Advanced elasticity

Welcome to this learning project about !

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.

Syllabus and Learning Materials

 * 1) Nonlinear Elasticity
 * 2) Deformation measures
 * 3) Motion, displacement, velocity, acceleration
 * 4) Strains and deformations
 * 5) Polar decomposition
 * 6) Spectral decompositions of kinematic quantities
 * 7) Volume change and area change
 * 8) Time derivatives and rate quantities
 * 9) Objectivity of kinematic quantities
 * 10) Stress measures
 * 11) Stress measures
 * 12) Deviatoric and volumetric stress
 * 13) Objective stress rates
 * 14)  Balance laws and entropy inequality
 * 15) Constitutive relations
 * 16) Cauchy elastic materials
 * 17)  Thermoelastic materials
 * 18) Relation between Cauchy stress and Green strain
 * 19) Maxwell relations for thermoelasticity
 * 20) Balance of energy
 * 21) Clausius-Duhem inequality
 * 22) Specific heat relations
 * 23) Nonlinear elastic materials
 * 24) Incompressible hyperelastic material
 * 25) Hyperelastic material models
 * 26) /Neo-Hookean material
 * 27) /Mooney-Rivlin material
 * 28) /Ogden material
 * 29) /Yeoh material
 * 30) Examples
 * 31) Buckling
 * 32) Refresh your basics
 * 33) Curvature
 * 34) /Linear buckling
 * 35) /Nonlinear buckling
 * 36) Examples
 * 37) Three-dimensional elastcity
 * 38) /Elastic potentials
 * 39) Examples
 * 40) Plates and Shells
 * 41) /Plates
 * 42) /Shells
 * 43) Examples
 * 44) Dynamics
 * 45) /Vibrations
 * 46) Examples
 * 47) Fracture
 * 48) 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


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