Modelling and Optimization in Physical Metallurgy

Instructor:Alexander Churyumov

Course Summary

The aim of the discipline is to develop students’ expertise and skills on the methods of the mathematical modeling and optimization of the metallic materials and processes and the development of the practical skills of computer modeling in physical metallurgy and metallography.

Course Format

Hours of lectureHours of practiceHours in laboratoryHours of independent studyTotal numbers of hours

Course Content

  1. Mathematical modeling. General classification of the mathematical models
    1. Simulation as a method of the objects investigation.
    2. Classification of the mathematical models: deterministic, statistical, object-oriented.
    3. Steps for building of the mathematical models.
  2. Regression analysis and artificial neural networks
    1. Methods of the regression models construction.
    2. The concepts of the artificial neural networks. Training methods for the artificial neural networks based models.
    3. Determination of the errors of calculation and verification of the adequacy of the models.
  3. Molecular dynamics. Calculation of the properties of metal materials based on first principles
    1. Basic concepts of molecular dynamics simulation.
    2. Interparticle interaction. Types of the pair potentials.
    3. The initial and boundary conditions for the molecular dynamics simulation.
    4. Equilibrium molecular dynamics models.
  4. The Monte Carlo method. Modeling of the deformed structure of metallic materials.
    1. Basics of the Monte-Carlo method
    2. The pseudo-random numbers generator.
    3. The sequence of the building Monte-Carlo based models
  5. The method of cellular automata. Modeling of the recrystallization process in deformed metallic materials
    1. The basic concepts of the cellular automata method.
    2. The application of the cellular automata in science and technology.
    3. Stages of the construction cellular automata based models.
    4. The concept of the method of non-static cellular automata
  6. The finite element method. Modelling of plastic deformation
    1. The basic principles of the finite element modeling.
    2. The implementation of the finite element method for the simulation of heat transfer.
    3. The implementation of the finite element method for the simulation of plastic deformation
    4. Basic software packages for finite element modeling.

Reading List

Primary textbooks:

  1. Zoe H. Barber. (Editor); Introduction to materials modeling; Maney Publishing; 2005
  2. D.U. Furrer, S.L. Semiatin (Editors); ASM HANDBOOK. Volume 22B. Metals Process Simulation; The Materials Information Company; 2010

Additional textbooks:

  1. D. Raabe; Computational Materials Science: The Simulation of Materials, Microstructures and Properties; Wiley-VCH; 1998
  2. R. Phillips
  3. Crystals, Defects and Microstructures: Modeling Across Scales; Cambridge University Press; 2001
  4. K. Ohno, K. Esfarjani and Y. Kawazoe; Computational Materials Science: From Ab Initio to Monte Carlo Methods; Springer; 1999
  5. R. H. Wagoner and J.-L. Chenot,; Metal Forming Analysis; Cambridge University Press; 2001
  6. K. M. Entwistle; Basic Principles of the Finite Element Method; The Institute of Materials; 1999
  7. Y. Shimizu,R. Hart, P. A. Cundall; Numerical modeling in Micromechanics via Particle Methods; Taylor and Francis; 2004
  8. S.S. Bhavikatti; Finite Element Analysis; New Age International; 2005