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CONTINUUM MECHANICS

with emphasis on metals & viscoelastic materials

DESCRIPTION

This website presents the principles of finite deformation continuum mechanics
with many example applications to metals and incompressible viscoelastic
materials (rubber). It can serve as lecture notes for a graduate level course in
continuum mechanics for engineers interested in the subject.

FRACTURE MECHANICS WEBSITE

Visit www.fracturemechanics.org, my new fracture mechanics website, It is under
development, but will eventually contain information on linear and nonlinear
fracture mechanics, as well as fatigue crack growth.

THANK YOU

Thank you for visiting this website. Feel free to email me if you have questions
or comments.

Also, please consider visiting an advertiser here. Doing so helps to cover
website hosting fees.

Bob McGinty
bmcginty@gmail.com

PDFS OF ENTIRE WEBSITE - $12.95

For $12.95, you receive two formatted PDFs (the first for 8.5" x 11" pages, the
second for tablets) of the entire website.

Click here to see a sample page in each of the two formats.

Email address to receive PDFs

Author Bob McGinty, PhD, PE Email bmcginty@gmail.com

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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. Coordinate Transformations
7. Transformation Matrices
8. Divergence Theorem
9. Cylindrical Coordinates

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 Derivative
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. COLUMN BUCKLING

1. Beam Bending
2. Column Buckling
3. Eccentric Column Buckling
4. Multi-Load Column Buckling

8. SIGNAL PROCESSING

1. Fourier Transforms
2. Wavelet Transforms
3. Wavelet Coefficients

9. MISCELLANEOUS TOPICS

1. Strain Gauges
2. Fasteners (in development)

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EXTERNAL LINKS

* https://mechanicalc.com/

* http://www.thefullwiki.org/Continuum_mechanics
* http://en.wikipedia.org/wiki/Continuum_mechanics
* http://en.wikipedia.org/wiki/Finite_strain_theory

--------------------------------------------------------------------------------

FRACTURE MECHANICS WEBSITE

Visit my sister website, www.fracturemechanics.org, for information on fracture
mechanics. It is under development, but will eventually contain information on
linear and nonlinear fracture mechanics, as well as fatigue crack growth.

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.

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

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

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THANK YOU

Thank you for visiting this website. Feel free to email me if you have
questions.

Also, please consider visiting an advertiser above. Doing so helps to cover
website hosting fees.

Bob McGinty
bmcginty@gmail.com

WEBSITE PRIVACY POLICY

See the PrivacyPolicy.html page for information concerning this website's
privacy policy.

PDFS OF ENTIRE WEBSITE - $12.95

For $12.95, you receive two formatted PDFs (the first for 8.5" x 11" pages, the
second for tablets) of the entire website.

Click here to see a sample page in each of the two formats.

Email address to receive PDFs

Introduction

Fasteners

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www.continuummechanics.org Open in urlscan Pro
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