# Advanced elasticity

Welcome to this learning project about Advanced elasticity!

## Learning Project Summary

* Project code:
* Suggested Prerequisites:
** Introduction to Elasticity
** Continuum mechanics
** Partial differential equations
* Time investment: 6 months
* Assessment suggestions:
* Portal:Engineering and Technology
* School:Engineering
* Department:Mechanical Engineering
* Stream:Applied Mechanics
* Level: First year graduate

## Content summary

This is an advanced course on the elastic deformations of solids.

## Goals

This learning project aims to.
* provide the mathematical foundations of advanced elasticity.

## Contents
### Syllabus and Learning Materials

* Nonlinear Elasticity
** Deformation measures
*** Motion, displacement, velocity, acceleration
*** Strains and deformations
*** Polar decomposition
*** Spectral decompositions of kinematic quantities
*** Volume change and area change
*** Time derivatives and rate quantities
*** Objectivity of kinematic quantities
** Stress measures
*** Stress measures
*** Deviatoric and volumetric stress
*** Objective stress rates
** Balance laws and entropy inequality
** Constitutive relations
*** Cauchy elastic materials
*** Thermoelastic materials
*** Relation between Cauchy stress and Green strain
*** Maxwell relations for thermoelasticity
*** Balance of energy
*** Clausius-Duhem inequality
*** Specific heat relations
*** Nonlinear elastic materials
**** Incompressible hyperelastic material
**** Hyperelastic material models
***** /Neo-Hookean material
***** /Mooney-Rivlin material
***** /Ogden material
***** /Yeoh material
** Examples
* Buckling
** Refresh your basics
*** Curvature
** /Linear buckling
** /Nonlinear buckling
** Examples
* Three-dimensional elastcity
** /Elastic potentials
** Examples
* Plates and Shells
** /Plates
** /Shells
** Examples
* Dynamics
** /Vibrations
** Examples
* Fracture
** Examples

### Assignments

* Homework 1 Problem set
** Solutions
* Homework 2 Problem set
** Solutions
* Homework 3 Problem set
** Solutions
* Homework 4 Problem set
** Solutions
* Homework 5 Problem set
** Solutions
* Homework 6 Problem set
** Solutions
* Homework 7 Problem set
** Solutions
* Homework 8 Problem set
** Solutions
* Homework 9 Problem set
** Solutions
* Homework 10 Problem set
** Solutions
* Homework 11 Problem set
** Solutions

### Tests and Quizzes

* Quiz 1
** Solutions

### Textbooks and References

Textbooks
* R.W. Ogden, (1984), Non-linear Elastic Deformations, Dover Publications.
* A.J.M Spencer (2004), Continuum Mechanics, Dover Publications. An excellent introduction to continuum mechanics. You should own a copy for your personal library.
* L.E. Malvern (1969), Introduction to the Mechanics of a Continuous Medium, Prentice-Hall. A good reference for continuum mechanics.
References
* Continuum Mechanics:
** R. M. Brannon (2004), Large Deformation Kinematics. An excellent introduction to kinematics.
** R. M. Brannon (2004), Rotation. Almost everything you ever wanted to know about rotations.
* Mathematics:
** R. M. Brannon (2004), Elementary Vector and Tensor Analysis for Engineers. This free online book is the best introduction I have seen for vector and tensor analysis for nonlinear mechanics.
** R. M. Brannon (2004), Curvilinear Coordinates. Very useful if you wish to follow the literature on the nonlinear deformation of shells.
** A.P.S. Selvadurai (2000), Partial Differential Equations in Mechanics 1,2. Springer. Excellent introductory text on partial differential equations with engineers in mind.

### Reading List

* Learning materials
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