Fall 2018
AE 337/AE 731 - Multiscale Modeling of Materials

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.

I will also be posting lecture notes on this webpage. The notes are in draft form and will be updated and revised as the course progresses. Unlike the version uploaded on the moodle, the one here is the most up-to-date version. Make sure you have the latest version of the notes (just check the date on the first page to differentiate between the various versions). 
  • 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.

Spring 2018 
AE 486/AE 639 - Continuum Mechanics

This is a senior undergraduate/beginning graduate elective in Continuum Mechanics.  Here are some slides that cover the material discussed in class. 
  • Introduction and Course Logistics (slides)
  • A minimal introduction to key concepts in continuum mechanics can be found in these slides.
I will add to the content here and refine the slides when I get some time. The material here is fairly standard, and can be found in a variety of textbooks/lecture notes. I would like to thank the teaching assistant for this course, Ashish Kumar Bodla, for drawing most of the figures in the slides based on my hand-drawn sketches. 

I would appreciate it if you can bring to my attention any typos or errors in the material. I would also like to hear your comments and/or feedback. Thanks!

Mathematical Background

An introduction to linear and multilinear algebra can be found in these notes. Note that you will need to know only basic vector and tensor algebra in Euclidean spaces for the exams. The additional details, while not necessary for the exams, will give you a firm understanding of linear and multilinear algebra, and prepare you for the advanced material in case you are interested.
  • Set Theory (pdf) - for self-study; not covered in the lectures.
  • Linear Algebra (pdf).
  • Multilinear Algebra (pdf).
Advanced material (not required for exams!) 

These are advanced notes on select topics in Continuum Mechanics. The notes are in draft form at the moment, and I will be adding more material whenever I get some time to type things out. For the most part, the standard reference I have followed is Mathematical Foundations of Elasticity by Marsden & Hughes.
  • Introduction to Manifolds and elementary definitions in Kinematics (pdf). 
  • Analysis of Deformation (pdf).