Du micro au macro en mécanique

The course concern the discrete-to-continuum elasticity, the up-scale from inhomogeneous continuum to "effective" material behavior and the basics of the kinetic theory of liquids and gazes. The last part introduces the topological protected elastic states.

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 and/or
6. Case studied : mechanical behaviour of single wall carbonne nanotubes (SWCNT)
7. Topological protected states in elastic networks : the 1d case
8. Topological protected states in elastic networks : Berry connection and curvature and the bulk-boundary correspondance