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Continuum Mechanics

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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). 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 website on fracture mechanics. It is under development, but will eventually contain information on linear and nonlinear fracture mechanics, as well as fatigue crack growth.

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Kick-Off Survey

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


Miscellaneous Links


Fracture Mechanics Website

Visit our 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 mechanisms.

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