6760-001 Continuum Mechanics: Solids
  
MW  03:00 PM-04:20 PM CSC 10
(Crocker Science Center)

Instructor:
Professor Andrej  Cherkaev
Department of Mathematics  
email: cherk@math.utah.edu 
phone : +1 801 - 581 6822, 
Office: JWB 225.

Syllabus

Continuum Mechanics of Solids deals with the mathematical description of deformations and stresses in solid bodies.

Topics: 
  1. Vectors and tensors, properties and basic operations;
  2. Kinematics of deformation; linearization and strain, stress tensor;
  3. Energy, conservation laws, constitutive equations; Linear and nonlinear elasticity;
  4. Introductory problems in finite and linear elasticity;
  5. Thermodynamics; viscous, and visco-elastic response;
  6. Topics from the theory of composites and adaptive materials, intro to optimal designs. 


The course is addressed to graduate and advanced undergraduate students in Applied Mathematics and Engineering.

Textbook: Introduction to Continuum Mechanics (4th Edition) by W Michael Lai, David Rubin, Erhard Krempl, Chapters 1- 5.
This book is the most popular text on the subject.

Additional recommended (not required) text is: Schaum's Outline of Continuum Mechanics by George Mase
The solution manual helps with homework problems.

Complementary online sources include
Continuum Mechanics Lecture Notes on The Mechanics of Elastic Solids by Rohan Abeyaratne (MIT), 
Lecture Notes by Allan Bower (Brown University),
and other.


The grade is based on homework assignments and the (optional) course project.

Assignment: Read the papers:

1.  Progress and puzzles in nonlinear elasticity by J.M. Ball
https://people.maths.ox.ac.uk/ball/Papers/Ball%20Udine%202009.pdf

2. On the Rank 1 Convexity of Stored Energy Functions of Physically Linear Stress-Strain Relations
by Albrecht Bertram ·Thomas Böhlke · Miroslav Šilhavý
https://pdfs.semanticscholar.org/2b94/b10911dde87441a1f11432be222daee1f476.pdf

3. Mathematical Foundations of Elasticity Theory
slides of the lecture by John Ball,
https://people.maths.ox.ac.uk/ball/Teaching/Mathematical_Foundations_of_Elasticity_Theory.pdf