From micro to macro in solid and fluid mechanics

Lecturer(s): Alexandre DANESCU, Mathieu CREYSSELS
Course ⋅ 12 hTC ⋅ 12 hStudy ⋅ 8 h

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

  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

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