HYD/EBS 205: Continuum Mechanics of Natural Systems
Fall Quarter, 2002 / 4.0 units                        
Lec. MWF / 10:00-10:50, 1342 Storer; Disc. W / 1:10-2:00, 3 Wellman    

Objective: Learn the principles of continuous solids and fluids in the context of natural systems.

Goal: Prepare for the application of continuum mechanics to static and dynamic problems in water, earth and biological systems.  Tensors include hydraulic, heat and electrical conductivity; diffusivity; strain; stress; deformation gradient; velocity gradient; stretch; and spin.

Prerequisites: Vector Analysis, differential equations, linear algebra and physics.  Knowledge of a symbolic manipulation language such as Mathematica is helpful.

Grading: Homework 20% (due class after assigned), midterm exam 30%, final exam 30% and project(s) 20%.  The project(s) is to review and present research recently published which illustrates the application of continuum mechanics.

Text Required:
Chadwick, P. 1976. Continuum Mechanics Concise Theory and Problems. Dover Publications, Inc. NY.
Mase, G. E. and Mase, G.T. 1999. Continuum Mechanics for Engineers 2nd Edition. CRC Press. Boca Raton, FL.

Instructor: Professor Wesley W. Wallender, Depts. of LAWR (Hydrology Program) and Bio/Agr. Engineering, 221 Veihmeyer Hall, wwwallender@ucdavis.edu, ftp and http  enthusiasm.ucdavis.edu, 752.0688.

Lecture Outline (Chadwick text+):
Vector and Tensor Theory
1. Vector algebra
2. Tensor algebra
3. The tensor product
4. Proper vectors and proper numbers
5. Symmetric tensors
6. Skew-symmetric tensors
7. Orthogonal tensors
8. Polar decomposition
9. Geometrical considerations: Coordinates
10. Scalar, vector and tensor fields
11. Integral theorems
Basic Kinematics
1. Bodies, configurations and motions
2. The referential and spatial descriptions
3. The deformation and velocity gradients
4. Stretch and rotation
5. Stretching and spin
6. Circulation and vorticity
Balance Laws, Field Equations and Jump Conditions
1. Mass
2. Momentum, force and torque
3. The theory of stress
4. Equations of motion
5. Energy
6. Jump conditions
7. Entropy
Linear Constitutive Equations

Prepared by:  W. W. Wallender, September, 2002.