26/05/2025

Homogenisation – C. Boutin

Sketch of the course of 10 lessons of 2h

May - July 2025

Departement DIMA – La Sapienza

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