The modern numerical methods now currently used in geomechanics allow to take into account advanced constitutive relations for geomaterials. The objective of these lectures is to present the most used constitutive models at an international level : isotropic and anisotropic non‐linear elasticity, associated and non‐associated elasto‐plasticity, visco‐elasto‐plasticity. First the most important mechanical properties to be described for soils are presented (compressibility, dilatancy, drained/undrained shear failure, ...). Then the general framework to build constitutive relations is given : definition of the constitutive functional, the incremental formalism for constitutive relations. The next chapter is devoted to non‐linear elasticity with examples like "hyperbolic" model. Then it is dealt with the elasto‐plasticity and the visco‐elasto‐plasticity with examples like "Cam‐Clay" model. Finally we introduce the incrementally non‐linear relations with applications like liquefaction phenomenon, instabilities and bifurcations in natural media, landslides and rockfalls modelling.
- Chapter 1 : Basic mechanical properties of soils
- Chapter 2 : Formalism for constitutive relations
- Chapter 3 : Isotropic and anisotropic non‐linear elasticity
- Chapter 4 : Associated and non‐associated elasto‐plasticity, visco‐elasto‐plasticity
- Chapter 5 : Incrementally non‐linear relations and applications to natural hazards