Strength of materials and structures

•  MMC, tensor algebra and analysis
•  Elastoplastic behavior (see 3^rd year Material behavior - Plasticity course)
•  Beam model (see 3^rd year Thin structures ans instablities course)

•  Discover the classical approaches of linear fracture mechanics
•  Discover the main characteristics of the fatigue phenomenon of materials and structures on simple examples
•  Know the classical approaches to fatigue called "uniaxial" and discover the current approaches to fatigue (multiaxial)
•  Acquire the concepts and calculation methods used in yield design and limit analysis

•  Part 1: Phenomena and Models
  -- Linear fracture mechanics: validity domain and typical problem
  -- Global approach to fracture: energy restitution rate and Griffith criterion
  -- Local approach to fracture: stress intensity factors and K1c criterion
  -- Comparison between the two classical approaches in linear fracture mechanics
  -- Influence of the loading path (monotonic or cyclic) on the fracture behavior of solid of solid structures: phenomenology and classification
  -- Uniaxial" fatigue with a large number of cycles: Wöhler curve and Haigh diagram; Paris law
  -- Uniaxial" fatigue at small number of cycles (oligocyclic): Manson-Coffin law
  -- Multiaxial fatigue at large number of cycles: macroscopic criterion of Sines and macro-micro of Dang Van
•  Part 2: Yield design and limit analysis
  -- Notions of limit loads and plastic failure mechanisms: examples of a lattice of bars and a cylindrical shaft in torsion
  -- Theory of yield design: notion of resistance criterion of materials, maximum resisting work and static approach for the calculation of loads potentially bearable by a structure
  -- Dual kinematic approach
  -- Notion of safety coefficient
  -- Application to beam structures, notion of plastic hinge in bending

•  Know the failure mechanisms
•  Know the main criteria of failure
•  Know how to determine the mechanisms that can lead to the failure of a given system
•  Know how to dimension a structure with respect to yield design

•  DS1 : written evaluation of 1 hour on the 1^st part (50%)
•  DS2 : written evaluation of 1 hour on the 2^nd part (50%)

•  J. Garrigues, Cinématique des milieux continus (en ligne)
•  J. Lemaître et J.-L. Chaboche, Mécanique des matériaux solides, éd. Dunod, 2004
•  D. François, A. Pineau et A. Zaoui, Viscoplasticité, endommagement, mécanique de la rupture, mécanique du contact, éd. Lavoisier, 2009
•  J. Salençon, Calcul à la rupture et analyse limite, Presses de l’ENPC, 1983

•  Thierry Désoyer
•  Stéphane Bourgeois