Advanced elasticity

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Welcome to this learning project about Advanced elasticity!

Learning Project Summary[edit]

Content summary[edit]

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

Goals[edit]

This learning project aims to.

  • provide the mathematical foundations of advanced elasticity.

Contents[edit]

Syllabus and Learning Materials[edit]

  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]

Tests and Quizzes[edit]

Textbooks and References[edit]

Textbooks

References

  • Continuum Mechanics:

Reading List[edit]

  • ...


Learning materials[edit]

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