ENME 670 / MATH 710, Fall 2002
Continuum Mechanics

Course information

Course:	ENME 670 / MATH 710: Continuum Mechanics
Time/Place:	MW 2:30pm-3:45pm, ECS 112
Instructor:	Dr. Rouben Rostamian
Office:	MP 417
Phone:	410-455-2458
Email:	rostamian@umbc.edu
Office hours:	MW 3:45-4:45 and by appointment

This paper gives wrong solutions to trivial problems. The basic error, however, is not new.

Clifford A. Truesdell in Mathematical Reviews, 12, 561a

We [he and Halmos] share a philosophy about linear algebra: we think basis-free, we write basis-free , but when the chips are down we close the office door and compute with matrices like fury.

Irving Kaplansky in Paul Halmos: Celebrating 50 Years of Mathematics

Course Description

This is an introductory course in continuum mechanics intended for graduate students of physics, engineering and mathematics.

Continuum mechanics is the study of the relationship between forces and deformations in continuous media. The subject encompasses fluid mechanics, gas dynamics, linear and nonlinear elasticity, viscoelasticity and many other types of material behavior.

Reading material

Peter Chadwick's Continuum Mechanics: Concise Theory and Problems will serve as the main textbook for this course. We will cover essentially all of it. Additional material will be drawn from Morton Gurtin's An Introduction to Continuum Mechanics which will serve as supplementary reading for this course. Unfortunately Gurtin's book is rather expensive. Although it will be available for purchase in the bookstore, one copy will be placed on reserve in the library for borrowing one-day-at-a-time for those who don't want to invest in it. [Note added August 30, 2002: it appears that Gurtin's book is out-of-print, therefore the bookstore may not be able to stock it.]

Gerhard Holzapfel's book, Nonlinear Solid Mechanics: A Continuum Approach for Engineering, is another good reference for this course. Give it a try and see if you like its exposition.

I have placed the books by Chadwick, Gurtin and Holzapfel on reserve in the library. They can be checked out for 2 hours, 2 days and 1 day, respectively.

Syllabus

Topics will include:

• Review of the prerequisite mathematics: operator theory, tensor algebra
• Kinematics, deformations, the transport theorem
• Balance of mass, momentum and angular momentum
• Stress and strain
• Constitutive equations
• Frame-invariance (objectivity)
• Symmetry, isotropy
• Representation theorems for isotropic tensor functions
• The Navier-Stokes equations: derivation and examples
• Nonlinear elasticity: derivation and examples
• Linear elasticity: derivation and examples

Applications to viscometric flows, elastic waves and gas dynamics will be added as time permits.

The subject will be developed starting from first principles. Prerequisites are:

• a working knowledge of basic concepts of physics, such as pressure, force, mass, acceleration, and Newton's laws.
• a solid knowledge of undergraduate-level linear algebra including eigenvalues and eigenvectors
• facility with multi-variable calculus

Talk with me if you are uncertain whether you meet the prerequisites.

Grading method

Course grade will be based on two mid-term and one final exams. I may also collect and grade homework, in which case part of the course grade will depend on homework.

The Official UMBC Honors Code

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal.

To read the full Student Academic Conduct Policy, consult the UMBC Student Handbook, the Faculty Handbook, or the UMBC Policies section of the UMBC Directory.