Fall 2006    3 credit hours
The first two meetings are at 10:45 AM-11:35 AM on Wed. Aug 23 and Fri. Aug 25 in NS 204

Instructor: Professor Andrej Cherkaev
        email: cherk@math.utah.edu,
        phone 581-6822,
        homepage: http://www.math.utah.edu/~cherk
        email: cherk@math.utah.edu

What is continuum mechanics?   Continuum mechanics studies forcible changes of shapes and forms, providing a uniform approach to elasticity, plasticity, viscosity, liquids, etc. The course focuses on linear and nonlinear elasticity, and the topics: mechanics of composite materials, biomaterials, and phase transition. We discuss related mathematical theories:tensor algebra and calculus, elements of multivariable calculus of variations, and homogenization, Several research papers and books' chapters will be suggested for review in class.

The course is addressed to graduate students in Applied Math, Science, and Engineering.

Text:

1. Notes (to be web-published )
2. Romesh C. Batra. Elements of Continuum Mechanics (AIAA Education Series) Chapters 1-5.

Preliminaries:

• Calculus of variation and Lagrangian mechanics
• Vectors and tensors: algebra and calculus

Continuum Mechanics:

• Linear elasticity
• Basic concepts: Stress, Strain, and Deformation
• Conservation principles and Energy: Nonlinear elasticity
• Entropy, Thermodynamics, Gibbs' principle

• Thermoelasticity, Viscoelasticity and Plasticity
  
• Homogenization
• Biomaterials, "Smart" materials and Phase transition
• Optimization