Search Continuum Mechanics Website

Continuum Mechanics

Prev Up Next
with emphasis on metals & viscoelastic materials

Description

mapping

This website presents the principles of finite deformation continuum mechanics with many example applications to metals and incompressible viscoelastic materials (rubber). Examples also cover both rectangular and cylindrical coordinates.

Homework

Homework #1
Homework #2
Homework #3
Homework #4
Homework #5
Homework #6
Homework #7
Homework #8
Homework #9
Homework #10
Homework #11
Homework #12
Homework #13 Due May 28, 2014

Homework Solutions

Homework #1 Solutions
Homework #2 Solutions
Homework #3 Solutions
Homework #4 Solutions
Homework #5 Solutions
Homework #6 Solutions
Homework #7 Solutions
Homework #8 Solutions
Homework #9 Solutions
Homework #10 Solutions
Homework #11 Solutions
Homework #12 Solutions
Homework #13 Solutions

Spring Break: April 14-18, 2014

We'll take the week of April 14-18 off for Spring Break. No classes on the 14th and 16th.
We start back on Monday, April 21.

Kick-Off Survey

Here is the MS-Word file. And here is the text.

Schedule

Feb 3, 2014 - June 4, 2014
Mondays and Wednesdays
10:00am - 11:30am EDT
Author   Bob McGinty, PhD, PE
Email    bmcginty@gmail.com



Table of Contents

  1. INTRODUCTION

    1. Interactive Calculation Pages

  2. BASIC MATHEMATICS

    1. Vectors
    2. Matrices & Tensors
    3. Vector Calculus
    4. Tensor Notation (Basic)
    5. Tensor Notation (Advanced)
    6. Divergence Theorem
    7. Coordinate Transformations
    8. Transformation Matrices
    9. Cylindrical Coordinates
    10. Fourier Transforms

  3. INTRODUCTORY MECHANICS

    1. Stress
    2. Strain
    3. Principal Stresses & Strains
    4. Hooke's Law

  4. DEFORMATIONS AND STRAIN

    1. Deformation Gradients
    2. Polar Decompositions
    3. Rotation Matrices
    4. Finite Element Mapping
    5. Small Scale Strains
    6. Green & Almansi Strains
    7. Principal Strains & Invariants
    8. Hydrostatic & Deviatoric Strains
    9. Velocity Gradients
    10. True Strain
    11. Material Derivatives
    12. Special Strain Topics

  5. STRESS

    1. Stress Introduction
    2. Traction Vectors
    3. Energetic Conjugates
    4. Stress Transformations
    5. Principal Stresses & Invariants
    6. Hydrostatic & Deviatoric Stresses
    7. Von Mises Stress
    8. Corotational Derivatives
    9. Equilibrium

  6. MATERIAL BEHAVIOR

    1. Continuity Equation
    2. Navier Stokes Equation
    3. Thermodynamics
    4. Hooke's Law
    5. Metal Plasticity
    6. Mooney-Rivlin Models
    7. Dynamic Material Properties
    8. Materials and Tire Behavior

  7. MISCELLANEOUS TOPICS

    1. Fasteners
    2. Strain Gauges
    3. Beam Bending
    4. Column Buckling
    5. Eccentric Column Buckling


Textbook

Introduction to the Mechanics of a Continuous Medium, Lawrence E. Malvern, 1969.

Also available electronically here (24MB):
http://www.scribd.com/doc/5987971/MALVERN-LE-Introduction-to-the-Mechanics-of-a-Continuous-Medium


Miscellaneous Links

A Note About The Web Technologies Used Here

Two relatively new web technologies are used on these pages. The first is Scalable Vector Graphics, or SVG. Pages on this site will display SVG files in compatible browsers, and PNG files in incompatible ones. The advantage of SVG over PNG is that SVG graphics can be scaled to any size without the onset of pixelization. SVG files used here were created using Inkscape, an excellent graphics program available free on the internet here.

The second new technology used here is MathJax, a Javascript based display engine for mathematical equations programmed in the LaTeX language. MathJax eliminates the need to display equations as GIF or PNG graphics files (or even SVG for that matter). MathJax requires only the following line of code in the <HEAD> segment of a webpage.

<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=default"></script>

It is then possible to program any math expression in the HTML source using the LaTeX language. For example, typing \(\sigma_{ij}\) produces \( \sigma_{ij} \).

I'm often asked what software I used to develop the webpages. The answer is... the Vim editor (www.vim.org). Vim is the Windows-based version of the venerable Vi editor on Unix, and now Linux systems. I typed everything by hand.

Bob McGinty
February 2012