Advanced elasticity

From Wikiversity
Jump to navigation Jump to search

Welcome to this learning project about Advanced elasticity!

Learning Project Summary[edit | edit source]

Content summary[edit | edit source]

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

Goals[edit | edit source]

This learning project aims to.

  • provide the mathematical foundations of advanced elasticity.

Contents[edit | edit source]

Syllabus and Learning Materials[edit | edit source]

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

Assignments[edit | edit source]

Tests and Quizzes[edit | edit source]

Textbooks and References[edit | edit source]



  • Continuum Mechanics:

Reading List[edit | edit source]

  • ...

Learning materials[edit | edit source]

Learning materials and learning projects are located in the main Wikiversity namespace. Simply make a link to the name of the lesson (lessons are independent pages in the main namespace) and start writing!

You should also read about the Wikiversity:Learning model. Lessons should center on learning activities for Wikiversity participants. Learning materials and learning projects can be used by multiple projects - and you are encouraged to cooperate with other departments that use the same learning resource.