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Teaching

Lecture notes and slides for the courses I teach can be found here. Note that most of these are in draft form (as indicated by a watermark in the notes) and will be continuously updated. Please let me know if you find any errors, or if you have any comments/criticisms/suggestions.

AE 337/AE 731 - Multiscale Modeling of Materials

Fall 2018

This is a new graduate level elective dealing with various aspects of modeling the mechanical behavior of crystalline materials across various length and time scales, from atomistic to the continuum. More information on the course objectives and policy can be found here. Assignments for the course will be uploaded on the IITB Moodle.

Here is a rough outline of the course with (partial) lecture notes:

  • Introduction to Multiscale Modeling. (slides)
  • A basic introduction to Quantum Mechanics. (pdf)
  • Introduction to multi-particle systems. (pdf)
  • Introduction to Density Functional Theory. (pdf)
  • Transition to Classical Mechanics. (pdf)
  • Elements of Statistical Mechanics.
  • Monte Carlo methods, Molecular Dynamics.
  • Transition to Continuum Mechanics - Irving-Kirkwood-Noll procedure.
  • Case study: multiscale modeling of plasticity in metals.

AE 486/AE 639 - Continuum Mechanics

Spring 2019

Course material will be uploaded here as the semester progresses. The TAs for this course this year are Sneha Cheryala and Lalit Bhola.

Here are some handouts that either summarize the content covered in the lectures, or present a slightly more general version of the topics taught in the classroom. More handouts will be uploaded as the semester progresses. These handouts are the primary reference for this course.

Please note that most of these handouts are in the draft form - they aren't fully proof-read yet. (Will be done eventually!)

  • Introduction and Course Logistics (slides).

Mathematical Prerequisites:

  • Basic Set Theory (handout).
  • Linear Algebra (handout).
  • Multilinear Algebra (handout).
  • Inner Product Spaces (handout).
  • Differentiation in Normed Vector Spaces (handout).
  • Euclidean Tensor Analysis (handout).
  • Special coordinate systems (Video lectures).

Kinematics:

Balance principles:

  • Continuum Thermodynamics (handout).
  • Cauchy Localization Theorem (handout).
  • Green-Naghdi-Rivlin Theorem (handout).
  • Local form of first and second law (handout).
  • Lagrangian form of balance equations (handout).

Constitutive Modeling:

  • General principles (handout).
  • Fluid Mechanics (handout).
  • Nonlinear Elasticity (Flipped classroom - Video lectures).
  • Linear Elasticity (Flipped classroom - Video lectures).

General References

Continuum Mechanics is a mature discipline with numerous outstanding textbooks. Here are a few references that I found useful when preparing the notes:

  • Mathematical Foundations of Elasticity by J.E. Marsden and T.J.R. Hughes. (This is the gold standard for Continuum Mechanics, in my opinion.)
  • Non-Linear Elastic Deformations by R.W. Ogden.
  • Elasticity and Plasticity of Large Deformations: An Introduction by A. Bertram.
  • Nonlinear Solid Mechanics - a continuum approach for engineering by G.A. Holzapfel.
  • Foundations and Applications of Mechanics: Volume 1 - Continuum Mechanics by C.S. Jog.

I also consulted the following lecture notes when preparing the course material:

  • Notes by Papadopoulos. I have referred to this source extensively.
  • Notes by Rohan Abeyaratne.
  • Notes by I-Shih Liu.
  • Notes by Michael Ortiz (private communication).

For the mathematical content related to linear and multilinear algebra, I found the book A course in modern mathematical physics: groups, Hilbert space and differential geometry by P. Szekeres to be quite useful.

Spring 2018

This is a senior undergraduate/beginning graduate elective in Continuum Mechanics. The course TA for this year is Ashish Kumar Bodla.

Please refer to the most recent offering of the course for slides and/or lecture notes.