Announcement

MATH 6760         Continuum Mechanics: Solids

Fall 2004    3 credit hours    M,W,F   2:00-2:50  PM 

What is continuous mechanics?  According to Clifford Truesdell, Continuous mechanics studies general principles that govern forcible changes of shapes and forms which we daily observe around. It provides a uniform mathematical framework for investigating specific areas of mechanics such as elasticity, plasticity, viscosity, liquids, etc.
Text: 1. Notes (to be published on the Web)
          2. Review papers
          3. Lawrence E. Malvern. Introduction to the Mechanics of a Continuous Medium

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

This course is addressed to graduate students in Math, Physics, and Engineering.
Grade is based on a referate, homework, and activity in the class. 
Syllabus (preliminary)
Preliminaries:
  • Lagrangian mechanics
  • Vectors and tensors: algebra and calculus
  • Basic concepts: Stress, Strain, and Deformation
General Principles of Continuum Mechanics:
  • Conservation of mass and momentum principles.
  • Energy balance, Entropy and the Second Law of Thermodynamics
  • Gibbs' principle
Constitutive equations:
  • Classical and nonlinear elasticity
  • Expandable and thermoelastic materials
  • Viscoelasticity and Plasticity
Heretogeneous materials:
  • Homogenization and effective properties
  • Extremal structures
Adjustable materials:
  • "Smart" materials and Phase transition
  • Optimization and bio-materials
  • Locally unstable materials

    • Why study continuous mechanics? 

    For those who value the beauty of mathematical theories, it is enough to cite Lagrange:

    "The admirers of the Analysis will be pleased to learn that Mechanics became one of its new branches"
     (Lagrange, Mécanique analytique)

    For more practically inclined people, we recall the Indian parable about a Big picture:


    Five foreign travelers found an elephant in a dark barn. Each felt the elephant and described it to the others: 
        "The elephant is like a rope," said the first traveler, feeling the tail. 
        "The elephant is like a wall," said the second traveler, feeling the side. 
        "The elephant is like a blanket," said the third traveler, feeling its ear. 
        "The elephant is like a tree," said the fourth traveler, feeling its trunk. 
        "The elephant is like a spear," said the fifth traveler, feeling its tusk. 

    In came the Elephant Keeper and opened the door of the barn, and everyone discerned the whole elephantness. 


    See you in class!
    Andrej Cherkaev