From micro to macro in solid and fluid mechanics

The objective of the course is to understand the laws of behaviour and the macroscopic models observed and studied in solid and fluid mechanics from a microscopic description of solids and fluids. The course will provide essential elements to integrate the fact that every body is made up of atoms or molecules interacting more or less strongly into the macroscopic laws of motion. The examples presented in tutorials will illustrate the application of the methods developed in the course. Examples include: carbon nanotubes, elasticity of metamaterials, design of auxetic materials, perfect gases and denser gases.

1. Discrete to continuum elasticity : one-dimensional problems
2. Discrete-to-continuum elasticity : multi-dimensional problems
3. Inhomogeneous to effective constitutive relations : the scalar case (thermal diffusion)
4. Inhomogeneous to effective constitutive relations : the vectorial case (elasticity)
5. Case studied : negative Poisson ratio materials
6. Case studied : mechanical behaviour of single wall carbonne nanotubes (SWCNT)
7. Kinetic theory of gases
8. The fundamental Boltzmann equation and its practical applications.