Continuum mechanics

The class starts with an introduction to the concept of constitution equation for materials with the help of simple uni-directional models. Then stresses and strains are introduced. After presenting basic concepts of elasticity with examples of application, conservation laws are discussed with application to the mechanics of incompressible fluids.

Detailed class content

  • Unidirectional rheology (2h) : Elastic solid, Newton fluid, visco-elasticity for both solid type and fluid type materials, plasticity and friction.
  • Forces and stresses (4h), linear algebra, stress tensor and stress vector; Mohr circle, change of frame of reference, equilibrium conditions.
  • Displacements and deformations (4h) Lagrangean and Eulerian frame of reference, deformation and displacement gradients. Large and small strain; compatibility conditions; particle motion, deformation and strain rate.
  • Elasticity (6h) Hooke solid, Navier’s equation with simple applications (beams, body waves); Elastic strain energy and a more general definition of elasticity with discussion of anisotropy. Airy stress functions with application to the hollow cylinder.
  • Continuum mechanics (4h) Paradigm of continuum mechanics : Mass conservation, momentum principle, conservation of energy.
  • Fluid mechanics (5h) Non compressible fluid mechanics with Navier Stokes equation and application to flow through parallel plates.
  • Applications to Earth Sciences are provided through practical exercises solved during tutorials with teaching assistants (25 h).