Homogenisation




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1-2. Introduction to asymptotic methods
- General
- Example: From continuum mechanics to beam theory

2-3. Methods of change of scale
- General information on heterogeneous media
- Representative elementary volume and separation of scale
- Overview of methods
Periodic homogenisation method
- Mathematical formulation of the change of scale
- Physical analysis and dimensionless formulation

4. Diffusion in heterogeneous media
- Determination of the effective heat transfer parameter
- Comparison/discussion on self-consistent approach

5-6. Elastic composites
- Determination of effective elastic parameters
- Dynamics of composites
- Strong contrasted composites

7-8. Darcy's law in porous media
- Assumptions and dimensioning
- From Navier-Stokes to Darcy
- Extensions of Darcy's law
- Application to acoustics

9. Homogenization of discrete media
- Principle
- 2D-Beam array
- Effective beam models

10. Synthesis and supplements
- Large deformations
- Beyond scale separation


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