Objectives
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.
Programme
- Discrete to continuum elasticity : one-dimensional problems
- Discrete-to-continuum elasticity : multi-dimensional problems
- Inhomogeneous to effective constitutive relations : the scalar case (thermal diffusion)
- Inhomogeneous to effective constitutive relations : the vectorial case (elasticity)
- Case studied : negative Poisson ratio materials and/or
- Case studied : mechanical behaviour of single wall carbonne nanotubes (SWCNT)
- Topological protected states in elastic networks : the 1d case
- Topological protected states in elastic networks : Berry connection and curvature and the bulk-boundary correspondance
Learning Outcomes
- - simplification of complex physical problems - formulation/computation of effective constitutive behavior in elasticity - understanding the interplay between microstructure geometry/physics and macroscopic mechanical behaviour
Assesment
Case studied results : 1/3 of the final mark Written examination (2h) : 2/3 of the final mark