials: Continuum, Atomistic and Multiscale Techniques (Cambridge University Press, 2011).   
  • CMT: Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations  (Cambridge University Press, 2012).
Recommended topics include:
  • Chapter 1 in MM. Introduction. This gives an overview of the theme and spirit of the course.
  • Chapter 2 in MM. Continuum Mechanics and Thermodynamics. For those unfamiliar with this subject it is a good idea to read this chapter carefully. In particular, read sections 2.1.1 and 2.1.5 on tensors, 2.2 on kinematics, 2.3.1, 2.3.2 and 2.3.4 on conservation and balance laws, 2.4.1, 2.4.3 and 2.4.6 on thermodynamics, 2.5 on constitutive relations, and 2.6 on boundary-value problems. All of these topics are covered in much greater depth in CMT if you would like to explore them further.
    Note: if you are unfamiliar with the nonlinear finite element method (FEM) – a computational approach used in continuum mechanics and multiscale methods – read Chapter 9 in CMT after reading Chapter 2 in MM.
  • Chapter 3 in MM. Crystals. For those unfamiliar with crystal structure, this provides the background. We will cover this rather briefly in the course. You should read section 3.2, 3.3 and 3.6 for the basics of crystal structure.
  • Chapter 4 in MM. Quantum Mechanics. If you are completely new to quantum mechanics, sections 4.1-4.3 will get you started. Section 4.4 focuses on density functional theory (DFT), which is the method of choice for computing solid state properties with quantum accuracy. We will discuss this briefly in the course, mostly as a motivation for empirical interatomic potentials and to get an appreciation for the effort involved in DFT. Many of these details are beyond the scope of the course for those not already familiar with quantum mechanics.
  • Chapter 5 in MM. Empirical Potentials. We will discuss sections 5.4-5.6 in considerable detail, and touch briefly on the other sections of this chapter. An important aspect of the course will be the Knowledgebase of Interatomic Models (KIM) project, which is not part of the MM book (see https://openkim.org for more information).
  • Chapter 6 in MM. Molecular Statics. Sections 6.1-6.2 and 6.4 will be covered in detail, while we will include examples related to 6.5. We will also do hands-on molecular statics calculations using a widely-used and freely available code called LAMMPS (https://lammps.sandia.gov).
  • Chapter 7 in MM. Statistical Mechanics. This chapter will be covered in some detail because it serves as the foundation for molecular dynamics. Read sections 7.1 and 7.2 for the basic background to statistical mechanics.
  • Chapter 8 in MM. Microscopic expressions for stress. We will discuss this important connection between atomistics and continuum mechanics, focusing only on the stress tensor as our example. This is partly covered in Section 6.4 of chapter 6 and also in sections 8.2-8.3.
  • Chapter 9 in MM. Molecular Dynamics. All of this chapter will be covered in considerable detail. Section 9.2 describes the basic molecular dynamics (MD) algorithm, and sections 9.3-9.5 describe the application of MD subject to different external constraints. We will also do hands-on MD calculations using LAMMPS.
  • Chapter 10 in MM. What is multiscale modeling? This is another gentle introduction chapter that gives an overview of the field.
  • Chapters 12 and 13 in MM. We will cover static multiscale methods in depth, and touch on dynamic methods as time permits. Since the focus will be on the static methods (and we will use the static quasicontinuum (QC) code in the hands-on part of the course, you might focus your attention on chapter 12. If you would like to download the QC code and play with it ahead of the course, visit http://qcmethod.org.
Finally, most chapters in both books have a small introductory paragraph or two before the first formal section title. Taken together, these introductory paragraphs form a concise snapshot of the topics covered.
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